text:
@online{centerforhistoryandnewmediaZoteroQuickStart,
  title = {Zotero {{Quick Start Guide}}},
  url = {http://zotero.org/support/quick_start_guide},
  author = {{Center for History and New Media}}
}

@article{ichterRealTimeStochasticKinodynamic2016,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1607.06886},
  primaryClass = {cs},
  title = {Real-{{Time Stochastic Kinodynamic Motion Planning}} via {{Multiobjective Search}} on {{GPUs}}},
  url = {http://arxiv.org/abs/1607.06886},
  abstract = {In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective Planning) algorithm for addressing the stochastic kinodynamic motion planning problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject to a constraint on collision probability (CP). To ensure exhaustive evaluation of candidate motion plans (as needed to tradeoff the competing objectives of performance and safety), PUMP incrementally builds the Pareto front of the problem, accounting for the optimization objective and an approximation of CP. This is performed by a massively parallel multiobjective search, here implemented with a focus on GPUs. Upon termination of the exploration phase, PUMP searches the Pareto set of motion plans to identify the lowest cost solution that is certified to satisfy the CP constraint (according to an asymptotically exact estimator). We introduce a novel particle-based CP approximation scheme, designed for efficient GPU implementation, which accounts for dependencies over the history of a trajectory execution. We present numerical experiments for quadrotor planning wherein PUMP identifies solutions in \textasciitilde{}100 ms, evaluating over one hundred thousand partial plans through the course of its exploration phase. The results show that this multiobjective search achieves a lower motion plan cost, for the same CP constraint, compared to a safety buffer-based search heuristic and repeated RRT trials.},
  urldate = {2018-02-21},
  date = {2016-07-22},
  keywords = {Computer Science - Robotics},
  author = {Ichter, Brian and Schmerling, Edward and Agha-mohammadi, Ali-akbar and Pavone, Marco},
  file = {/Users/olepor/Zotero/storage/2EUAQ9N4/Ichter et al. - 2016 - Real-Time Stochastic Kinodynamic Motion Planning v.pdf;/Users/olepor/Zotero/storage/VJ5X4DRF/1607.html}
}

@article{esfahaniMotionPlanningContinuous2016,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1211.1138},
  title = {Motion {{Planning}} for {{Continuous Time Stochastic Processes}}: {{A Dynamic Programming Approach}}},
  volume = {61},
  issn = {0018-9286, 1558-2523},
  url = {http://arxiv.org/abs/1211.1138},
  doi = {10.1109/TAC.2015.2500638},
  shorttitle = {Motion {{Planning}} for {{Continuous Time Stochastic Processes}}},
  abstract = {We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first introduce two basic notions of motion planning, and then establish a connection to a class of stochastic optimal control problems concerned with sequential stopping times. A weak dynamic programming principle (DPP) is then proposed, which characterizes the set of initial states that admit a control enabling the process to execute the desired maneuver with probability no less than some pre-specified value. The proposed DPP comprises auxiliary value functions defined in terms of discontinuous payoff functions. A concrete instance of the use of this novel DPP in the case of diffusion processes is also presented. In this case, we establish that the aforementioned set of initial states can be characterized as the level set of a discontinuous viscosity solution to a sequence of partial differential equations, for which the first one has a known boundary condition, while the boundary conditions of the subsequent ones are determined by the solutions to the preceding steps. Finally, the generality and flexibility of the theoretical results are illustrated on an example involving biological switches.},
  number = {8},
  journaltitle = {IEEE Transactions on Automatic Control},
  urldate = {2018-02-21},
  date = {2016-08},
  pages = {2155-2170},
  keywords = {Computer Science - Systems and Control,Mathematics - Optimization and Control,Mathematics - Probability},
  author = {Esfahani, Peyman Mohajerin and Chatterjee, Debasish and Lygeros, John},
  file = {/Users/olepor/Zotero/storage/Z4U5Y4EN/Esfahani et al. - 2016 - Motion Planning for Continuous Time Stochastic Pro.pdf;/Users/olepor/Zotero/storage/AKXPBPYX/1211.html}
}

@book{s.m.lavalleMotionPlanning,
  title = {Motion {{Planning}}},
  keywords = {book,motion planning},
  author = {S.M. La Valle}
}

@misc{HttpMslCs,
  title = {{{http://msl.cs.uiuc.edu/\textasciitilde{}lavalle/cs497/jokane.pdf}}}
}

@article{HttpsLinkSpringer,
  title = {{{https://link.springer.com/content/pdf/10.1007\%2Fs10846-011-9642-9.pdf}}},
  url = {https://link.springer.com/content/pdf/10.1007%2Fs10846-011-9642-9.pdf}
}

@incollection{vandenbergMotionPlanningUncertainty2017,
  langid = {english},
  location = {{Cham}},
  title = {Motion {{Planning Under Uncertainty Using Differential Dynamic Programming}} in {{Belief Space}}},
  volume = {100},
  isbn = {978-3-319-29362-2 978-3-319-29363-9},
  url = {http://link.springer.com/10.1007/978-3-319-29363-9_27},
  abstract = {We present an approach to motion planning under motion and sensing uncertainty, formally described as a continuous partially-observable Markov decision process (POMDP). Our approach is designed for non-linear dynamics and observation models, and follows the general POMDP solution framework in which we represent beliefs by Gaussian distributions, approximate the belief dynamics using an extended Kalman ﬁlter (EKF), and represent the value function by a quadratic function that is valid in the vicinity of a nominal trajectory through belief space. Using a variant of differential dynamic programming, our approach iterates with second-order convergence towards a linear control policy over the belief space that is locally-optimal with respect to a user-deﬁned cost function. Unlike previous work, our approach does not assume maximum-likelihood observations, does not assume ﬁxed estimator or control gains, takes into account obstacles in the environment, and does not require discretization of the belief space. The running time of the algorithm is polynomial in the dimension of the state space. We demonstrate the potential of our approach in several continuous partially-observable planning domains with obstacles for robots with non-linear dynamics and observation models.},
  booktitle = {Robotics {{Research}}},
  publisher = {{Springer International Publishing}},
  urldate = {2018-04-26},
  date = {2017},
  pages = {473-490},
  keywords = {promising,stochastic,POMD,uncertainty,mobile robotics},
  author = {van den Berg, Jur and Patil, Sachin and Alterovitz, Ron},
  editor = {Christensen, Henrik I. and Khatib, Oussama},
  options = {useprefix=true},
  file = {/Users/olepor/Zotero/storage/6NCZMY4S/van den Berg et al. - 2017 - Motion Planning Under Uncertainty Using Differenti.pdf;/Users/olepor/Zotero/storage/RZ629YSK/van den Berg et al. - 2017 - Motion Planning Under Uncertainty Using Differenti.pdf},
  doi = {10.1007/978-3-319-29363-9_27}
}

@online{MotionPlanningUnderUncertainty,
  title = {{{MotionPlanningUnderUncertainty}}},
  url = {http://sauravag.com/software-2/},
  keywords = {uncertainty,OMPL,matlab,C++}
}

@inproceedings{bryRapidlyexploringRandomBelief2011,
  langid = {english},
  title = {Rapidly-Exploring {{Random Belief Trees}} for Motion Planning under Uncertainty},
  isbn = {978-1-61284-386-5},
  url = {http://ieeexplore.ieee.org/document/5980508/},
  doi = {10.1109/ICRA.2011.5980508},
  abstract = {In this paper we address the problem of motion planning in the presence of state uncertainty, also known as planning in belief space. The work is motivated by planning domains involving nontrivial dynamics, spatially varying measurement properties, and obstacle constraints. To make the problem tractable, we restrict the motion plan to a nominal trajectory stabilized with a linear estimator and controller. This allows us to predict distributions over future states given a candidate nominal trajectory. Using these distributions to ensure a bounded probability of collision, the algorithm incrementally constructs a graph of trajectories through state space, while efﬁciently searching over candidate paths through the graph at each iteration. This process results in a search tree in belief space that provably converges to the optimal path. We analyze the algorithm theoretically and also provide simulation results demonstrating its utility for balancing information gathering to reduce uncertainty and ﬁnding low cost paths.},
  publisher = {{IEEE}},
  urldate = {2018-05-10},
  date = {2011-05},
  pages = {723-730},
  keywords = {promising,stochastic,RRT},
  author = {Bry, Adam and Roy, Nicholas},
  file = {/Users/olepor/Zotero/storage/ZBU8CTNJ/Bry and Roy - 2011 - Rapidly-exploring Random Belief Trees for motion p.pdf}
}

@article{agha-mohammadiPeriodicnodeGraphbasedFramework,
  langid = {english},
  title = {Periodic-Node {{Graph}}-Based {{Framework}} for {{Stochastic Control}} of {{Non}}-Point-Stabilizable {{Systems}}},
  abstract = {This paper presents a strategy for stochastic control of small aerial vehicles under uncertainty using graph-based methods. In planning with graph-based methods, such as the Probabilistic Roadmap Method (PRM) in state space or the Information RoadMaps (IRM) in information-state (belief) space, the local planners (along the edges) are responsible to drive the state/belief to the ﬁnal node of the edge. However, for aerial vehicles with minimum velocity constraints, driving the system belief to a sampled belief is a challenge. In this paper, we propose a novel method based on periodic controllers, in which instead of stabilizing the belief to a predeﬁned probability distribution, the belief is stabilized to an orbit (periodic path) of probability distributions. Choosing nodes along these orbits, the node reachability in belief space is achieved and we can form a graph in belief space that can handle higher-order-dynamics or non-stoppable systems (whose velocity cannot be zero), such as ﬁxedwing aircraft. The proposed method takes obstacles into account and provides a query-independent graph, since its edge costs are independent of each other, thus it satisﬁes the principle of optimality. Therefore, dynamic programming can be utilized to compute the best feedback on the graph. We demonstrate the method’s performance on a unicycle robot and a six degree of freedom small aerial vehicle.},
  pages = {19},
  author = {Agha-mohammadi, Ali-akbar and Agarwal, Saurav and Chakravorty, Suman},
  file = {/Users/olepor/Zotero/storage/BVZEIB2F/Agha-mohammadi et al. - Periodic-node Graph-based Framework for Stochastic.pdf}
}

@inproceedings{vitusHierarchicalMethodStochastic2012,
  langid = {english},
  title = {A Hierarchical Method for Stochastic Motion Planning in Uncertain Environments},
  isbn = {978-1-4673-1736-8 978-1-4673-1737-5 978-1-4673-1735-1},
  url = {http://ieeexplore.ieee.org/document/6385724/},
  doi = {10.1109/IROS.2012.6385724},
  abstract = {This paper considers the problem of stochastic motion planning in uncertain environments, and extends existing chance constrained optimal control solutions. Due to the imperfect knowledge of the system state caused by motion uncertainty, sensor noise and environment uncertainty, the system constraints cannot be guaranteed to be satisﬁed and consequently must be considered probabilistically. To account for the uncertainty, the constraints are formulated as convex constraints on a random variable, known as chance constraints, with the violation probability of all the constraints guaranteed to be below a threshold. Standard chance constrained stochastic motion planning methods do not incorporate environmental sensing which typically leads to overly-conservative solutions. To address this, a novel hierarchical framework is proposed that consists of two main steps: an expected shortest path problem on an uncertain graph and a chance constrained motion planning problem. The ﬁrst successful, real-time experimental demonstration of chance constrained control with uncertain constraint parameters and variables is also presented for a quadrotor equipped with a Kinect sensor navigating through an uncertain, cluttered 3D environment.},
  publisher = {{IEEE}},
  urldate = {2018-05-10},
  date = {2012-10},
  pages = {2263-2268},
  author = {Vitus, Michael P. and Zhang, Wei and Tomlin, Claire J.},
  file = {/Users/olepor/Zotero/storage/LXVUCDXP/Vitus et al. - 2012 - A hierarchical method for stochastic motion planni.pdf}
}

@article{liSamplingBasedRealTimeMotion2014,
  langid = {english},
  title = {Sampling-{{Based Real}}-{{Time Motion Planning}} under {{State Uncertainty}} for {{Autonomous Micro}}-{{Aerial Vehicles}} in {{GPS}}-{{Denied Environments}}},
  volume = {14},
  issn = {1424-8220},
  url = {http://www.mdpi.com/1424-8220/14/11/21791},
  doi = {10.3390/s141121791},
  abstract = {This paper presents a real-time motion planning approach for autonomous vehicles with complex dynamics and state uncertainty. The approach is motivated by the motion planning problem for autonomous vehicles navigating in GPS-denied dynamic environments, which involves non-linear and/or non-holonomic vehicle dynamics, incomplete state estimates, and constraints imposed by uncertain and cluttered environments. To address the above motion planning problem, we propose an extension of the closed-loop rapid belief trees, the closed-loop random belief trees (CL-RBT), which incorporates predictions of the position estimation uncertainty, using a factored form of the covariance provided by the Kalman filter-based estimator. The proposed motion planner operates by incrementally constructing a tree of dynamically feasible trajectories using the closed-loop prediction, while selecting candidate paths with low uncertainty using efficient covariance update and propagation. The algorithm can operate in real-time, continuously providing the controller with feasible paths for execution, enabling the vehicle to account for dynamic and uncertain environments. Simulation results demonstrate that the proposed approach can generate feasible trajectories that reduce the state estimation uncertainty, while handling complex vehicle dynamics and environment constraints.},
  number = {11},
  journaltitle = {Sensors},
  urldate = {2018-05-10},
  date = {2014-11-18},
  pages = {21791-21825},
  author = {Li, Dachuan and Li, Qing and Cheng, Nong and Song, Jingyan},
  file = {/Users/olepor/Zotero/storage/WT8LWA39/Li et al. - 2014 - Sampling-Based Real-Time Motion Planning under Sta.pdf}
}

