Sampling-based min-max uncertainty path planning

We propose a new sampling-based path planning algorithm, the Min-Max Rapidly Exploring Random Tree (MM-RRT*), for robot path planning under localization uncertainty. The projected growth of error in a robot's state estimate is curbed by minimizing the maximum state estimate uncertainty encountered on a path. The algorithm builds and maintains a tree that is shared in state space and belief space, with a single belief per robot state. Due to the fact that many states will share the same maximum uncertainty, resulting from a shared parent node, the algorithm uses secondary objective functions to break ties among neighboring nodes with identical maximum uncertainty. The algorithm offers a compelling alternative to sampling-based algorithms with additive cost representations of uncertainty, which will penalize high-precision navigation routes that are longer in duration.

[1]  N. Roy,et al.  The Belief Roadmap: Efficient Planning in Belief Space by Factoring the Covariance , 2009, Int. J. Robotics Res..

[2]  Jonathan P. How,et al.  Robust Sampling-based Motion Planning with Asymptotic Optimality Guarantees , 2013 .

[3]  Jur P. van den Berg,et al.  Robust belief space planning under intermittent sensing via a maximum eigenvalue-based bound , 2016, Int. J. Robotics Res..

[4]  Mike Stilman,et al.  Global Manipulation Planning in Robot Joint Space With Task Constraints , 2010, IEEE Transactions on Robotics.

[5]  Eric Walter,et al.  Reliable robust path planner , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[6]  P. Abbeel,et al.  LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information , 2011 .

[7]  Didier Devaurs,et al.  Efficient Sampling-Based Approaches to Optimal Path Planning in Complex Cost Spaces , 2014, WAFR.

[8]  Alberto Speranzon,et al.  Multiobjective Path Planning: Localization Constraints and Collision Probability , 2015, IEEE Transactions on Robotics.

[9]  Jonathan P. How,et al.  An optimizing sampling-based motion planner with guaranteed robustness to bounded uncertainty , 2014, 2014 American Control Conference.

[10]  Nicholas M. Patrikalakis,et al.  Asymptotically optimal inspection planning using systems with differential constraints , 2013, 2013 IEEE International Conference on Robotics and Automation.

[11]  Emilio Frazzoli,et al.  Incremental sampling-based algorithm for minimum-violation motion planning , 2013, 52nd IEEE Conference on Decision and Control.

[12]  Emilio Frazzoli,et al.  An incremental sampling-based algorithm for stochastic optimal control , 2012, 2012 IEEE International Conference on Robotics and Automation.

[13]  Nancy M. Amato,et al.  FIRM: Sampling-based feedback motion-planning under motion uncertainty and imperfect measurements , 2014, Int. J. Robotics Res..

[14]  Hanna Kurniawati,et al.  An Online POMDP Solver for Uncertainty Planning in Dynamic Environment , 2013, ISRR.

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

[16]  Nicholas Roy,et al.  Rapidly-exploring Random Belief Trees for motion planning under uncertainty , 2011, 2011 IEEE International Conference on Robotics and Automation.

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

[18]  Franz S. Hover,et al.  Three-dimensional coverage planning for an underwater inspection robot , 2013, Int. J. Robotics Res..

[19]  Geoffrey A. Hollinger,et al.  Sampling-based robotic information gathering algorithms , 2014, Int. J. Robotics Res..

[20]  Yuko Okamoto,et al.  A novel algorithm for calculation of the extreme eigenvalues of large Hermitian matrices , 1993 .

[21]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[22]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..