Motion Planning for Multi-Legged Robots Using Levenberg-Marquardt Optimization with Bézier Parametrization

This paper presents a novel formulation of motion planning for multi-legged walking robots. In the proposed method, a single-step motion is formulated as a nonlinear equation problem (NLE): including kinematic, stability, and collision constraints. For the given start and goal configurations, the robot's path is parametrized as Bézier curve in the configuration space. The resulting NLE is solved using Levenberg-Marquardt optimization implemented using a sparse matrix solver. We propose handling the trigonometric kinematic constraints with the polynomial path parametrization. A relaxation of the constraint is used while guaranteeing a desired tolerance along the planned path. Although the proposed method does not explicitly optimize any criterion, it produces high-quality paths. The method is deployed in transforming a sequence of discrete configurations produced by a step sequence planner into a valid path for a multi-legged walking robot in challenging planning scenarios where a regular locomotion gait cannot be used because of sparse footholds.