@article{dadkhahSurveyMotionPlanning2012,
  langid = {english},
  title = {Survey of {{Motion Planning Literature}} in the {{Presence}} of {{Uncertainty}}: {{Considerations}} for {{UAV Guidance}}},
  volume = {65},
  issn = {0921-0296, 1573-0409},
  url = {http://link.springer.com/10.1007/s10846-011-9642-9},
  doi = {10.1007/s10846-011-9642-9},
  shorttitle = {Survey of {{Motion Planning Literature}} in the {{Presence}} of {{Uncertainty}}},
  abstract = {This paper provides a survey of motion planning techniques under uncertainty with a focus on their application to autonomous guidance of unmanned aerial vehicles (UAVs). The paper first describes the primary sources of uncertainty arising in UAV guidance and then describes relevant practical techniques that have been reported in the literature. The paper makes a point of distinguishing between contributions from the field of robotics and artif icial intelligence, and the field of dynamical systems and controls. Mutual and individual contributions for these fields are highlighted providing a roadmap for tackling the UAV guidance problem.},
  number = {1-4},
  journaltitle = {Journal of Intelligent \& Robotic Systems},
  urldate = {2018-05-10},
  date = {2012-01},
  pages = {233-246},
  author = {Dadkhah, Navid and Mettler, Bérénice},
  file = {/Users/olepor/Zotero/storage/KSPGJH7F/Dadkhah and Mettler - 2012 - Survey of Motion Planning Literature in the Presen.pdf}
}

@article{hoyAlgorithmsCollisionfreeNavigation2015,
  langid = {english},
  title = {Algorithms for Collision-Free Navigation of Mobile Robots in Complex Cluttered Environments: A Survey},
  volume = {33},
  issn = {0263-5747, 1469-8668},
  url = {http://www.journals.cambridge.org/abstract_S0263574714000289},
  doi = {10.1017/S0263574714000289},
  shorttitle = {Algorithms for Collision-Free Navigation of Mobile Robots in Complex Cluttered Environments},
  abstract = {We review a range of techniques related to navigation of unmanned vehicles through unknown environments with obstacles, especially those that rigorously ensure collision avoidance (given certain assumptions about the system). This topic continues to be an active area of research, and we highlight some directions in which available approaches may be improved. The paper discusses models of the sensors and vehicle kinematics, assumptions about the environment, and performance criteria. Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are all reviewed. In preference to global approaches based on full knowledge of the environment, particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.},
  number = {03},
  journaltitle = {Robotica},
  urldate = {2018-05-10},
  date = {2015-03},
  pages = {463-497},
  author = {Hoy, Michael and Matveev, Alexey S. and Savkin, Andrey V.},
  file = {/Users/olepor/Zotero/storage/8GAQXYLL/Hoy et al. - 2015 - Algorithms for collision-free navigation of mobile.pdf}
}

@article{kurniawatiGlobalMotionPlanning,
  langid = {english},
  title = {Global {{Motion Planning}} under {{Uncertain Motion}}, {{Sensing}}, and {{Environment Map}}},
  volume = {VII},
  abstract = {Motion planning that takes into account uncertainty in motion, sensing, and environment map, is critical for autonomous robots to operate reliably in our living spaces. Partially Observable Markov Decision Processes (POMDPs) is a principled and general framework for planning under uncertainty. Although recent development of point-based POMDPs have drastically increased the speed of POMDP planning, even the best POMDP planner today, fails to generate reasonable motion strategies when the environment map is not known exactly. This paper presents Guided Cluster Sampling (GCS), a new point-based POMDP planner for motion planning with uncertain motion, sensing, and environment map, when the robot has active sensing capability. It uses our observations that in this problem, the belief space B can be partitioned into a collection of much smaller sub-spaces, and an optimal policy can often be generated by sufﬁcient sampling of a small subset of the collection. GCS samples B using two-stage cluster sampling, a subspace is sampled from the collection and then a belief is sampled from the subspace. It uses information from the set of sampled sub-spaces and sampled beliefs to guide subsequent sampling. Preliminary results suggest that GCS generates reasonable policies for motion planning problems with uncertain motion, sensing, and environment map, that are unsolvable by the best point-based POMDP planner today, within reasonable time. Furthermore, GCS handles POMDPs with continuous state, action, and observation spaces. We show that for a class of POMDPs that often occur in robot motion planning, GCS converges to the optimal policy, given enough time. To the best of our knowledge, this is the ﬁrst convergence result for point-based POMDPs with continuous action space.},
  journaltitle = {Robotics: Science and Systems},
  pages = {8},
  author = {Kurniawati, Hanna and Bandyopadhyay, Tirthankar and Patrikalakis, Nicholas M},
  file = {/Users/olepor/Zotero/storage/ANXGSWWM/Kurniawati et al. - 2012 - Global motion planning under uncertain motion, sen.pdf;/Users/olepor/Zotero/storage/TBGW7TNS/Kurniawati et al. - Global Motion Planning under Uncertain Motion, Sen.pdf}
}

@inproceedings{agha-mohammadiRobustOnlineBelief2014,
  langid = {english},
  title = {Robust Online Belief Space Planning in Changing Environments: {{Application}} to Physical Mobile Robots},
  isbn = {978-1-4799-3685-4},
  url = {http://ieeexplore.ieee.org/document/6906602/},
  doi = {10.1109/ICRA.2014.6906602},
  shorttitle = {Robust Online Belief Space Planning in Changing Environments},
  abstract = {Motion planning in belief space (under motion and sensing uncertainty) is a challenging problem due to the computational intractability of its exact solution. The Feedback-based Information RoadMap (FIRM) framework made an important theoretical step toward enabling roadmap-based planning in belief space and provided a computationally tractable version of belief space planning. However, there are still challenges in applying belief space planners to physical systems, such as the discrepancy between computational models and real physical models. In this paper, we propose a dynamic replanning scheme in belief space to address such challenges. Moreover, we present techniques to cope with changes in the environment (e.g., changes in the obstacle map), as well as unforeseen large deviations in the robot’s location (e.g., the kidnapped robot problem). We then utilize these techniques to implement the ﬁrst online replanning scheme in belief space on a physical mobile robot that is robust to changes in the environment and large disturbances. This method demonstrates that belief space planning is a practical tool for robot motion planning.},
  publisher = {{IEEE}},
  urldate = {2018-05-10},
  date = {2014-05},
  pages = {149-156},
  author = {Agha-mohammadi, Ali-akbar and Agarwal, Saurav and Mahadevan, Aditya and Chakravorty, Suman and Tomkins, Daniel and Denny, Jory and Amato, Nancy M.},
  file = {/Users/olepor/Zotero/storage/QD528SH8/Agha-mohammadi et al. - 2014 - Robust online belief space planning in changing en.pdf}
}

@inproceedings{lavalleEvaluatingMotionStrategies1996,
  langid = {english},
  title = {Evaluating Motion Strategies under Nondeterministic or Probabilistic Uncertainties in Sensing and Control},
  volume = {4},
  isbn = {978-0-7803-2988-1},
  url = {http://ieeexplore.ieee.org/document/509173/},
  doi = {10.1109/ROBOT.1996.509173},
  abstract = {In this paper we provide a method for characterizing future configurations under the implementation of a motion strategy in the presence of sensing and control uncertainties. W e provide general techniques which can apply to either nondeterministic models of uncertainty (as typically considered in preimage planning research) or probabilistic models. Information-space concepts from modern control theory are utilized t o define the notion of a strategy in this general context. W e have implemented algorithms and show several computed examples that generalize the forward projection concepts f r o m tradition literature in this area.},
  publisher = {{IEEE}},
  urldate = {2018-05-10},
  date = {1996},
  pages = {3034-3039},
  author = {LaValle, S.M. and Hutchinson, S.A.},
  file = {/Users/olepor/Zotero/storage/LSNB4S2I/LaValle and Hutchinson - 1996 - Evaluating motion strategies under nondeterministi.pdf}
}

@article{padenSurveyMotionPlanning2016,
  langid = {english},
  title = {A {{Survey}} of {{Motion Planning}} and {{Control Techniques}} for {{Self}}-{{Driving Urban Vehicles}}},
  volume = {1},
  issn = {2379-8904, 2379-8858},
  url = {http://ieeexplore.ieee.org/document/7490340/},
  doi = {10.1109/TIV.2016.2578706},
  abstract = {Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efﬁciency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.},
  number = {1},
  journaltitle = {IEEE Transactions on Intelligent Vehicles},
  urldate = {2018-05-10},
  date = {2016-03},
  pages = {33-55},
  author = {Paden, Brian and Cap, Michal and Yong, Sze Zheng and Yershov, Dmitry and Frazzoli, Emilio},
  file = {/Users/olepor/Zotero/storage/AAUPYDFJ/Paden et al. - 2016 - A Survey of Motion Planning and Control Techniques.pdf}
}

@inproceedings{lavalleFrameworkMotionPlanning1995,
  langid = {english},
  title = {A Framework for Motion Planning in Stochastic Environments: Modeling and Analysis},
  volume = {3},
  isbn = {978-0-7803-1965-3},
  url = {http://ieeexplore.ieee.org/document/525719/},
  doi = {10.1109/ROBOT.1995.525719},
  shorttitle = {A Framework for Motion Planning in Stochastic Environments},
  abstract = {W e present a framework for analyzing and determining motion plans for a robot that operates in a n environment that changes over time in a n uncertain manner. W e first classify sources of uncertainty in motion planning into four categories, and argue that the framework addressed in this paper characterizes a n important, yet little-explored category. W e treat the changing environment in a flexible manner by combining traditional configuration space concepts with a Markov process that models the environment. For this context, we then propose the use of a motion strategy, which provides a motion command for the robot for each contingency that it could be confronted with. W e allow the specification of a desired performance criterion, such as time or distance, and the goal is t o determine a motion strategy that is optimal with respect to that criterion. A motion planning problem in this framework is formulated as the design of a stochastic optimal controller. Applications and computational issues are discussed in a companion paper [12].},
  publisher = {{IEEE}},
  urldate = {2018-05-13},
  date = {1995},
  pages = {3057-3062},
  author = {LaValle, S.M. and Sharma, R.},
  file = {/Users/olepor/Zotero/storage/WEHNMJNB/LaValle and Sharma - 1995 - A framework for motion planning in stochastic envi.pdf}
}

@article{christosh.papadimitriouComplexityMarkovDecision1987,
  eprinttype = {jstor},
  eprint = {3689975},
  langid = {english},
  title = {The {{Complexity}} of {{Markov Decision Processes}}},
  volume = {12},
  number = {3},
  journaltitle = {Mathematics of Operations Research},
  date = {1987},
  pages = {441-450},
  author = {Christos H. Papadimitriou and John N. Tsitsiklis},
  file = {/Users/olepor/Zotero/storage/HSH6WHI5/Christos H. Papadimitriou and John N. Tsitsiklis - 1987 - The Complexity of Markov Decision Processes.pdf}
}

@article{kaelblingPlanningActingPartially1998,
  langid = {english},
  title = {Planning and Acting in Partially Observable Stochastic Domains},
  volume = {101},
  issn = {00043702},
  url = {http://linkinghub.elsevier.com/retrieve/pii/S000437029800023X},
  doi = {10.1016/S0004-3702(98)00023-X},
  abstract = {In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (MDPs) and partially observable MDPs (POMDPs). We then outline a novel algorithm for solving POMDPs off line and show how, in some cases, a ﬁnite-memory controller can be extracted from the solution to a POMDP. We conclude with a discussion of how our approach relates to previous work, the complexity of ﬁnding exact solutions to POMDPs, and of some possibilities for ﬁnding approximate solutions. © 1998 Elsevier Science B.V. All rights reserved.},
  number = {1-2},
  journaltitle = {Artificial Intelligence},
  urldate = {2018-05-13},
  date = {1998-05},
  pages = {99-134},
  author = {Kaelbling, Leslie Pack and Littman, Michael L. and Cassandra, Anthony R.},
  file = {/Users/olepor/Zotero/storage/GEVLUVFU/Kaelbling et al. - 1998 - Planning and acting in partially observable stocha.pdf}
}

@article{kearnsSparseSamplingAlgorithm,
  langid = {english},
  title = {A {{Sparse Sampling Algorithm}} for {{Near}}-{{Optimal Planning}} in {{Large Markov Decision Processes}}},
  abstract = {A critical issue for the application of Markov decision processes (MDPs) to realistic problems is how the complexity of planning scales with the size of the MDP. In stochastic environments with very large or inﬁnite state spaces, traditional planning and reinforcement learning algorithms may be inapplicable, since their running time typically grows linearly with the state space size in the worst case. In this paper we present a new algorithm that, given only a generative model (a natural and common type of simulator) for an arbitrary MDP, performs on-line, near-optimal planning with a per-state running time that has no dependence on the number of states. The running time is exponential in the horizon time (which depends only on the discount factor γ and the desired degree of approximation to the optimal policy). Our algorithm thus provides a different complexity trade-off than classical algorithms such as value iteration—rather than scaling linearly in both horizon time and state space size, our running time trades an exponential dependence on the former in exchange for no dependence on the latter.},
  pages = {16},
  author = {KEARNS, MICHAEL},
  file = {/Users/olepor/Zotero/storage/V9XTU8V9/KEARNS - A Sparse Sampling Algorithm for Near-Optimal Plann.pdf}
}

