## The Stochastic Motion Roadmap: A sampling framework for planning with Markov motion uncertainty (2008)

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Venue: | in Robotics: Science and Systems III (Proc. RSS 2007 |

Citations: | 52 - 16 self |

### BibTeX

@INPROCEEDINGS{Alterovitz08thestochastic,

author = {Ron Alterovitz and Thierry Siméon and Ken Goldberg},

title = {The Stochastic Motion Roadmap: A sampling framework for planning with Markov motion uncertainty},

booktitle = {in Robotics: Science and Systems III (Proc. RSS 2007},

year = {2008},

pages = {246--253},

publisher = {MIT Press}

}

### OpenURL

### Abstract

Abstract — We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collision-free states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMR) thus combines a sampling-based roadmap representation of the configuration space, as in PRM’s, with the well-established theory of MDP’s. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problem-specific or grid-based discretizations. We demonstrate the SMR framework by applying it to nonholonomic steerable needles, a new class of medical needles that follow curved paths through soft tissue, and confirm that SMR’s generate motion plans with significantly higher probabilities of success compared to traditional shortest-path plans. I.

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