A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state.

[1]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .

[2]  Jean-Claude Latombe,et al.  Robot Motion Planning with Uncertainty in Control and Sensing , 1991, Artif. Intell..

[3]  Jean-Claude Latombe,et al.  Sensory uncertainty field for mobile robot navigation , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[4]  Jean-Claude Latombe,et al.  Planning the Motions of a Mobile Robot in a Sensory Uncertainty Field , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Rachid Alami,et al.  Planning robust motion strategies for a mobile robot , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[6]  A. C. Sanderson,et al.  A path-space search algorithm for motion planning with uncertainties , 1995, Proceedings. IEEE International Symposium on Assembly and Task Planning.

[7]  Jérôme Barraquand,et al.  Motion planning with uncertainty: the information space approach , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[8]  Arthur C. Sanderson,et al.  Robot motion planning for sensor-based control with uncertainties , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[9]  Rachid Alami,et al.  A numerical technique for planning motion strategies of a mobile robot in presence of uncertainty , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[10]  Panos E. Trahanias,et al.  Robot motion planning: multi-sensory uncertainty fields enhanced with obstacle avoidance , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[11]  Jeffrey K. Uhlmann,et al.  Nondivergent simultaneous map building and localization using covariance intersection , 1997, Defense, Security, and Sensing.

[12]  Thierry Siméon,et al.  Indoor navigation with uncertainty using sensor-based motions , 1997, Proceedings of International Conference on Robotics and Automation.

[13]  Panayiotis Tsanakas,et al.  A sensory uncertainty field model for unknown and non-stationary mobile robot environments , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[14]  Thierry Fraichard,et al.  Path planning with uncertainty for car-like robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[15]  Sebastian Thrun,et al.  Coastal Navigation with Mobile Robots , 1999, NIPS.

[16]  Nadine Le Fort-Piat,et al.  Safe Task Planning Integrating Uncertainties and Local Maps Federations , 2000, Int. J. Robotics Res..

[17]  Antonio Bicchi,et al.  Optimal exploratory paths for a mobile rover , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[18]  Alexei Makarenko,et al.  An experiment in integrated exploration , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Joris De Schutter,et al.  A multisine approach for trajectory optimization based on information gain , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[20]  Dominique Gruyer,et al.  Safe path planning in an uncertain-configuration space , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[21]  Joris De Schutter,et al.  A multisine approach for trajectory optimization based on information gain , 2003, Robotics Auton. Syst..

[22]  Anthony Stentz,et al.  Planning with uncertainty in position an optimal and efficient planner , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  Jean-Claude Latombe,et al.  Landmark-Based Robot Navigation , 1992, Algorithmica.

[24]  Wolfram Burgard,et al.  Probabilistic Robotics (Intelligent Robotics and Autonomous Agents) , 2005 .

[25]  Jason M. O'Kane,et al.  Almost-Sensorless Localization , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[26]  Steven M. LaValle,et al.  Algorithms for Planning under Uncertainty in Prediction and Sensing , 2006, Autonomous Mobile Robots.

[27]  L. Blackmore.  A Probabilistic Particle Control Approach to Optimal, Robust Predictive Control , 2006 .

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

[29]  Frank L. Lewis,et al.  Autonomous Mobile Robots : Sensing, Control, Decision Making and Applications , 2006 .

[30]  Jason M. O'Kane,et al.  Global localization using odometry , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[31]  Alain Lambert,et al.  Safe Path Planning in an Uncertain-Configuration Space using RRT , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[32]  Hui X. Li,et al.  A probabilistic approach to optimal robust path planning with obstacles , 2006, 2006 American Control Conference.

[33]  Anthony Stentz,et al.  Planning with Uncertainty in Position Using High-Resolution Maps , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[34]  Kristine L. Bell,et al.  Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking , 2007 .

[35]  L. Blackmore,et al.  Optimal, Robust Predictive Control of Nonlinear Systems under Probabilistic Uncertainty using Particles , 2007, 2007 American Control Conference.

[36]  Leslie Pack Kaelbling,et al.  Grasping POMDPs , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[37]  Jason M. O'Kane,et al.  Localization With Limited Sensing , 2007, IEEE Transactions on Robotics.

[38]  Andrea Censi,et al.  On achievable accuracy for range-finder localization , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[39]  Thierry Siméon,et al.  The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty , 2007, Robotics: Science and Systems.

[40]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.