Geometric Heat Flow Method for Legged Locomotion Planning
This addresses motion planning for legged robots, which is challenging due to hybrid dynamics and contact constraints, representing an incremental improvement by applying an existing geometric framework to this specific domain.
The authors tackled motion planning for legged robots by encoding hybrid dynamics and contact constraints into a Riemannian inner product, using geometric heat flow to deform paths into admissible motions, resulting in a method that automatically generates trajectories for center of mass, foot positions, and forces on uneven terrain.
We propose in this paper a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The motion planning task is challenging due to the hybrid nature of dynamics and contact constraints. We encode the hybrid dynamics and constraints into Riemannian inner product, and this inner product is defined so that short curves correspond to admissible motions for the system. We rely on the affine geometric heat flow to deform an arbitrary path connecting the desired initial and final states to this admissible motion. The method is able to automatically find the trajectory of robot's center of mass, feet contact positions and forces on uneven terrain.