Completeness of Randomized Kinodynamic Planners with State-based Steering¶
Authors: Stephane Caron, Quang-Cuong Pham, Yoshihiko Nakamura
Published: 2015 (Journal Paper)
Source: Robotics and Autonomous Systems (RAS)
arXiv: 1511.05259
DOI: 10.1016/j.robot.2016.12.002
Summary¶
Proves probabilistic completeness for state-based (interpolating) kinodynamic planners under verifiable assumptions. Identifies second-order continuity as the key design requirement. Nice explanation of state-based steering and its beneficial properties as compraed with e.g. randomized action-propagation steering. Contains a great Section 2.3 on the differences between categories of steering functions.
Abstract¶
Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for such planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.
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Tags¶
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Kinodynamic planning
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Probabilistic completeness
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State-based steering
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Steering function
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Interpolation