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Trajectory optimization is becoming increasingly powerful in addressingmotion planning problems of underactuated robotic systems. Numerous priorstudies solve such a class of large non-convex optimal control problems in ahierarchical fashion. However, numerical accuracy issues are prone to occurwhen one uses a full-order model to track reference trajectories generated froma reduced-order model. This study investigates an approach of AlternatingDirection Method of Multipliers (ADMM) and proposes a new splitting scheme forlegged locomotion problems. Rigid body dynamics constraints and other generalconstraints such as box and cone constraints are decomposed to multiplesub-problems in a principled manner. The resulting multi-block ADMM frameworkenables us to leverage the efficiency of an unconstrained optimizationmethod--Differential Dynamical Programming--to iteratively solve theoptimizations using centroidal and whole-body models. Furthermore, we propose aStage-wise Accelerated ADMM with over-relaxation and varying-penalty schemes toimprove the overall convergence rate. We evaluate and validate the performanceof the proposed ADMM algorithm on a car-parking example and a bipedallocomotion problem over rough terrains.

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