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

arXiv: https://arxiv.org/abs/2003.08019 · HTML: https://mlsanity.com/paper/2003.08019/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots](https://mlsanity.com/paper/2207.01418/) (2022)
- [Adversarially Regularized Policy Learning Guided by Trajectory Optimization](https://mlsanity.com/paper/2109.07627/) (2021)

## Abstract (arXiv)

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.