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.

中文翻译：

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腿部运动计划的几何热流方法

本文提出了一种基于几何热流框架的腿式机器人运动规划方法。由于动力学和接触约束的混合性质，运动计划任务具有挑战性。我们将混合动力和约束编码为黎曼内积，并定义了该内积，以便短曲线对应于系统的容许运动。我们依靠仿射几何热流使连接所需的初始状态和最终状态与此允许运动的任意路径变形。该方法能够自动找到机器人质心的轨迹，脚部接触位置以及在不平坦地形上的作用力。