From Discrete to Continuous Motion Planning

In this paper, we demonstrate an equivalence between a large class of discrete motion planning problems, and piano mover’s problems, which we refer to as ”continuous motion planning problems”. We first prove that under some assumptions, discrete motion planning in d dimensions can be transformed into continuous motion planning in 2d + 1 dimensions. Then we prove a more specific, similar equivalence for which the number of dimensions of the configuration space does not necessarily have to be increased.We study two simple cases where this theorem applies, and show that it can lead to original and efficient motion planning algorithms, which could probably be applied to a wide range of multi-contact planning problems.We apply this equivalence to a simulation of legged locomotion planning for a hexapod robot.

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