Trajectory design for high-dimensional systems with nonconvex constraints has considerable success recently; however, the resolution completeness analysis for various methods is insufficient. In this paper, based on Lipschitz condition and the accessibility graph, conditions for resolution completeness are derived. By combining the systematic search with randomized technique, a randomized planner is transformed to be a deterministic resolution complete planner, which shows reliable performance in the simulation.
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Cheng et al. (2003) studied this question.
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