Variations of Augmented Lagrangian for Robotic Multi-Contact Simulation

2025-02-24

AI Summary

In robotic multicontact simulation, solving the nonlinear complementarity problem (NCP) under dense contacts and rigid interactions poses a fundamental trade-off between accuracy and efficiency. To address this, we propose a novel solver framework grounded in augmented Lagrangian (AL) theory, introducing two AL variants: CANAL (Cascaded Newton-type AL) and SubADMM (Subsystem-based ADMM). CANAL enhances contact robustness and numerical stability via cascaded Newton iterations; SubADMM integrates subsystem decomposition with parallel ADMM to significantly improve scalability. Experiments demonstrate that CANAL substantially improves contact accuracy and simulation convergence, while SubADMM achieves a 3.2× speedup in high-degree-of-freedom multicontact scenarios, enabling real-time parallel simulation. This work establishes a new paradigm for high-performance multicontact dynamics simulation—rigorous in theory and practical in engineering deployment.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Safety and Robustness

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

The multi-contact 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 multi-contact 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 multi-contact 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 multi-contact 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.

Problem

• Solving multi-contact nonlinear complementarity problem
• Improving accuracy and efficiency in simulations
• Handling stiff interactions and intensive contacts

Innovation

• Augmented Lagrangian for NCP
• CANAL ensures robust accuracy
• SubADMM enhances computational speed