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Optimal Kinodynamic Motion Planning using Incremental Sampling-based Methods

Author(s)
Karaman, Sertac; Frazzoli, Emilio
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Abstract
Sampling-based algorithms such as the Rapidly-exploring Random Tree (RRT) have been recently proposed as an effective approach to computationally hard motion planning problem. However, while the RRT algorithm is known to be able to find a feasible solution quickly, there are no guarantees on the quality of such solution, e.g., with respect to a given cost functional. To address this limitation, the authors recently proposed a new algorithm, called RRT*, which ensures asymptotic optimality, i.e., almost sure convergence of the solution returned by the algorithm to an optimal solution, while maintaining the same properties of the standard RRT algorithm, both in terms of computation of feasible solutions, and of computational complexity. In this paper, the RRT* algorithm is extended to deal with differential constraints. A sufficient condition for asymptotic optimality is provided. It is shown that the RRT* algorithm equipped with any local steering procedure that satisfies this condition converges to an optimal solution almost surely. In particular, simple local steering procedures are provided for a Dubins' vehicle as well as a double integrator. Simulation examples are also provided for these systems comparing the RRT and the RRT* algorithms.
Description
Issue Date: 15-17 Dec. 2010; Date of Current Version: 22 February 2011
Date issued
2011-02
URI
http://hdl.handle.net/1721.1/65847
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
49th IEEE Conference on Decision and Control (CDC), 2010
Publisher
Institute of Electrical and Electronics Engineers
Citation
Karaman, Sertac, and Emilio Frazzoli. “Optimal Kinodynamic Motion Planning Using Incremental Sampling-based Methods.” 49th IEEE Conference on Decision and Control (CDC). Atlanta, GA, USA, 2010. 7681-7687. © Copyright 2010 IEEE
Version: Final published version
ISBN
978-1-4244-7745-6
ISSN
0743-1546

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