Variations of Augmented Lagrangian for Robotic Multicontact Simulation

The multicontact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in scenarios involving intensive contacts and stiff interactions. In this article, we introduce a new class of multicontact NCP solvers based on the theory of the augmented Lagrangian (AL). We detail how the standard derivation of AL in convex optimization can be adapted to handle multicontact NCP through the iteration of surrogate problem solutions and the subsequent update of primal-dual variables. Specifically, we present two tailored variations of AL for robotic simulations: the cascaded Newton-based augmented Lagrangian (CANAL) and the subsystem-based alternating direction method of multipliers (SubADMM). We demonstrate how CANAL can manage multicontact NCP in an accurate and robust manner, while SubADMM offers superior computational speed, scalability, and parallelizability for high degrees-of-freedom multibody systems with numerous contacts. Our results showcase the effectiveness of the proposed solver framework, illustrating its advantages in various robotic manipulation scenarios.