Precise Jump Planning using Centroidal Dynamics based Bilevel Optimization

摘要

This paper deals with a problem of precise jumping for legged robots: what are the control inputs required to perform a jump that results in a desired landing point? We propose a novel precise jump planning method, formulated as a bilevel optimization problem. The presented formulation exploits certain insights into the jump dynamics, leading to a low-dimensional optimization problem, and allowing fast computation. During the Flight phase of a jump there are no external forces other than gravity acting on the robot, so its centroidal angular momentum (CAM) is conserved, and its center of mass (COM) follows a ballistic trajectory. This trajectory depends solely on COM position and velocity at Liftoff. We define a bilevel optimization problem consisting of a nonlinear upper-level problem, and a lower-level quadratic programming (QP) problem. The upper-level problem selects COM position and velocity at Liftoff that result in a desired landing point, while minimizing CAM at Liftoff. The lower-level problem selects ground reaction forces during Push-Off that achieve desired COM position and velocity at Liftoff. The results are presented on a simulated one-legged robot, but the proposed approach can be extended to bipeds and multi-legged robots.