Closed-loop safety assessment of uncertain roadmaps

The main contribution of this paper is a novel method for assessing the safety of trajectories by means of their collision probability in dynamic and uncertain environments. The future trajectories of the robot are represented as directed graphs and the uncertain states of the obstacles are represented by probability distributions. Instead of evaluating the safety of the graph by determining the route with the smallest collision probability, the optimal policy minimizing the collision probability is used. The policy allows one to replan the route depending on the future probability distributions of the obstacles. Since these distributions are unknown at the time point of the assessment, they are simulated and represented by compound probability distributions. These compound distributions represent all possible future distributions of the obstacles. It is shown that this novel method is always less conservative than previous approaches. Two example implementations are presented, one using Gaussian distributions and one using motion patterns for representing the uncertain states of the obstacles. Simulation scenarios are used for validating the proposed concept.

[1]  Christian Laugier,et al.  Probabilistic decision making for collision avoidance systems: Postponing decisions , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[2]  Matthias Althoff,et al.  Probabilistic collision state checker for crowded environments , 2010, 2010 IEEE International Conference on Robotics and Automation.

[3]  Joel W. Burdick,et al.  Robotic motion planning in dynamic, cluttered, uncertain environments , 2010, 2010 IEEE International Conference on Robotics and Automation.

[4]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[5]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[6]  Reid G. Simmons,et al.  Point-Based POMDP Algorithms: Improved Analysis and Implementation , 2005, UAI.

[7]  Martin Buss,et al.  Following route graphs in urban environments , 2011, 2011 RO-MAN.

[8]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[9]  Brahim Chaib-draa,et al.  Quasi-Deterministic Partially Observable Markov Decision Processes , 2009, ICONIP.

[10]  Franz S. Hover,et al.  Motion planning with an analytic risk cost for holonomic vehicles , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[11]  Leonidas J. Guibas,et al.  Bounded Uncertainty Roadmaps for Path Planning , 2008, WAFR.

[12]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[13]  William Whittaker,et al.  Autonomous Driving in Traffic: Boss and the Urban Challenge , 2009, AI Mag..

[14]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[15]  D. Rubin.  Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician , 1984 .

[16]  Thao Dang,et al.  A novel approach for the probabilistic computation of Time-To-Collision , 2012, 2012 IEEE Intelligent Vehicles Symposium.

[17]  Leslie Pack Kaelbling,et al.  Belief space planning assuming maximum likelihood observations , 2010, Robotics: Science and Systems.

[18]  Jonas Jansson,et al.  Collision Avoidance Theory : with Application to Automotive Collision Mitigation , 2005 .

[19]  Amaury Nègre,et al.  Probabilistic Analysis of Dynamic Scenes and Collision Risks Assessment to Improve Driving Safety , 2011, IEEE Intelligent Transportation Systems Magazine.

[20]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[21]  Rachid Alami,et al.  A Human-Aware Manipulation Planner , 2012, IEEE Transactions on Robotics.

[22]  Dominique Gruyer,et al.  Collision Probability Assessment for Speed Control , 2008, 2008 11th International IEEE Conference on Intelligent Transportation Systems.

[23]  Martin Buss,et al.  On-line Trajectory Generation for Safe and Optimal Vehicle Motion Planning , 2012, AMS.

[24]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[25]  Richard Dearden,et al.  Navigation Planning in Probabilistic Roadmaps with Uncertainty , 2009, ICAPS.

[26]  Jonathan P. How,et al.  Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns , 2013, Auton. Robots.

[27]  Rüdiger Dillmann,et al.  Probabilistic decision-making under uncertainty for autonomous driving using continuous POMDPs , 2014, 17th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[28]  Rina Dechter,et al.  Generalized best-first search strategies and the optimality of A* , 1985, JACM.

[29]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[30]  Ron Alterovitz,et al.  Estimating probability of collision for safe motion planning under Gaussian motion and sensing uncertainty , 2012, 2012 IEEE International Conference on Robotics and Automation.

[31]  Lars Petersson,et al.  Statistical Threat Assessment for General Road Scenes Using Monte Carlo Sampling , 2008, IEEE Transactions on Intelligent Transportation Systems.

[32]  Manuel Mucientes,et al.  A State Lattice Approach for Motion Planning under Control and Sensor Uncertainty , 2013, ROBOT.

[33]  David Hsu,et al.  Motion planning under uncertainty for robotic tasks with long time horizons , 2011, Int. J. Robotics Res..

[34]  T. Kanade,et al.  Monte Carlo road safety reasoning , 2005, IEEE Proceedings. Intelligent Vehicles Symposium, 2005..

[35]  Martin Buss,et al.  Safety assessment of robot trajectories for navigation in uncertain and dynamic environments , 2011, Autonomous Robots.

[36]  Sebastian Thrun,et al.  Towards fully autonomous driving: Systems and algorithms , 2011, 2011 IEEE Intelligent Vehicles Symposium (IV).

[37]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[38]  Julius Ziegler,et al.  Optimal trajectory generation for dynamic street scenarios in a Frenét Frame , 2010, 2010 IEEE International Conference on Robotics and Automation.

[39]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[40]  Masahiro Ono,et al.  A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control , 2010, IEEE Transactions on Robotics.

[41]  Maxim Likhachev,et al.  Time-bounded lattice for efficient planning in dynamic environments , 2009, 2009 IEEE International Conference on Robotics and Automation.

[42]  Christoph Hermes,et al.  Long-term vehicle motion prediction , 2009, 2009 IEEE Intelligent Vehicles Symposium.

[43]  Dominique Gruyer,et al.  A fast Monte Carlo algorithm for collision probability estimation , 2008, 2008 10th International Conference on Control, Automation, Robotics and Vision.

[44]  Blai Bonet,et al.  Deterministic POMDPs Revisited , 2009, UAI.

[45]  Roland Philippsen.  Motion planning and obstacle avoidance for mobile robots in highly cluttered dynamic environments , 2004 .

[46]  Autonomous navigation in dynamic uncertain environment using probabilistic models of perception and collision risk prediction. , 2009 .

[47]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[48]  Robert W. Grubbström,et al.  The moments and central moments of a compound distribution , 2006, Eur. J. Oper. Res..

[49]  Julius Ziegler,et al.  Optimal trajectories for time-critical street scenarios using discretized terminal manifolds , 2012, Int. J. Robotics Res..

[50]  Nicholas Roy,et al.  Adapting probabilistic roadmaps to handle uncertain maps , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[51]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[52]  Pieter Abbeel,et al.  LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information , 2010, Int. J. Robotics Res..

[53]  Edward P. F. Chan,et al.  Shortest Path Tree Computation in Dynamic Graphs , 2009, IEEE Transactions on Computers.