A Provably Good Approximation Algorithm for Optimal-Time Trajectory Planning
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We consider the following problem: given a robot system, find a minimal-time trajectory from a start position and velocity to a goal position and velocity, while avoiding obstacles and respecting dynamic constraints on velocity and acceleration. Based on the theoretical results of [CDRX], we have developed and implemented a new, provably good approximation algorithm for the minimum-time trajectory problem. Our algorithm differs from previous work in three ways. First, it is possible to bound the goodness of the approximation by an error term