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We propose in this paper a motion planning method for legged robot locomotionbased on Geometric Heat Flow framework. The motion planning task is challengingdue to the hybrid nature of dynamics and contact constraints. We encode thehybrid dynamics and constraints into Riemannian inner product, and this innerproduct is defined so that short curves correspond to admissible motions forthe system. We rely on the affine geometric heat flow to deform an arbitrarypath connecting the desired initial and final states to this admissible motion.The method is able to automatically find the trajectory of robot's center ofmass, feet contact positions and forces on uneven terrain.

Geometric Heat Flow Method for Legged Locomotion Planning