Trajectory Generation for Legged Robots Based on a Closed-Form Solution of Centroidal Dynamics

This letter proposes a novel reduced-order model of rigid body dynamics that can be used for versatile motion generation of legged robots. It can express both linear CoM movement and rotation of the base link, and it is applicable to general multi-contact setup including flight. Moreover, its closed-form solution enables optimization of long trajectories consisting of more than 20 contact phases in less than 100ms. Various trajectory optimization examples of biped and quadruped models together with trajectory tracking simulation using whole-body MPC are shown to demonstrate the flexibility and practical applicability of the proposed model.