Accelerated ADMM based Trajectory Optimization for Legged Locomotion with Coupled Rigid Body Dynamics

TL;DR

This paper introduces an accelerated ADMM-based approach with a novel splitting scheme for efficient trajectory optimization in legged robots, addressing accuracy and convergence issues in complex dynamic models.

Contribution

It proposes a new multi-block ADMM framework with stage-wise acceleration and over-relaxation for improved convergence in legged locomotion trajectory optimization.

Findings

Effective in solving complex legged locomotion problems

Improves convergence rate with accelerated ADMM scheme

Validated on car-parking and rough terrain bipedal tasks

Abstract

Trajectory optimization is becoming increasingly powerful in addressing motion planning problems of underactuated robotic systems. Numerous prior studies solve such a class of large non-convex optimal control problems in a hierarchical fashion. However, numerical accuracy issues are prone to occur when one uses a full-order model to track reference trajectories generated from a reduced-order model. This study investigates an approach of Alternating Direction Method of Multipliers (ADMM) and proposes a new splitting scheme for legged locomotion problems. Rigid body dynamics constraints and other general constraints such as box and cone constraints are decomposed to multiple sub-problems in a principled manner. The resulting multi-block ADMM framework enables us to leverage the efficiency of an unconstrained optimization method--Differential Dynamical Programming--to iteratively solve the optimizations using centroidal and whole-body models. Furthermore, we propose a Stage-wise Accelerated ADMM with over-relaxation and varying-penalty schemes to improve the overall convergence rate. We evaluate and validate the performance of the proposed ADMM algorithm on a car-parking example and a bipedal locomotion problem over rough terrains.