@article{stentzOptimalEfficientPath,
  langid = {english},
  title = {Optimal and {{Efficient Path Planning}} for {{Partially}}-{{Known Environments}}},
  abstract = {The task of planning trajectories for a mobile robot has received considerable attention in the research literature. Most of the work assumes the robot has a complete and accurate model of its environment before it begins to move; less attention has been paid to the problem of partially known environments. This situation occurs for an exploratory robot or one that must move to a goal location without the benefit of a floorplan or terrain map. Existing approaches plan an initial path based on known information and then modify the plan locally or replan the entire path as the robot discovers obstacles with its sensors, sacriﬁcing optimality or computational efﬁciency respectively. This paper introduces a new algorithm, D*, capable of planning paths in unknown, partially known, and changing environments in an efficient, optimal, and complete manner.},
  pages = {8},
  author = {Stentz, Anthony},
  file = {/Users/olepor/Zotero/storage/9A3N2XH8/Stentz - Optimal and Efﬁcient Path Planning for Partially-K.pdf}
}

@inproceedings{karamanAnytimeMotionPlanning2011,
  langid = {english},
  title = {Anytime {{Motion Planning}} Using the {{RRT}}*},
  isbn = {978-1-61284-386-5},
  url = {http://ieeexplore.ieee.org/document/5980479/},
  doi = {10.1109/ICRA.2011.5980479},
  abstract = {The Rapidly-exploring Random Tree (RRT) algorithm, based on incremental sampling, efﬁciently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime” algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT⇤ which (like the RRT) ﬁnds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT⇤, committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efﬁcient use of computation time online, resulting in an anytime algorithm for real-time implementation. We evaluate the method using a series of Monte Carlo runs in a high-ﬁdelity simulation environment, and compare the operation of the RRT and RRT⇤ methods. We also demonstrate experimental results for an outdoor wheeled robotic vehicle.},
  publisher = {{IEEE}},
  urldate = {2018-05-13},
  date = {2011-05},
  pages = {1478-1483},
  author = {Karaman, Sertac and Walter, Matthew R. and Perez, Alejandro and Frazzoli, Emilio and Teller, Seth},
  file = {/Users/olepor/Zotero/storage/2QC6P7XF/Karaman et al. - 2011 - Anytime Motion Planning using the RRT.pdf}
}

@article{likhachevAnytimeSearchDynamic2008,
  langid = {english},
  title = {Anytime Search in Dynamic Graphs},
  volume = {172},
  issn = {00043702},
  url = {http://linkinghub.elsevier.com/retrieve/pii/S000437020800060X},
  doi = {10.1016/j.artint.2007.11.009},
  abstract = {Agents operating in the real world often have limited time available for planning their next actions. Producing optimal plans is infeasible in these scenarios. Instead, agents must be satisﬁed with the best plans they can generate within the time available. One class of planners well-suited to this task are anytime planners, which quickly ﬁnd an initial, highly suboptimal plan, and then improve this plan until time runs out.},
  number = {14},
  journaltitle = {Artificial Intelligence},
  urldate = {2018-05-15},
  date = {2008-09},
  pages = {1613-1643},
  author = {Likhachev, Maxim and Ferguson, Dave and Gordon, Geoff and Stentz, Anthony and Thrun, Sebastian},
  file = {/Users/olepor/Zotero/storage/PY3N7EZH/Likhachev et al. - 2008 - Anytime search in dynamic graphs.pdf}
}

@article{thrunRoboticMappingSurvey,
  langid = {english},
  title = {Robotic {{Mapping}}: {{A Survey}}},
  abstract = {This article provides a comprehensive introduction into the ﬁeld of robotic mapping, with a focus on indoor mapping. It describes and compares various probabilistic techniques, as they are presently being applied to a vast array of mobile robot mapping problems. The history of robotic mapping is also described, along with an extensive list of open research problems.},
  pages = {31},
  author = {Thrun, Sebastian},
  file = {/Users/olepor/Zotero/storage/7A4G2E84/Thrun - Robotic Mapping A Survey.pdf}
}

@inproceedings{carrilloAutonomousRoboticExploration2015,
  langid = {english},
  title = {Autonomous Robotic Exploration Using Occupancy Grid Maps and Graph {{SLAM}} Based on {{Shannon}} and {{Rényi Entropy}}},
  isbn = {978-1-4799-6923-4},
  url = {http://ieeexplore.ieee.org/document/7139224/},
  doi = {10.1109/ICRA.2015.7139224},
  abstract = {In this paper we examine the problem of autonomously exploring and mapping an environment using a mobile robot. The robot uses a graph-based SLAM system to perform mapping and represents the map as an occupancy grid. In this setting, the robot must trade-off between exploring new area to complete the task and exploiting the existing information to maintain good localization. Selecting actions that decrease the map uncertainty while not signiﬁcantly increasing the robot’s localization uncertainty is challenging. We present a novel information-theoretic utility function that uses both Shannon’s and Re´nyi’s deﬁnitions of entropy to jointly consider the uncertainty of the robot and the map. This allows us to fuse both uncertainties without the use of manual tuning. We present simulations and experiments comparing the proposed utility function to state-of-the-art utility functions, which only use Shannon’s entropy. We show that by using the proposed utility function, the robot and map uncertainties are smaller than using other existing methods.},
  publisher = {{IEEE}},
  urldate = {2018-05-15},
  date = {2015-05},
  pages = {487-494},
  author = {Carrillo, Henry and Dames, Philip and Kumar, Vijay and Castellanos, Jose A.},
  file = {/Users/olepor/Zotero/storage/NEB9VC65/Carrillo et al. - 2015 - Autonomous robotic exploration using occupancy gri.pdf}
}

@article{blakeEfficientComputationCollision2018,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1804.05384},
  primaryClass = {cs, math},
  langid = {english},
  title = {Efficient {{Computation}} of {{Collision Probabilities}} for {{Safe Motion Planning}}},
  url = {http://arxiv.org/abs/1804.05384},
  abstract = {We address the problem of safe motion planning. As mobile robots and autonomous vehicles become increasingly more prevalent in human-centered environments, the need to ensure safety in the sense of guaranteed collision free behaviour has taken renewed urgency. Achieving this when perceptual modules provide only noisy estimates of objects in the environment requires new approaches. Working within a probabilistic framework for describing the environment, we present methods for efﬁciently calculating a probabilistic risk of collision for a candidate path. This may be used to stratify a set of candidate trajectories by levels of a safety threshold. Given such a stratiﬁcation, based on user-deﬁned thresholds, motion synthesis techniques could optimise for secondary criteria with the assurance that a primary safety criterion is already being satisﬁed. A key contribution of this paper is the use of a ‘convolution trick’ to factor the calculation of integrals providing bounds on collision risk, enabling an O(1) computation even in cluttered and complex environments.},
  urldate = {2018-05-16},
  date = {2018-04-15},
  keywords = {Computer Science - Robotics,Mathematics - Optimization and Control,68T40,I.2.9},
  author = {Blake, Andrew and Bordallo, Alejandro and Hawasly, Majd and Penkov, Svetlin and Ramamoorthy, Subramanian and Silva, Alexandre},
  file = {/Users/olepor/Zotero/storage/FSMZK8WR/Blake et al. - 2018 - Efficient Computation of Collision Probabilities f.pdf}
}

@article{gonzalezReviewMotionPlanning2016,
  langid = {english},
  title = {A {{Review}} of {{Motion Planning Techniques}} for {{Automated Vehicles}}},
  volume = {17},
  issn = {1524-9050, 1558-0016},
  url = {http://ieeexplore.ieee.org/document/7339478/},
  doi = {10.1109/TITS.2015.2498841},
  abstract = {Intelligent vehicles have increased their capabilities for highly, and even fully, automated driving under controlled environments. Scene information is received using on-board sensors and communication network systems–i.e. infrastructure and other vehicles. Considering the available information, different motion planning and control techniques have been implemented to autonomously driving on complex environments. The main goal is focused on executing strategies to improve safety, comfort and energy optimization. However, research challenges such as navigation in urban dynamic environments with obstacle avoidance capabilities–i.e. Vulnerable Road Users (VRU) and vehicles–and cooperative maneuvers among automated and semiautomated vehicles still need further efforts for a real environment implementation. This paper presents a review of motion planning techniques implemented in the intelligent vehicles literature. A description of the technique used by research teams, their contributions in motion planning and a comparison among these techniques is also presented. Relevant works in the overtaking and obstacle avoidance maneuvers is presented, allowing to understand the gaps and challenges to be addressed in the next years. Finally, an overview of future research direction and applications is given.},
  number = {4},
  journaltitle = {IEEE Transactions on Intelligent Transportation Systems},
  urldate = {2018-05-16},
  date = {2016-04},
  pages = {1135-1145},
  author = {Gonzalez, David and Perez, Joshue and Milanes, Vicente and Nashashibi, Fawzi},
  file = {/Users/olepor/Zotero/storage/P9IAXXVZ/Gonzalez et al. - 2016 - A Review of Motion Planning Techniques for Automat.pdf}
}

@inproceedings{gindeleBayesianOccupancyGrid2009,
  langid = {english},
  title = {Bayesian {{Occupancy}} Grid {{Filter}} for Dynamic Environments Using Prior Map Knowledge},
  isbn = {978-1-4244-3503-6},
  url = {http://ieeexplore.ieee.org/document/5164357/},
  doi = {10.1109/IVS.2009.5164357},
  abstract = {Building a model of the environment is essential for mobile robotics. It allows the robot to reason about its sourroundings and plan actions according to its intentions. To enable safe motion planning it is vital to anticipate object movements. This paper presents an improved formulation for occupancy ﬁltering. Our approach is closely related to the Bayesian Occupancy Filter (BOF) presented in [4]. The basic idea of occupancy ﬁlters is to represent the environment as a 2dimensional grid of cells holding information about their state of occupancy and velocity. To improve the accuracy of predictions, prior knowledge about the motion preferences is used, derived from map data that can be obtained from navigation systems. In combination with a physically accurate transition model, it is possible to estimate the environment dynamics. Experiments show that this yields reliable estimates even for occluded regions.},
  publisher = {{IEEE}},
  urldate = {2018-05-16},
  date = {2009-06},
  pages = {669-676},
  author = {Gindele, Tobias and Brechtel, Sebastian and Schroder, Joachim and Dillmann, Rudiger},
  file = {/Users/olepor/Zotero/storage/ND436TBJ/Gindele et al. - 2009 - Bayesian Occupancy grid Filter for dynamic environ.pdf}
}

@inproceedings{huangRRTSLAMMotionPlanning2008,
  title = {{{RRT}}-{{SLAM}} for Motion Planning with Motion and Map Uncertainty for Robot Exploration},
  doi = {10.1109/IROS.2008.4651183},
  abstract = {We address the motion planning (MP) subproblem that arises in a robotic exploration and mapping task. We consider sensing, localization and mapping uncertainties in the motion planning subproblem. The robot is holonomic with known size and shape, and is equipped with a laser range sensor. We use a rapidly exploring randomized tree (RRT) in conjunction with a simulated particle based Simultaneous Localization and Mapping (SLAM) algorithm to expand the tree. The simulated SLAM explicitly accounts for sensor, localization and mapping uncertainty in the planning stage. Moreover, the RRT itself is represented in the augmented configuration space where an extra dimension of uncertainty is used. The collision likelihood along a planned path is explicitly computed and is used to select a planned path. Preliminary simulations show the effectiveness and benefits of our integrated approach.},
  eventtitle = {2008 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}}},
  booktitle = {2008 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}}},
  date = {2008-09},
  pages = {1077-1082},
  keywords = {motion planning,Collision avoidance,Computational modeling,Distance measurement,map uncertainty,motion uncertainty,path planning,rapidly exploring randomized tree,robot exploration,Robot sensing systems,Robots,RRT-SLAM,Sensors,SLAM (robots),trees (mathematics),uncertain systems,Uncertainty},
  author = {Huang, Yifeng and Gupta, K.},
  file = {/Users/olepor/Zotero/storage/LPB45SX7/Yifeng Huang and Gupta - 2008 - RRT-SLAM for motion planning with motion and map u.pdf;/Users/olepor/Zotero/storage/L6SVNNJZ/4651183.html}
}

