Galileo: A Pseudospectral Collocation Framework for Legged Robots

TL;DR

Galileo introduces a pseudospectral collocation framework for legged robots that optimizes trajectories directly on Lie Groups, enabling dynamic maneuvers with complex contact constraints.

Contribution

The paper presents a novel transcription scheme for pseudospectral collocation on Lie Groups, improving trajectory optimization for legged robots without normalization constraints.

Findings

Successfully optimized trajectories for various legged robots.

Implemented as an MPC and validated on real robots.

Demonstrated feasibility of planned dynamic motions.

Abstract

Dynamic maneuvers for legged robots present a difficult challenge due to the complex dynamics and contact constraints. This paper introduces a versatile trajectory optimization framework for continuous-time multi-phase problems. We introduce a new transcription scheme that enables pseudospectral collocation to optimize directly on Lie Groups, such as SE(3) and quaternions without special normalization constraints. The key insight is the change of variables - we choose to optimize over the history of the tangent vectors rather than the states themselves. Our approach uses a modified Legendre-Gauss-Radau (LGR) method to produce dynamic motions for various legged robots. We implement our approach as a Model Predictive Controller (MPC) and track the MPC output using a Quadratic Program (QP) based whole-body controller. Results on the Go1 Unitree and WPI HURON humanoid confirm the feasibility of the planned trajectories.