Asymptotically optimal sampling-based kinodynamic planning

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamic...

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Bibliographic Details
Published in:The International journal of robotics research 2016-04, Vol.35 (5), p.528-564
Main Authors: Li, Yanbo, Littlefield, Zakary, Bekris, Kostas E.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Boundary value problems
Dynamical systems
Dynamics
Geometry
Graph theory
Mathematical analysis
Optimization
Robots
Sampling
Solvers
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Summary:Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, STABLE_SPARSE_RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.
ISSN:0278-3649
1741-3176
DOI:10.1177/0278364915614386