@article{vandenbergLQGMPOptimizedPath2011,
  langid = {english},
  title = {{{LQG}}-{{MP}}: {{Optimized}} Path Planning for Robots with Motion Uncertainty and Imperfect State Information},
  volume = {30},
  issn = {0278-3649, 1741-3176},
  url = {http://journals.sagepub.com/doi/10.1177/0278364911406562},
  doi = {10.1177/0278364911406562},
  shorttitle = {{{LQG}}-{{MP}}},
  abstract = {In this paper we present LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during the execution of the robot’s path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e. before execution) the a priori probability distributions of the state of the robot along its path. These distributions can be used to assess the quality of the path, for instance by computing the probability of avoiding collisions. Many methods can be used to generate the required ensemble of candidate paths from which the best path is selected; in this paper we report results using rapidly exploring random trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: (A) a kinodynamic car-like robot, (B) multi-robot planning with differential-drive robots, and (C) a 6-DOF serial manipulator. We also present a method that applies Kalman smoothing to make paths Ck-continuous and apply LQG-MP to precomputed roadmaps using a variant of Dijkstra’s algorithm to efﬁciently ﬁnd high-quality paths.},
  number = {7},
  journaltitle = {The International Journal of Robotics Research},
  urldate = {2018-05-16},
  date = {2011-06},
  pages = {895-913},
  author = {van den Berg, Jur and Abbeel, Pieter and Goldberg, Ken},
  options = {useprefix=true},
  file = {/Users/olepor/Zotero/storage/8WJTJGY2/van den Berg et al. - 2011 - LQG-MP Optimized path planning for robots with mo.pdf}
}

@article{silverMonteCarloPlanningLarge,
  langid = {english},
  title = {Monte-{{Carlo Planning}} in {{Large POMDPs}}},
  abstract = {This paper introduces a Monte-Carlo algorithm for online planning in large POMDPs. The algorithm combines a Monte-Carlo update of the agent’s belief state with a Monte-Carlo tree search from the current belief state. The new algorithm, POMCP, has two important properties. First, MonteCarlo sampling is used to break the curse of dimensionality both during belief state updates and during planning. Second, only a black box simulator of the POMDP is required, rather than explicit probability distributions. These properties enable POMCP to plan eﬀectively in signiﬁcantly larger POMDPs than has previously been possible. We demonstrate its effectiveness in three large POMDPs. We scale up a well-known benchmark problem, rocksample, by several orders of magnitude. We also introduce two challenging new POMDPs: 10 × 10 battleship and partially observable PacMan, with approximately 1018 and 1056 states respectively. Our MonteCarlo planning algorithm achieved a high level of performance with no prior knowledge, and was also able to exploit simple domain knowledge to achieve better results with less search. POMCP is the ﬁrst general purpose planner to achieve high performance in such large and unfactored POMDPs.},
  pages = {9},
  author = {Silver, David and Veness, Joel},
  file = {/Users/olepor/Zotero/storage/E7VNR55F/Silver and Veness - Monte-Carlo Planning in Large POMDPs.pdf}
}

@article{lavalleObjectiveBasedStochasticFramework,
  langid = {english},
  title = {An {{Objective}}-{{Based Stochastic Framework}} for {{Manipulation Planning}}},
  pages = {8},
  author = {LaValle, Steven M and Hutchinson, Seth A},
  file = {/Users/olepor/Zotero/storage/H64YIJZI/LaValle and Hutchinson - An Objective-Based Stochastic Framework for Manipu.pdf}
}

@article{shaniSurveyPointbasedPOMDP2013,
  langid = {english},
  title = {A Survey of Point-Based {{POMDP}} Solvers},
  volume = {27},
  issn = {1387-2532, 1573-7454},
  url = {http://link.springer.com/10.1007/s10458-012-9200-2},
  doi = {10.1007/s10458-012-9200-2},
  abstract = {The past decade has seen a significant breakthrough in research on solving partially observable Markov decision processes (POMDPs). Where past solvers could not scale beyond perhaps a dozen states, modern solvers can handle complex domains with many thousands of states. This breakthrough was mainly due to the idea of restricting value function computations to a ﬁnite subset of the belief space, permitting only local value updates for this subset. This approach, known as point-based value iteration, avoids the exponential growth of the value function, and is thus applicable for domains with longer horizons, even with relatively large state spaces. Many extensions were suggested to this basic idea, focusing on various aspects of the algorithm—mainly the selection of the belief space subset, and the order of value function updates. In this survey, we walk the reader through the fundamentals of point-based value iteration, explaining the main concepts and ideas. Then, we survey the major extensions to the basic algorithm, discussing their merits. Finally, we include an extensive empirical analysis using well known benchmarks, in order to shed light on the strengths and limitations of the various approaches.},
  number = {1},
  journaltitle = {Autonomous Agents and Multi-Agent Systems},
  urldate = {2018-05-16},
  date = {2013-07},
  pages = {1-51},
  author = {Shani, Guy and Pineau, Joelle and Kaplow, Robert},
  file = {/Users/olepor/Zotero/storage/SKQWNEZN/Shani et al. - 2013 - A survey of point-based POMDP solvers.pdf}
}

@article{HttpsLinkSpringera,
  title = {{{https://link.springer.com/article/10.1007/s10846-009-9383-1}}}
}

@article{FileUsersAndrhage,
  title = {File:///{{C}}:/{{Users}}/Andrhage/{{Downloads}}/52527.Pdf}
}

@article{HttpJournalsSagepub,
  title = {{{http://journals.sagepub.com/doi/full/10.1177/0278364913501564}}}
}

@inproceedings{melchiorParticleRRTPath2007,
  langid = {english},
  title = {Particle {{RRT}} for {{Path Planning}} with {{Uncertainty}}},
  isbn = {978-1-4244-0602-9 978-1-4244-0601-2},
  url = {http://ieeexplore.ieee.org/document/4209319/},
  doi = {10.1109/ROBOT.2007.363555},
  abstract = {This paper describes a new extension to the Rapidly–exploring Random Tree (RRT) path planning algorithm. The Particle RRT algorithm explicitly considers uncertainty in its domain, similar to the operation of a particle ﬁlter. Each extension to the search tree is treated as a stochastic process and is simulated multiple times. The behavior of the robot can be characterized based on the speciﬁed uncertainty in the environment, and guarantees can be made as to the performance under this uncertainty. Extensions to the search tree, and therefore entire paths, may be chosen based on the expected probability of successful execution. The beneﬁt of this algorithm is demonstrated in the simulation of a rover operating in rough terrain with unknown coefﬁcients of friction.},
  publisher = {{IEEE}},
  urldate = {2018-05-18},
  date = {2007-04},
  pages = {1617-1624},
  author = {Melchior, Nik A. and Simmons, Reid},
  file = {/Users/olepor/Zotero/storage/Y8F4XTG7/Melchior and Simmons - 2007 - Particle RRT for Path Planning with Uncertainty.pdf}
}

@article{djekouneSensorBasedNavigation2009,
  langid = {english},
  title = {A {{Sensor Based Navigation Algorithm}} for a {{Mobile Robot}} Using the {{DVFF Approach}}},
  volume = {6},
  issn = {1729-8814, 1729-8814},
  url = {http://journals.sagepub.com/doi/10.5772/6797},
  doi = {10.5772/6797},
  abstract = {Often autonomous mobile robots operate in environment for which prior maps are incomplete or inaccurate. They require the safe execution for a collision free motion to a goal position. This paper addresses a complete navigation method for a mobile robot that moves in unknown environment. Thus, a novel method called DVFF combining the Virtual Force Field (VFF) obstacle avoidance approach and global path planning based on D* algorithm is proposed. While D* generates global path information towards a goal position, the VFF local controller generates the admissible trajectories that ensure safe robot motion. Results and analysis from a battery of experiments with this new method implemented on a ATRV2 mobile robot are shown.},
  number = {2},
  journaltitle = {International Journal of Advanced Robotic Systems},
  urldate = {2018-05-18},
  date = {2009-06},
  pages = {14},
  author = {Djekoune, A. Oualid and Achour, Karim and Toumi, Redouane},
  file = {/Users/olepor/Zotero/storage/3NWAQB2T/Djekoune et al. - 2009 - A Sensor Based Navigation Algorithm for a Mobile R.pdf}
}

@article{noreenComparisonRRTRRT2016,
  langid = {english},
  title = {A {{Comparison}} of {{RRT}}, {{RRT}}* and {{RRT}}*-{{Smart Path Planning Algorithms}}},
  abstract = {Sampling based planning algorithm such as RRT and RRT* are extensively used in recent years for path planning of mobile robots. They are probabilistic complete algorithms and have natural support for solving high dimensional complex problems. RRT*-Smart is an extension of RRT* with faster convergence as compared to its predecessors. This paper provides an analytical review of the three algorithms. Impact of different parameters on algorithm’s performance is also evaluated. Moreover, a performance comparison for different optimality criteria such as path cost, run time and total number of nodes in tree is performed through simulation based experiments. Further, the comparative analysis is concluded with future research directions.},
  date = {2016},
  pages = {8},
  author = {Noreen, Iram and Khan, Amna and Habib, Zulfiqar},
  file = {/Users/olepor/Zotero/storage/944AGSTG/Noreen et al. - 2016 - A Comparison of RRT, RRT and RRT-Smart Path Plan.pdf}
}

@inproceedings{haitMotionPlanningRough1996,
  langid = {english},
  title = {Motion Planning on Rough Terrain for an Articulated Vehicle in Presence of Uncertainties},
  volume = {3},
  isbn = {978-0-7803-3213-3},
  url = {http://ieeexplore.ieee.org/document/568961/},
  doi = {10.1109/IROS.1996.568961},
  abstract = {This paper addresses motion planning for a mobile robot moving on a rough terrain. We proposed in [14] a geometrical planner for a particular architecture of robot. The approach was based on a discrete search technique operating in the (z, y, e ) configuration space of the robot, and on the evaluation of elementary feasible paths between two configurations. The overall efficiency of the approach was made possible by the use of fast algorithms for solving the placement problem and checking the validity of such placements. The contribution of this paper is twofold. First, we study the extension of this approach to an articulated vehicle composed of three axles connected to the chassis by joints allowing the roll and pitch movements. We also propose new algorithms to improve the robustness of the planner by considering additionnal constraints: uncertainties in the terrain model and existence of a free channel around the computed trajectory. Some simulation results presented at the end of the paper show the effectivenessof the planner which turns out to be both fast and capable of solving difficult problems.},
  publisher = {{IEEE}},
  urldate = {2018-05-20},
  date = {1996},
  pages = {1126-1133},
  author = {Hait, A. and Simeon, T.},
  file = {/Users/olepor/Zotero/storage/PWTLIETJ/Hait and Simeon - 1996 - Motion planning on rough terrain for an articulate.pdf}
}

@inproceedings{iagnemmaRapidPhysicsbasedRoughterrain1999,
  langid = {english},
  title = {Rapid Physics-Based Rough-Terrain Rover Planning with Sensor and Control Uncertainty},
  volume = {3},
  isbn = {978-0-7803-5180-6},
  url = {http://ieeexplore.ieee.org/document/770446/},
  doi = {10.1109/ROBOT.1999.770446},
  abstract = {In future planetary exploration missions, rovers will be required to autonomously traverse challenging environments. Much of the previous work in robot motion planning cannot be successfully applied to the rough-terrain planning problem. A model-based planning method is presented in this paper that is computationally efficient and takes into account uncertainty in the robot model, terrain model, range sensor data, and rover pathfollowing errors. It is based on rapid path planning through the visible terrain map with a simple graph-search algorithm, followed by a physics-based evaluation of the path with a rover model. Simulation results are presented which demonstrate the method’s effectiveness.},
  publisher = {{IEEE}},
  urldate = {2018-05-20},
  date = {1999},
  pages = {2286-2291},
  author = {Iagnemma, K. and Genot, F. and Dubowsky, S.},
  file = {/Users/olepor/Zotero/storage/GRYI33YK/Iagnemma et al. - 1999 - Rapid physics-based rough-terrain rover planning w.pdf}
}

@article{kellyReliableRoadAutonomous2006,
  langid = {english},
  title = {Toward {{Reliable Off Road Autonomous Vehicles Operating}} in {{Challenging Environments}}},
  volume = {25},
  issn = {0278-3649, 1741-3176},
  url = {http://journals.sagepub.com/doi/10.1177/0278364906065543},
  doi = {10.1177/0278364906065543},
  number = {5-6},
  journaltitle = {The International Journal of Robotics Research},
  urldate = {2018-05-21},
  date = {2006-05},
  pages = {449-483},
  author = {Kelly, Alonzo and Stentz, Anthony and Amidi, Omead and Bode, Mike and Bradley, David and Diaz-Calderon, Antonio and Happold, Mike and Herman, Herman and Mandelbaum, Robert and Pilarski, Tom and Rander, Pete and Thayer, Scott and Vallidis, Nick and Warner, Randy},
  file = {/Users/olepor/Zotero/storage/ILPS7HWR/Kelly et al. - 2006 - Toward Reliable Off Road Autonomous Vehicles Opera.pdf}
}

@inproceedings{galliPathPlanningUsing2017,
  title = {Path Planning Using {{Matlab}}-{{ROS}} Integration Applied to Mobile Robots},
  doi = {10.1109/ICARSC.2017.7964059},
  abstract = {In this paper the possibilities that Matlab provides to design, implementation and monitoring programs of autonomous navigation for mobile robots, on both simulated and real platforms, through its new toolbox for robotics will be explored. Robotics System Toolbox has established itself as a solid tool of integration between Matlab and robot operating under ROS environment. It will be studied the tools available in this toolbox that allow achieving the connection between the two platforms, in addition to the generation of algorithms of location, path planning, mapping and autonomous navigation.},
  eventtitle = {2017 {{IEEE International Conference}} on {{Autonomous Robot Systems}} and {{Competitions}} ({{ICARSC}})},
  booktitle = {2017 {{IEEE International Conference}} on {{Autonomous Robot Systems}} and {{Competitions}} ({{ICARSC}})},
  date = {2017-04},
  pages = {98-103},
  keywords = {path planning,Robot sensing systems,autonomous navigation,control engineering computing,design,mathematics computing,MATLAB,Matlab-ROS integration,mobile robots,Mobile robots,monitoring programs,navigation,operating systems (computers),robotics system toolbox,Tools,Trajectory},
  author = {Galli, M. and Barber, R. and Garrido, S. and Moreno, L.},
  file = {/Users/olepor/Zotero/storage/IXZ6MPVV/7964059.html}
}

@software{samUAVMotionPlannerEnsembleMatlabMotion2018,
  title = {{{UAV}}-{{Motion}}-{{Planner}}-{{Ensemble}}: {{A Matlab}} Motion Planner Ensemble of a Global {{Voronoi}}  Model and a Local {{Potential Field}} Model},
  url = {https://github.com/Elucidation/UAV-Motion-Planner-Ensemble},
  shorttitle = {{{UAV}}-{{Motion}}-{{Planner}}-{{Ensemble}}},
  urldate = {2018-05-23},
  date = {2018-05-10T07:15:40Z},
  author = {Sam},
  origdate = {2011-12-13T05:29:48Z}
}

@article{murphyPlanningExploringUncertainty,
  langid = {english},
  title = {Planning and {{Exploring Under Uncertainty}}},
  abstract = {Scalable autonomy requires a robot to be able to recognize and contend with the uncertainty in its knowledge of the world stemming from its noisy sensors and actuators. The regions it chooses to explore, and the paths it takes to get there, must take this uncertainty into account. In this thesis we outline probabilistic approaches to represent that world; to construct plans over it; and to determine which part of it to explore next.},
  pages = {251},
  author = {Murphy, Elizabeth},
  file = {/Users/olepor/Zotero/storage/98LKHJC5/Murphy - Planning and Exploring Under Uncertainty.pdf}
}

@inproceedings{lenzHeuristicSearchBelief2015,
  langid = {english},
  title = {Heuristic Search in Belief Space for Motion Planning under Uncertainties},
  isbn = {978-1-4799-9994-1},
  url = {http://ieeexplore.ieee.org/document/7353740/},
  doi = {10.1109/IROS.2015.7353740},
  abstract = {In order to fully exploit the capabilities of a robotic systems, it is necessary to consider the limitations and errors of actuators and sensors already during the motion planning phase. In this paper, a framework for path planning is introduced, that uses heuristic search to build up a search graph in belief space, an extension to the deterministic state space considering the uncertainty associated with this space. As sources of uncertainty actuator errors and map uncertainties are considered. We apply this framework to various scenarios for a non-holonomic vehicle and compare the resulting paths to heuristic state space planners and LQG-MP[1] with the help of simulations. As a result, paths generated with this framework could either not be found with worst-case assumptions or have a higher probability of being successfully executed compared to planners with more relaxed constraints.},
  publisher = {{IEEE}},
  urldate = {2018-05-23},
  date = {2015-09},
  pages = {2659-2665},
  author = {Lenz, David and Rickert, Markus and Knoll, Alois},
  file = {/Users/olepor/Zotero/storage/BR8TX9FZ/Lenz et al. - 2015 - Heuristic search in belief space for motion planni.pdf}
}

@inproceedings{abbadiPATHPLANNINGIMPLEMENTATION2014,
  title = {{{PATH PLANNING IMPLEMENTATION USING MATLAB}}},
  doi = {10.13140/2.1.3324.5767},
  abstract = {Motion planning is essential part in robotics science; it is responsible for planning paths for robots. The robot follow this plan in order to reach the goal from its position, while avoid collision with obstacles. Planning modules could be configured to check the optimality, completeness, power saving, shortness of path, minimal number of turn, or the turn sharpness, etc. In this technical paper we review the probabilistically planner RRT (rapidly exploring random tree) as local/global planner and Cell Decomposition as global planner guide the RRT. We focus on implementation of these methods in Matlab environments.},
  date = {2014-11-04},
  author = {Abbadi, Ahmad and Matousek, Radek},
  file = {/Users/olepor/Zotero/storage/DIATXG2V/Abbadi and Matousek - 2014 - PATH PLANNING IMPLEMENTATION USING MATLAB.pdf}
}

@online{LocalizeTurtleBotUsing,
  title = {Localize {{TurtleBot Using Monte Carlo Localization}} - {{MATLAB}} \& {{Simulink}} - {{MathWorks Nordic}}},
  url = {https://se.mathworks.com/help/robotics/examples/localize-turtlebot-using-monte-carlo-localization.html},
  urldate = {2018-05-23}
}

@online{MappingKnownPoses,
  title = {Mapping {{With Known Poses}} - {{MATLAB}} \& {{Simulink}} - {{MathWorks Nordic}}},
  url = {https://se.mathworks.com/help/robotics/examples/mapping-with-known-poses.html},
  urldate = {2018-05-23}
}

@article{majumdarFunnelLibrariesRealtime2017,
  langid = {english},
  title = {Funnel Libraries for Real-Time Robust Feedback Motion Planning},
  volume = {36},
  issn = {0278-3649, 1741-3176},
  url = {http://journals.sagepub.com/doi/10.1177/0278364917712421},
  doi = {10.1177/0278364917712421},
  abstract = {We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real-time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of “funnels” along di↵erent maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the e↵ect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances.},
  number = {8},
  journaltitle = {The International Journal of Robotics Research},
  urldate = {2018-08-21},
  date = {2017-07},
  pages = {947-982},
  keywords = {Computer Science - Robotics,Computer Science - Systems and Control,Mathematics - Optimization and Control,Mathematics - Dynamical Systems,Computer Science - Artificial Intelligence},
  author = {Majumdar, Anirudha and Tedrake, Russ},
  file = {/Users/olepor/Zotero/storage/AVHSMXHP/Majumdar and Tedrake - 2016 - Funnel Libraries for Real-Time Robust Feedback Mot.pdf;/Users/olepor/Zotero/storage/LZR8PJH3/Majumdar and Tedrake - 2017 - Funnel libraries for real-time robust feedback mot.pdf}
}

@article{barryHighspeedAutonomousObstacle2018,
  langid = {english},
  title = {High-Speed Autonomous Obstacle Avoidance with Pushbroom Stereo},
  volume = {35},
  issn = {15564959},
  url = {http://doi.wiley.com/10.1002/rob.21741},
  doi = {10.1002/rob.21741},
  abstract = {This thesis presents the design and implementation of a small autonomous unmanned aerial vehicle capable of high-speed ﬂight through complex natural environments. Using only onboard sensing and computation, we perform obstacle detection, planning, and feedback control in realtime. We introduce a novel stereo vision algorithm, pushbroom stereo, capable of detecting obstacles at 120 frames per second without overburdening our lightweight processors. Our use of model-based planning and control techniques allows us to track precise trajectories that avoid obstacles identiﬁed by the vision system. We demonstrate a complete working system avoiding trees at up to 14 m/s (31 MPH). To the best of our knowledge this is the fastest lightweight aerial vehicle to perform collision avoidance in such a complex environment.},
  number = {1},
  journaltitle = {Journal of Field Robotics},
  urldate = {2018-08-21},
  date = {2018-01},
  pages = {52-68},
  author = {Barry, Andrew J. and Florence, Peter R. and Tedrake, Russ},
  file = {/Users/olepor/Zotero/storage/BXVX5VJ4/Barry et al. - 2018 - High-speed autonomous obstacle avoidance with push.pdf}
}

@article{ahmadiDSOSSDSOSOptimization2017,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1706.02586},
  primaryClass = {cs, math, stat},
  langid = {english},
  title = {{{DSOS}} and {{SDSOS Optimization}}: {{More Tractable Alternatives}} to {{Sum}} of {{Squares}} and {{Semidefinite Optimization}}},
  url = {http://arxiv.org/abs/1706.02586},
  shorttitle = {{{DSOS}} and {{SDSOS Optimization}}},
  abstract = {In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semideﬁnite programs however, has limited the scale of problems to which it can be applied. In this paper, we introduce DSOS and SDSOS optimization as more tractable alternatives to sum of squares optimization that rely instead on linear and second order cone programs respectively. These are optimization problems over certain subsets of sum of squares polynomials (or equivalently subsets of positive semideﬁnite matrices), which can be of interest in general applications of semideﬁnite programming where scalability is a limitation. We show that some basic theorems from SOS optimization which rely on results from real algebraic geometry are still valid for DSOS and SDSOS optimization. Furthermore, we show with numerical experiments from diverse application areas—polynomial optimization, statistics and machine learning, derivative pricing, and control theory—that with reasonable tradeo↵s in accuracy, we can handle problems at scales that are currently far beyond the reach of sum of squares approaches. Finally, we provide a review of recent techniques that bridge the gap between our DSOS/SDSOS approach and the SOS approach at the expense of additional running time. The appendix of the paper introduces an accompanying MATLAB package for DSOS and SDSOS optimization.},
  urldate = {2018-08-24},
  date = {2017-06-08},
  keywords = {Computer Science - Systems and Control,Mathematics - Optimization and Control,Computer Science - Data Structures and Algorithms,Statistics - Machine Learning},
  author = {Ahmadi, Amir Ali and Majumdar, Anirudha},
  file = {/Users/olepor/Zotero/storage/9FM2AUPE/Ahmadi and Majumdar - 2017 - DSOS and SDSOS Optimization More Tractable Altern.pdf}
}

@incollection{majumdarRobustOnlineMotion2013,
  langid = {english},
  location = {{Berlin, Heidelberg}},
  title = {Robust {{Online Motion Planning}} with {{Regions}} of {{Finite Time Invariance}}},
  volume = {86},
  isbn = {978-3-642-36278-1 978-3-642-36279-8},
  url = {http://link.springer.com/10.1007/978-3-642-36279-8_33},
  abstract = {In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to ofﬂine planning due to the computational cost of safety veriﬁcation. Here we take a trajectory library approach by designing controllers that stabilize the nominal trajectories in the library and precomputing regions of ﬁnite time invariance (“funnels”) for the resulting closed loop system. We leverage sums-of-squares programming in order to efﬁciently compute funnels which take into account bounded disturbances and uncertainty. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate our method on a simulation of a plane ﬂying through a two dimensional forest of polygonal trees with parametric uncertainty and disturbances in the form of a bounded “cross-wind”.},
  booktitle = {Algorithmic {{Foundations}} of {{Robotics X}}},
  publisher = {{Springer Berlin Heidelberg}},
  urldate = {2018-08-24},
  date = {2013},
  pages = {543-558},
  author = {Majumdar, Anirudha and Tedrake, Russ},
  editor = {Frazzoli, Emilio and Lozano-Perez, Tomas and Roy, Nicholas and Rus, Daniela},
  file = {/Users/olepor/Zotero/storage/GQDCMPJD/Majumdar and Tedrake - 2013 - Robust Online Motion Planning with Regions of Fini.pdf},
  doi = {10.1007/978-3-642-36279-8_33}
}

@inproceedings{tedrakeLQRtreesFeedbackMotion2009,
  langid = {english},
  title = {{{LQR}}-Trees: {{Feedback}} Motion Planning on Sparse Randomized Trees},
  isbn = {978-0-262-51463-7},
  url = {http://www.roboticsproceedings.org/rss05/p3.pdf},
  doi = {10.15607/RSS.2009.V.003},
  shorttitle = {{{LQR}}-Trees},
  abstract = {Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efﬁciently evaluate regions of stability for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses these results to efﬁciently combine locally valid linear quadratic regulator (LQR) controllers into a nonlinear feedback policy which probabilistically covers the reachable area of a (bounded) state space with a region of stability, certifying that all initial conditions that are capable of reaching the goal will stabilize to the goal. We investigate the properties of this systematic nonlinear feedback control design algorithm on simple underactuated systems and discuss the potential for control of more complicated control problems like bipedal walking.},
  eventtitle = {Robotics: {{Science}} and {{Systems}} 2009},
  booktitle = {Robotics: {{Science}} and {{Systems V}}},
  publisher = {{Robotics: Science and Systems Foundation}},
  urldate = {2018-08-24},
  date = {2009-06-28},
  author = {Tedrake, R.},
  file = {/Users/olepor/Zotero/storage/V8L2G9IT/Tedrake - 2009 - LQR-trees Feedback motion planning on sparse rand.pdf}
}

@article{tobenkinInvariantFunnelsTrajectories2010,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1010.3013},
  primaryClass = {math},
  langid = {english},
  title = {Invariant {{Funnels}} around {{Trajectories}} Using {{Sum}}-of-{{Squares Programming}}},
  url = {http://arxiv.org/abs/1010.3013},
  abstract = {This paper presents numerical methods for computing regions of ﬁnite-time invariance (funnels) around solutions of polynomial di↵erential equations. First, we present a method which exactly certiﬁes su cient conditions for invariance despite relying on approximate trajectories from numerical integration. Our second method relaxes the constraints of the ﬁrst by sampling in time. In applications, this can recover almost identical funnels but is much faster to compute. In both cases, funnels are veriﬁed using Sum-of-Squares programming to search over a family of time-varying polynomial Lyapunov functions. Initial candidate Lyapunov functions are constructed using the linearization about the trajectory, and associated time-varying Lyapunov and Riccati di↵erential equations. The methods are compared on stabilized trajectories of a six-state model of a satellite.},
  urldate = {2018-08-24},
  date = {2010-10-14},
  keywords = {Mathematics - Dynamical Systems},
  author = {Tobenkin, Mark M. and Manchester, Ian R. and Tedrake, Russ},
  file = {/Users/olepor/Zotero/storage/DJL659E6/Tobenkin et al. - 2010 - Invariant Funnels around Trajectories using Sum-of.pdf}
}

@inproceedings{singhRobustOnlineMotion2017,
  langid = {english},
  location = {{Singapore, Singapore}},
  title = {Robust Online Motion Planning via Contraction Theory and Convex Optimization},
  isbn = {978-1-5090-4633-1},
  url = {http://ieeexplore.ieee.org/document/7989693/},
  doi = {10.1109/ICRA.2017.7989693},
  abstract = {We present a framework for online generation of robust motion plans for robotic systems with nonlinear dynamics subject to bounded disturbances, control constraints, and online state constraints such as obstacles. In an ofﬂine phase, one computes the structure of a feedback controller that can be efﬁciently implemented online to track any feasible nominal trajectory. The ofﬂine phase leverages contraction theory and convex optimization to characterize a ﬁxed-size “tube” that the state is guaranteed to remain within while tracking a nominal trajectory (representing the center of the tube). In the online phase, when the robot is faced with obstacles, a motion planner uses such a tube as a robustness margin for collision checking, yielding nominal trajectories that can be safely executed, i.e., tracked without collisions under disturbances. In contrast to recent work on robust online planning using funnel libraries, our approach is not restricted to a ﬁxed library of maneuvers computed ofﬂine and is thus particularly well-suited to applications such as UAV ﬂight in densely cluttered environments where complex maneuvers may be required to reach a goal. We demonstrate our approach through simulations of a 6-state planar quadrotor navigating cluttered environments in the presence of a cross-wind. We also discuss applications of our approach to Tube Model Predictive Control (TMPC) and compare the merits of our method with state-of-the-art nonlinear TMPC techniques.},
  eventtitle = {2017 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  booktitle = {2017 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  publisher = {{IEEE}},
  urldate = {2018-08-24},
  date = {2017-05},
  pages = {5883-5890},
  author = {Singh, Sumeet and Majumdar, Anirudha and Slotine, Jean-Jacques and Pavone, Marco},
  file = {/Users/olepor/Zotero/storage/6X7X7U4U/Singh et al. - 2017 - Robust online motion planning via contraction theo.pdf}
}

@article{divelbissTrajectoryTrackingControl1997,
  langid = {english},
  title = {Trajectory Tracking Control of a Car-Trailer System},
  volume = {5},
  issn = {10636536},
  url = {http://ieeexplore.ieee.org/document/572125/},
  doi = {10.1109/87.572125},
  abstract = {This paper presents the experimental results of the tracking control of a car-trailer system. The proposed scheme involves three steps: 1) generate a path off-line using a path space iterative algorithm; 2) linearize the kinematic model about a trajectory which is constructed using the path; and 3) apply a time-varying linear quadratic regulator to track the trajectory. Experiments presented include parallel parking a car, docking a tractor-trailer vehicle, and parallel parking a double tractortrailer vehicle.},
  number = {3},
  journaltitle = {IEEE Transactions on Control Systems Technology},
  urldate = {2018-09-20},
  date = {1997-05},
  pages = {269-278},
  author = {Divelbiss, A.W. and Wen, J.T.},
  file = {/Users/olepor/Zotero/storage/LX8DH53A/Divelbiss and Wen - 1997 - Trajectory tracking control of a car-trailer syste.pdf}
}

@article{kousikSafeTrajectorySynthesis2017,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1705.00091},
  primaryClass = {cs},
  langid = {english},
  title = {Safe {{Trajectory Synthesis}} for {{Autonomous Driving}} in {{Unforeseen Environments}}},
  url = {http://arxiv.org/abs/1705.00091},
  abstract = {Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-ﬁdelity model. To address this problem, this paper develops a method to perform trajectory design by considering a low-ﬁdelity model that accounts for model mismatch. The presented method begins by computing a conservative Forward Reachable Set (FRS) of a high-ﬁdelity model’s trajectories produced when tracking trajectories of a low-ﬁdelity model over a ﬁnite time horizon. At runtime, the vehicle intersects this FRS with obstacles in the environment to eliminate trajectories that can lead to a collision, then selects an optimal plan from the remaining safe set. By bounding the time for this set intersection and subsequent path selection, this paper proves a lower bound for the FRS time horizon and sensing horizon to guarantee safety. This method is demonstrated in simulation using a kinematic Dubin’s car as the low-ﬁdelity model and a dynamic unicycle as the highﬁdelity model.},
  urldate = {2018-10-10},
  date = {2017-04-28},
  keywords = {Computer Science - Robotics,Computer Science - Systems and Control},
  author = {Kousik, Shreyas and Vaskov, Sean and Johnson-Roberson, Matthew and Vasudevan, Ramanarayan},
  file = {/Users/olepor/Zotero/storage/G88WG6M2/Kousik et al. - 2017 - Safe Trajectory Synthesis for Autonomous Driving i.pdf}
}

@article{xuCorrectnessGuaranteesComposition2016,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1609.06807},
  primaryClass = {cs, math},
  langid = {english},
  title = {Correctness {{Guarantees}} for the {{Composition}} of {{Lane Keeping}} and {{Adaptive Cruise Control}}},
  url = {http://arxiv.org/abs/1609.06807},
  abstract = {This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety speciﬁcations for these driver assistance modules are expressed in terms of set invariance. Control barrier functions are used to design a family of control solutions that guarantee the forward invariance of a set, which implies satisfaction of the safety speciﬁcations. The control barrier functions are synthesized through a combination of sum-of-squares program and physics-based modeling and optimization. A real-time quadratic program is posed to combine the control barrier functions with the performancebased controllers, which can be either expressed as control Lyapunov function conditions or as black-box legacy controllers. In both cases, the resulting feedback control guarantees the safety of the composed driver assistance modules in a formally correct manner. Importantly, the quadratic program admits a closed-form solution that can be easily implemented. The effectiveness of the control approach is demonstrated by simulations in the industry-standard vehicle simulator Carsim.},
  urldate = {2018-10-10},
  date = {2016-09-21},
  keywords = {Computer Science - Systems and Control,Mathematics - Optimization and Control},
  author = {Xu, Xiangru and Grizzle, Jessy W. and Tabuada, Paulo and Ames, Aaron D.},
  file = {/Users/olepor/Zotero/storage/QTIZW5QY/mason-mechanicsofmanipulation.pdf;/Users/olepor/Zotero/storage/UPS2PNKG/Xu et al. - 2016 - Correctness Guarantees for the Composition of Lane.pdf;/Users/olepor/Zotero/storage/VX2SVRTR/Majumdar-Tedrake2013_Chapter_RobustOnlineMotionPlanningWith.pdf}
}

@article{kimComputingForwardReachable2018,
  langid = {english},
  title = {Computing the {{Forward Reachable Set}} for a {{Multirotor Under First}}-{{Order Aerodynamic Effects}}},
  volume = {3},
  issn = {2377-3766, 2377-3774},
  url = {https://ieeexplore.ieee.org/document/8387437/},
  doi = {10.1109/LRA.2018.2848302},
  abstract = {Collision avoidance plays a crucial role in safe multirotor ﬂight in cluttered environments. Even though a given reference trajectory is designed to be collision free, it might lead to collision due to imperfect tracking caused by external disturbances. In this work, we tackle this problem by computing the Forward Reachable Set (FRS), which is the set of positions and velocities that a multirotor can reach while following a reference trajectory due to tracking errors. Hence, if the FRS is computed before ﬂight, we can utilize it to check the safety of a given trajectory in terms of collision avoidance. To compute a realistic FRS that covers an agile ﬂight envelope, we consider ﬁrst-order aerodynamic effects, which have the most salient inﬂuence on the vehicle. For computing FRS, we conduct a thorought stability analysis including these aerodynamic effects. Then, we present a FRS computation method which can easily be adapted to newly given reference trajectories. The presented method is validated by comparing the FRS with real ﬂight data collected during agile and high-speed ﬂight. In addition, we compare the FRS computed with and without compensating for ﬁrstorder aerodynamic effect to highlight their signiﬁcance on the trajectory tracking performance. To the best of our knowledge, this is the ﬁrst attempt to compute FRSs by incorporating ﬁrstorder aerodynamic effects for multirotors.},
  number = {4},
  journaltitle = {IEEE Robotics and Automation Letters},
  urldate = {2018-10-10},
  date = {2018-10},
  pages = {2934-2941},
  author = {Kim, Suseong and Falanga, Davide and Scaramuzza, Davide},
  file = {/Users/olepor/Zotero/storage/CBM7HI8N/Kim et al. - 2018 - Computing the Forward Reachable Set for a Multirot.pdf}
}

@article{majumdarTechnicalReportConvex2013,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1305.7484},
  primaryClass = {cs, math},
  langid = {english},
  title = {Technical {{Report}}: {{Convex Optimization}} of {{Nonlinear Feedback Controllers}} via {{Occupation Measures}}},
  url = {http://arxiv.org/abs/1305.7484},
  shorttitle = {Technical {{Report}}},
  abstract = {In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an inﬁnite dimensional linear program (LP) and provide ﬁnite dimensional approximations of this LP in terms of semideﬁnite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efﬁcacy and scalability of our approach on ﬁve nonlinear systems.},
  urldate = {2018-10-17},
  date = {2013-05-31},
  keywords = {Computer Science - Robotics,Computer Science - Systems and Control,Mathematics - Optimization and Control},
  author = {Majumdar, Anirudha and Vasudevan, Ram and Tobenkin, Mark M. and Tedrake, Russ},
  file = {/Users/olepor/Zotero/storage/8J4VPJM4/Majumdar et al. - 2013 - Technical Report Convex Optimization of Nonlinear.pdf}
}

@article{palmieriNovelRRTExtend,
  langid = {english},
  title = {A {{Novel RRT Extend Function}} for {{E}} Cient and {{Smooth Mobile Robot Motion Planning}}},
  abstract = {In this paper we introduce a novel RRT extend function for wheeled mobile robots. The approach computes closed-loop forward simulations based on the kinematic model of the robot and enables the planner to e ciently generate smooth and feasible paths that connect any pairs of states. We extend the control law of an existing discontinuous state feedback controller to make it usable as an RRT extend function and prove that all relevant stability properties are retained. We study the properties of the new approach as extender for RRT and RRT* and compare it systematically to a spline-based approach and a large and small set of motion primitives. The results show that our approach generally produces smoother paths to the goal in less time with smaller trees. For RRT*, the approach produces also the shortest paths and achieves the lowest cost solutions when given more planning time.},
  pages = {7},
  author = {Palmieri, Luigi and Arras, Kai O},
  file = {/Users/olepor/Zotero/storage/CMG2LQNR/Palmieri and Arras - A Novel RRT Extend Function for E cient and Smooth.pdf}
}

@inproceedings{parkFeedbackMotionPlanning2015,
  langid = {english},
  location = {{Hamburg, Germany}},
  title = {Feedback Motion Planning via Non-Holonomic {{RRT}}* for Mobile Robots},
  isbn = {978-1-4799-9994-1},
  url = {http://ieeexplore.ieee.org/document/7353946/},
  doi = {10.1109/IROS.2015.7353946},
  abstract = {Here we present a non-holonomic distance function for unicycle-type vehicles, and use this distance function ⇤ to extend the optimal path planner RRT to handle nonholonomic constraints. The critical feature of our proposed distance function is that it is also a control-Lyapunov function. We show that this allows us to construct feedback policies that stabilizes the system to a target pose, and to generate the optimal path that respects the non-holonomic constraints ⇤ of the system via the non-holonomic RRT . The composition of the Lyapunov function that is obtained as a result of this planning process provides stabilizing feedback and the cost-togo to the ﬁnal destination in the neighborhood of the planned path, adding much ﬂexibility and robustness to the plan.},
  eventtitle = {2015 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}} ({{IROS}})},
  booktitle = {2015 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}} ({{IROS}})},
  publisher = {{IEEE}},
  urldate = {2019-01-10},
  date = {2015-09},
  pages = {4035-4040},
  author = {Park, Jong Jin and Kuipers, Benjamin},
  file = {/Users/olepor/Zotero/storage/SFD8V9MV/Park and Kuipers - 2015 - Feedback motion planning via non-holonomic RRT fo.pdf}
}

@article{kroeseSpatialProcessGeneration,
  langid = {english},
  title = {Spatial {{Process Generation}}},
  pages = {41},
  author = {Kroese, Dirk P and Botev, Zdravko I},
  file = {/Users/olepor/Zotero/storage/GZUUPAYL/Kroese and Botev - Spatial Process Generation.pdf}
}

@inproceedings{masonMechanicsManipulation1985,
  langid = {english},
  location = {{St. Louis, MO, USA}},
  title = {The Mechanics of Manipulation},
  volume = {2},
  url = {http://ieeexplore.ieee.org/document/1087242/},
  doi = {10.1109/ROBOT.1985.1087242},
  eventtitle = {1985 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  booktitle = {Proceedings. 1985 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  publisher = {{Institute of Electrical and Electronics Engineers}},
  urldate = {2019-02-10},
  date = {1985},
  pages = {544-548},
  author = {Mason, M.},
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}

@online{tedrakeUnderactuatedRoboticsAlgorithms2019,
  title = {Underactuated {{Robotics}}: {{Algorithms}} for {{Walking}}, {{Running}}, {{Swimming}}, {{Flying}}, and {{Manipulation}} ({{Course Notes}} for {{MIT}} 6.832)},
  url = {http://underactuated.mit.edu/},
  date = {2019-12-02},
  author = {Tedrake, Russ}
}

@thesis{parilloStructuredSemidefinitePrograms,
  langid = {english},
  location = {{Pasadena, California}},
  title = {Structured {{Semidefinite Programs}} and {{Semialgebraic Geometry Methods}} in {{Robustness}} and {{Optimization}}},
  url = {https://thesis.library.caltech.edu/1647/1/Parrilo-Thesis.pdf},
  pagetotal = {135},
  institution = {{California Institute of Technology}},
  author = {Parillo, Pablo A.},
  file = {/Users/olepor/Zotero/storage/XW7K42CP/Parrilo-Thesis.pdf}
}

@artwork{alexandrovConvexConeIllust2019,
  title = {Convex\_cone\_illust},
  url = {https://commons.wikimedia.org/w/index.php?curid=2083523},
  shorttitle = {Convex Cone Illustrated},
  abstract = {By Oleg Alexandrov - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=2083523},
  date = {2019-02-10},
  author = {Alexandrov, Oleg}
}

@article{2000Hosp,
  langid = {english},
  title = {Handbook of Semidefinite Programming : Theory, Algorithms, and Applications},
  volume = {27},
  series = {International Series in Operations Research \& Management Science},
  date = {2000},
  keywords = {Lineær programmering,Lineær programmering (Bedriftsorganisasjon),Optimalisering},
  location = {{Boston}},
  publisher = {{Kluwer}},
  isbn = {0792377710}
}

@book{zotero-202,
  type = {book}
}

@collection{wolkowiczHandbookSemidefiniteProgramming2000,
  location = {{Boston}},
  title = {Handbook of Semidefinite Programming: Theory, Algorithms, and Applications},
  isbn = {978-0-7923-7771-9},
  shorttitle = {Handbook of Semidefinite Programming},
  pagetotal = {654},
  number = {27},
  series = {International Series in Operations Research \& Management Science},
  publisher = {{Kluwer Academic Publishers}},
  date = {2000},
  keywords = {Linear programming,Mathematical optimization},
  editor = {Wolkowicz, Henry and Saigal, Romesh and Vandenberghe, Lieven}
}

@book{mosek,
  title = {The {{MOSEK}} Optimization Toolbox for {{MATLAB}} Manual. {{Version}} 8.1.},
  url = {http://docs.mosek.com/8.1/toolbox/index.html},
  date = {2017},
  author = {ApS, MOSEK}
}

@book{sostools,
  location = {{http://arxiv.org/abs/1310.4716}},
  title = {{{SOSTOOLS}}: {{Sum}} of Squares Optimization Toolbox for {{MATLAB}}},
  date = {2013},
  author = {{A. Papachristodoulou, J. Anderson, G. Valmorbida, S. Prajna, P. Seiler} and Parrilo, P. A.},
  note = {Available from http://www.eng.ox.ac.uk/control/sostools, http://www.cds.caltech.edu/sostools and
http://www.mit.edu/parrilo/sostools}
}

@inproceedings{Lofberg2004,
  title = {{{YALMIP}} : {{A Toolbox}} for {{Modeling}} and {{Optimization}} in {{MATLAB}}},
  booktitle = {In {{Proceedings}} of the {{CACSD Conference}}},
  date = {2004},
  author = {Löfberg, J.},
  venue = {Taipei, Taiwan}
}

@article{Lofberg2009,
  title = {Pre- and Post-Processing Sum-of-Squares Programs in Practice},
  volume = {54},
  number = {5},
  journaltitle = {IEEE Transactions on Automatic Control},
  date = {2009},
  pages = {1007-1011},
  author = {Löfberg, Johan}
}

@article{lavalleLav98cPdf1998,
  title = {Lav98c.Pdf},
  volume = {Department of Computer Science, Iowa State University},
  url = {http://msl.cs.illinois.edu/~lavalle/papers/Lav98c.pdf},
  journaltitle = {Technical report},
  date = {1998-11},
  author = {LaValle, Steven M},
  file = {/Users/olepor/Zotero/storage/XX2CGZIJ/Lav98c.pdf}
}

@article{article,
  title = {Rapidly-{{Exploring Random Trees}}: {{A New Tool}} for {{Path Planning}}},
  date = {1999-05},
  author = {M. Lavalle, Steven}
}

@article{aurenhammerVoronoiDiagramsSurvey1991,
  langid = {english},
  title = {Voronoi Diagrams---a Survey of a Fundamental Geometric Data Structure},
  volume = {23},
  issn = {03600300},
  url = {http://portal.acm.org/citation.cfm?doid=116873.116880},
  doi = {10.1145/116873.116880},
  number = {3},
  journaltitle = {ACM Computing Surveys},
  urldate = {2019-02-19},
  date = {1991-09-01},
  pages = {345-405},
  author = {Aurenhammer, Franz},
  file = {/Users/olepor/Zotero/storage/C8NQPCBY/Aurenhammer - 1991 - Voronoi diagrams---a survey of a fundamental geome.pdf}
}

@article{lavalleMotionPlanningEssentials,
  langid = {english},
  title = {Motion {{Planning}}: {{The Essentials}}},
  pages = {10},
  author = {LaValle, Steven M},
  file = {/Users/olepor/Zotero/storage/5IBGC8RA/LaValle - Motion Planning The Essentials.pdf}
}

@book{Lav06,
  location = {{Cambridge, U.K.}},
  title = {Planning {{Algorithms}}},
  publisher = {{Cambridge University Press}},
  date = {2006},
  author = {LaValle, S. M.},
  note = {Available at http://planning.cs.uiuc.edu/}
}

@article{lay2005linear,
  title = {Linear {{Algebra}} and Its {{Applications}}, 3rd Updated {{Edition}}},
  date = {2005},
  author = {Lay, David C},
  publisher = {{Addison Wesley}}
}

@inproceedings{lenySequentialCompositionRobust2012,
  langid = {english},
  location = {{St Paul, MN, USA}},
  title = {Sequential Composition of Robust Controller Specifications},
  isbn = {978-1-4673-1405-3 978-1-4673-1403-9 978-1-4673-1578-4 978-1-4673-1404-6},
  url = {http://ieeexplore.ieee.org/document/6224797/},
  doi = {10.1109/ICRA.2012.6224797},
  abstract = {We present a general notion of robust controller speciﬁcation and a mechanism for sequentially composing them. These speciﬁcations form tubular abstractions of the trajectories of a system in different control modes, and are motivated by the techniques available for certifying the performance of low-level controllers. The notion of controller speciﬁcation provides a rigorous interface for connecting a planner and lower-level controllers that are designed independently. With this approach, the planning layer does not integrate the closed-loop system dynamics and does not require the knowledge of how the controllers operate, but relies only on the speciﬁcations of the output tracking performance achieved by these controllers. The control layer aims at satisfying speciﬁcations that account quantitatively for robustness to unmodeled dynamics and various sources of disturbance and sensor noise, so that this robustness does not need to be revalidated at the planning level. As an illustrative example, we describe a randomized planner that composes different controller speciﬁcations from a given database to guarantee that any corresponding sequence of control modes steers a robot to a given region while avoiding obstacles.},
  eventtitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  booktitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  publisher = {{IEEE}},
  urldate = {2019-02-28},
  date = {2012-05},
  pages = {5190-5195},
  author = {Le Ny, Jerome and Pappas, George J.},
  file = {/Users/olepor/Zotero/storage/RQCZKGV8/Le Ny and Pappas - 2012 - Sequential composition of robust controller specif.pdf}
}

@article{drake,
  title = {Drake: {{A}} Planning, Control, and Analysis Toolbox for Nonlinear Dynamical Systems},
  url = {https://drake.mit.edu},
  date = {2016},
  author = {Tedrake, Russ and {the Drake Development Team}}
}

@article{AM69,
  title = {Introduction to Commutative Algebra},
  date = {1969},
  pages = {ix+128},
  author = {Atiyah, M. F. and Macdonald, I. G.},
  publisher = {{Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.}},
  mrclass = {13.00},
  mrnumber = {0242802 (39 \#4129)},
  mrreviewer = {J. A. Johnson}
}

@article{Har77,
  title = {Algebraic Geometry},
  date = {1977},
  author = {Hartshorne, R.},
  publisher = {{Springer-Verlag, New York-Heidelberg}},
  isbn = {0-387-90244-9},
  mrclass = {14-01},
  mrnumber = {0463157 (57 \#3116)},
  mrreviewer = {Robert Speiser},
  note = {Graduate Texts in Mathematics, No. 52}
}

@article{sucan2012the-open-motion-planning-library,
  title = {The {{Open Motion Planning Library}}},
  volume = {19},
  doi = {10.1109/MRA.2012.2205651},
  number = {4},
  journaltitle = {IEEE Robotics \& Automation Magazine},
  date = {2012-12},
  pages = {72-82},
  author = {Şucan, Ioan A. and Moll, Mark and Kavraki, Lydia E.},
  note = {http://ompl.kavrakilab.org}
}

@article{moll2015benchmarking-motion-planning-algorithms,
  title = {Benchmarking {{Motion Planning Algorithms}}: {{An Extensible Infrastructure}} for {{Analysis}} and {{Visualization}}},
  volume = {22},
  doi = {10.1109/MRA.2015.2448276},
  number = {3},
  journaltitle = {IEEE Robotics \& Automation Magazine},
  date = {2015-09},
  pages = {96-102},
  author = {Moll, Mark and Şucan, Ioan A. and Kavraki, Lydia E.}
}

@thesis{Cassandra:1998:EAA:926710,
  location = {{Providence, RI, USA}},
  title = {Exact and {{Approximate Algorithms}} for {{Partially Observable Markov Decision Processes}}},
  institution = {{Brown University}},
  date = {1998},
  author = {Cassandra, Anthony Rocco},
  isbn = {0-591-83322-0},
  advisor = {Kaelbling, Leslie Pack},
  note = {AAI9830418}
}

@article{koenig2002d,
  title = {D* {{Lite}}},
  volume = {28},
  journaltitle = {AAAI/IAAI},
  date = {2002},
  author = {Koenig, Sven and Likhachev, Maxim}
}

@inproceedings{stentz1995focussed,
  title = {The Focussed {{D}}\^* Algorithm for Real-Time Replanning},
  volume = {95},
  booktitle = {{{IJCAI}}},
  date = {1995},
  pages = {1652-1659},
  author = {Stentz, Anthony and others}
}

@inproceedings{moravec1985high,
  title = {High Resolution Maps from Wide Angle Sonar},
  volume = {2},
  booktitle = {Robotics and {{Automation}}. {{Proceedings}}. 1985 {{IEEE International Conference}} On},
  date = {1985},
  pages = {116-121},
  author = {Moravec, Hans and Elfes, Alberto},
  organization = {{IEEE}}
}

@article{elfes1989using,
  title = {Using Occupancy Grids for Mobile Robot Perception and Navigation},
  volume = {22},
  number = {6},
  journaltitle = {Computer},
  date = {1989},
  pages = {46-57},
  author = {Elfes, Alberto},
  publisher = {{IEEE}}
}

@inproceedings{kriegman1987mobile,
  title = {A Mobile Robot: {{Sensing}}, Planning and Locomotion},
  volume = {4},
  booktitle = {Robotics and {{Automation}}. {{Proceedings}}. 1987 {{IEEE International Conference}} On},
  date = {1987},
  pages = {402-408},
  author = {Kriegman, DAVIDJ and Triendl, Ernst and Binford, THOMASO},
  organization = {{IEEE}}
}

@inproceedings{elfes1990occupancy,
  title = {Occupancy Grids: {{A}} Stochastic Spatial Representation for Active Robot Perception},
  volume = {2929},
  booktitle = {Proceedings of the {{Sixth Conference}} on {{Uncertainty}} in {{AI}}},
  date = {1990},
  pages = {6},
  author = {Elfes, Alberto}
}

@inproceedings{Luders_2013,
  title = {Robust {{Sampling}}-Based {{Motion Planning}} with {{Asymptotic Optimality Guarantees}}},
  url = {https://doi.org/10.2514%2F6.2013-5097},
  doi = {10.2514/6.2013-5097},
  booktitle = {{{AIAA Guidance}}, {{Navigation}}, and {{Control}} ({{GNC}}) {{Conference}}},
  publisher = {{American Institute of Aeronautics and Astronautics}},
  date = {2013-08},
  author = {Luders, Brandon D. and Karaman, Sertac and How, Jonathan P.}
}

@inproceedings{vonasekGlobalMotionPlanning2013,
  langid = {english},
  location = {{Karlsruhe, Germany}},
  title = {Global Motion Planning for Modular Robots with Local Motion Primitives},
  isbn = {978-1-4673-5643-5 978-1-4673-5641-1},
  url = {http://ieeexplore.ieee.org/document/6630912/},
  doi = {10.1109/ICRA.2013.6630912},
  abstract = {The ability to move in complex environments is a key property required for deployment of modular robots in challenging applications like search \& rescue missions or space exploration. Wide range of motion types like crawling or walking can be achieved using Central Pattern Generators producing periodic control signals. Although these motions can be very effective to steer robots in their vicinity or in a given direction, they need to be switched to reach a far position in the environment. This paper presents a novel modiﬁcation of Rapidly Exploring Random Tree (RRT) algorithm for modular robots. For efﬁcient exploration of the conﬁguration space, predeﬁned motion primitives are used. While the motion primitives provide effective local motions, the RRT-based planner switches them in order to reach the desired global goal.},
  eventtitle = {2013 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  booktitle = {2013 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  publisher = {{IEEE}},
  urldate = {2019-03-06},
  date = {2013-05},
  pages = {2465-2470},
  author = {Vonasek, Vojtech and Saska, Martin and Kosnar, Karel and Preucil, Libor},
  file = {/Users/olepor/Zotero/storage/HTQURRCX/Vonasek et al. - 2013 - Global motion planning for modular robots with loc.pdf}
}

@incollection{hauserUsingMotionPrimitives2008,
  langid = {english},
  location = {{Berlin, Heidelberg}},
  title = {Using {{Motion Primitives}} in {{Probabilistic Sample}}-{{Based Planning}} for {{Humanoid Robots}}},
  volume = {47},
  isbn = {978-3-540-68404-6 978-3-540-68405-3},
  url = {http://link.springer.com/10.1007/978-3-540-68405-3_32},
  abstract = {This paper presents a method of computing e cient and naturallooking motions for humanoid robots walking on varied terrain. It uses a small set of high-quality motion primitives (such as a ﬁxed gait on ﬂat ground) that have been generated o✏ine. But rather than restrict motion to these primitives, it uses them to derive a sampling strategy for a probabilistic, sample-based planner. Results in simulation on several di↵erent terrains demonstrate a reduction in planning time and a marked increase in motion quality.},
  booktitle = {Algorithmic {{Foundation}} of {{Robotics VII}}},
  publisher = {{Springer Berlin Heidelberg}},
  urldate = {2019-03-06},
  date = {2008},
  pages = {507-522},
  author = {Hauser, Kris and Bretl, Timothy and Harada, Kensuke and Latombe, Jean-Claude},
  editor = {Akella, Srinivas and Amato, Nancy M. and Huang, Wesley H. and Mishra, Bud},
  file = {/Users/olepor/Zotero/storage/NFC8PIHY/Hauser et al. - 2008 - Using Motion Primitives in Probabilistic Sample-Ba.pdf},
  doi = {10.1007/978-3-540-68405-3_32}
}

@article{vonasekHighlevelMotionPlanning2015,
  langid = {english},
  title = {High-Level Motion Planning for {{CPG}}-Driven Modular Robots},
  volume = {68},
  issn = {09218890},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0921889015000147},
  doi = {10.1016/j.robot.2015.01.006},
  abstract = {Modular robots may become candidates for search and rescue operations or even for future space missions, as they can change their structure to adapt to terrain conditions and to better fulfill a given task. A core problem in such missions is the ability to visit distant places in rough terrain. Traditionally, the motion of modular robots is modeled using locomotion generators that can provide various gaits, e.g. crawling or walking. However, pure locomotion generation cannot ensure that desired places in a complex environment with obstacles will in fact be reached. These cases require several locomotion generators providing motion primitives that are switched using a planning process that takes the obstacles into account. In this paper, we present a novel motion planning method for modular robots equipped with elementary motion primitives. The utilization of primitives significantly reduces the complexity of the motion planning which enables plans to be created for robots of arbitrary shapes. The primitives used here do not need to cope with environmental changes, which can therefore be realized using simple locomotion generators that are scalable, i.e., the primitives can provide motion for robots with many modules. As the motion primitives are realized using locomotion generators, no reconfiguration is required and the proposed approach can thus be used even for modular robots without self-reconfiguration capabilities. The performance of the proposed algorithm has been experimentally verified in various environments, in physical simulations and also in hardware experiments.},
  journaltitle = {Robotics and Autonomous Systems},
  urldate = {2019-03-06},
  date = {2015-06},
  pages = {116-128},
  author = {Vonásek, Vojtěch and Saska, Martin and Winkler, Lutz and Přeučil, Libor},
  file = {/Users/olepor/Zotero/storage/WPQT3EZG/Vonásek et al. - 2015 - High-level motion planning for CPG-driven modular .pdf}
}

@inproceedings{kuffnerEffectiveSamplingDistance2004,
  langid = {english},
  location = {{New Orleans, LA, USA}},
  title = {Effective Sampling and Distance Metrics for {{3D}} Rigid Body Path Planning},
  isbn = {978-0-7803-8232-9},
  url = {http://ieeexplore.ieee.org/document/1308895/},
  doi = {10.1109/ROBOT.2004.1308895},
  abstract = {Important implementation issues in rigid body path planning are often overlooked. In particular, sampling-based motion planning algorithms typically require a distance metric deﬁned on the conﬁguration space, a sampling function, and a method for interpolating sampled points. The conﬁguration space of a 3D rigid body is identiﬁed with the Lie group SE(3). Deﬁning proper metrics, sampling, and interpolation techniques for SE(3) is not obvious, and can become a hidden source of failure for many planning algorithm implementations. This paper examines some of these issues and presents techniques which have been found to be effective experimentally for Rigid Body path planning.},
  eventtitle = {{{IEEE International Conference}} on {{Robotics}} and {{Automation}}, 2004. {{Proceedings}}. {{ICRA}} '04. 2004},
  booktitle = {{{IEEE International Conference}} on {{Robotics}} and {{Automation}}, 2004. {{Proceedings}}. {{ICRA}} '04. 2004},
  publisher = {{IEEE}},
  urldate = {2019-03-14},
  date = {2004},
  pages = {3993-3998 Vol.4},
  author = {Kuffner, J.J.},
  file = {/Users/olepor/Zotero/storage/QPZ7K4LL/Kuffner - 2004 - Effective sampling and distance metrics for 3D rig.pdf}
}

@inproceedings{pengchengReducingMetricSensitivity2001,
  langid = {english},
  location = {{Maui, HI, USA}},
  title = {Reducing Metric Sensitivity in Randomized Trajectory Design},
  volume = {1},
  isbn = {978-0-7803-6612-1},
  url = {http://ieeexplore.ieee.org/document/973334/},
  doi = {10.1109/IROS.2001.973334},
  abstract = {This paper addresses trajectory design for generic problems that involve: 1) complicated global constraints that include nonconvex obstacles, 2) nonlinear equations of motion that involve substantial drift due to momentum, 3) a high-dimensional state space. Our approach to this challenging problems is to develop randomized planning algorithms on the basis of Rapidlyexploring Random Trees (RRTs). RRTs use metricinduced heuristics to conduct a greedy exploration of the state space; however, performance substantially degrades when the chosen metric does not adequately reﬂect the true cost-to-go. In this paper, we present an adaptive version of the RRT that is capable of reﬁning its exploration strategy in the presence of a poor metric. Initial experiments on problems in vehicle dynamics and spacecraft navigation indicate substantial performance improvement over existing techniques.},
  eventtitle = {{{RSJ}}/{{IEEE International Conference}} on {{Intelligent Robots}} and {{Systems}}},
  booktitle = {Proceedings 2001 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}}. {{Expanding}} the {{Societal Role}} of {{Robotics}} in the the {{Next Millennium}} ({{Cat}}. {{No}}.{{01CH37180}})},
  publisher = {{IEEE}},
  urldate = {2019-03-15},
  date = {2001},
  pages = {43-48},
  author = {{Peng Cheng} and LaValle, S.M.},
  file = {/Users/olepor/Zotero/storage/6UDSLNVL/Peng Cheng and LaValle - 2001 - Reducing metric sensitivity in randomized trajecto.pdf}
}

@inproceedings{perezLQRRRTOptimalSamplingbased2012,
  langid = {english},
  location = {{St Paul, MN, USA}},
  title = {{{LQR}}-{{RRT}}*: {{Optimal}} Sampling-Based Motion Planning with Automatically Derived Extension Heuristics},
  isbn = {978-1-4673-1405-3 978-1-4673-1403-9 978-1-4673-1578-4 978-1-4673-1404-6},
  url = {http://ieeexplore.ieee.org/document/6225177/},
  doi = {10.1109/ICRA.2012.6225177},
  shorttitle = {{{LQR}}-{{RRT}}*},
  abstract = {The RRT∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT∗ is difﬁcult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-speciﬁc extension heuristics: a distance metric and node extension method. We propose automatically deriving these two heuristics for RRT∗ by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR). The resulting algorithm, LQR-RRT∗, ﬁnds optimal plans in domains with complex or underactuated dynamics without requiring domain-speciﬁc design choices. We demonstrate its application in domains that are successively torquelimited, underactuated, and in belief space.},
  eventtitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  booktitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  publisher = {{IEEE}},
  urldate = {2019-03-15},
  date = {2012-05},
  pages = {2537-2542},
  author = {Perez, Alejandro and Platt, Robert and Konidaris, George and Kaelbling, Leslie and Lozano-Perez, Tomas},
  file = {/Users/olepor/Zotero/storage/N3HWK5I4/Perez et al. - 2012 - LQR-RRT Optimal sampling-based motion planning w.pdf}
}

@inproceedings{pengchengReducingMetricSensitivity2001a,
  langid = {english},
  location = {{Maui, HI, USA}},
  title = {Reducing Metric Sensitivity in Randomized Trajectory Design},
  volume = {1},
  isbn = {978-0-7803-6612-1},
  url = {http://ieeexplore.ieee.org/document/973334/},
  doi = {10.1109/IROS.2001.973334},
  abstract = {This paper addresses trajectory design for generic problems that involve: 1) complicated global constraints that include nonconvex obstacles, 2) nonlinear equations of motion that involve substantial drift due to momentum, 3) a high-dimensional state space. Our approach to this challenging problems is to develop randomized planning algorithms on the basis of Rapidlyexploring Random Trees (RRTs). RRTs use metricinduced heuristics to conduct a greedy exploration of the state space; however, performance substantially degrades when the chosen metric does not adequately reﬂect the true cost-to-go. In this paper, we present an adaptive version of the RRT that is capable of reﬁning its exploration strategy in the presence of a poor metric. Initial experiments on problems in vehicle dynamics and spacecraft navigation indicate substantial performance improvement over existing techniques.},
  eventtitle = {{{RSJ}}/{{IEEE International Conference}} on {{Intelligent Robots}} and {{Systems}}},
  booktitle = {Proceedings 2001 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}}. {{Expanding}} the {{Societal Role}} of {{Robotics}} in the the {{Next Millennium}} ({{Cat}}. {{No}}.{{01CH37180}})},
  publisher = {{IEEE}},
  urldate = {2019-03-15},
  date = {2001},
  pages = {43-48},
  author = {{Peng Cheng} and LaValle, S.M.},
  file = {/Users/olepor/Zotero/storage/RAS7BSXR/Peng Cheng and LaValle - 2001 - Reducing metric sensitivity in randomized trajecto.pdf}
}

@inproceedings{perezLQRRRTOptimalSamplingbased2012a,
  langid = {english},
  location = {{St Paul, MN, USA}},
  title = {{{LQR}}-{{RRT}}*: {{Optimal}} Sampling-Based Motion Planning with Automatically Derived Extension Heuristics},
  isbn = {978-1-4673-1405-3 978-1-4673-1403-9 978-1-4673-1578-4 978-1-4673-1404-6},
  url = {http://ieeexplore.ieee.org/document/6225177/},
  doi = {10.1109/ICRA.2012.6225177},
  shorttitle = {{{LQR}}-{{RRT}}*},
  abstract = {The RRT∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT∗ is difﬁcult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-speciﬁc extension heuristics: a distance metric and node extension method. We propose automatically deriving these two heuristics for RRT∗ by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR). The resulting algorithm, LQR-RRT∗, ﬁnds optimal plans in domains with complex or underactuated dynamics without requiring domain-speciﬁc design choices. We demonstrate its application in domains that are successively torquelimited, underactuated, and in belief space.},
  eventtitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}} ({{ICRA}})},
  booktitle = {2012 {{IEEE International Conference}} on {{Robotics}} and {{Automation}}},
  publisher = {{IEEE}},
  urldate = {2019-03-15},
  date = {2012-05},
  pages = {2537-2542},
  author = {Perez, Alejandro and Platt, Robert and Konidaris, George and Kaelbling, Leslie and Lozano-Perez, Tomas},
  file = {/Users/olepor/Zotero/storage/6FYE97RK/Perez et al. - 2012 - LQR-RRT Optimal sampling-based motion planning w.pdf}
}

@inproceedings{mooreControlSynthesisVerification2012,
  langid = {english},
  location = {{Maui, HI, USA}},
  title = {Control Synthesis and Verification for a Perching {{UAV}} Using {{LQR}}-{{Trees}}},
  isbn = {978-1-4673-2066-5 978-1-4673-2065-8 978-1-4673-2063-4 978-1-467

repository: oleorhagen/article

repo_name: oleorhagen/article