提出两种新型算法，高效求解机器人多接触仿真中的复杂力学问题。
Variations of Augmented Lagrangian for Robotic Multi-Contact Simulation
- 基于增广拉格朗日法，设计可迭代求解多接触非线性互补问题的新框架
- CANAL保证高精度与鲁棒性，SubADMM实现高速并行计算，适合大规模系统
- 适用于高自由度机器人操作场景，尤其适合密集接触和刚性交互
多接触非线性互补问题（NCP）是机器人仿真中自然出现的挑战。在涉及密集接触和刚性相互作用的场景下，同时实现高精度与高效率仍具难度。本文基于增广拉格朗日（AL）理论，提出一类新的多接触NCP求解器。通过迭代求解代理问题并更新原-对偶变量，将标准凸优化中的AL推导拓展至多接触场景。具体提出两种定制化变体：基于级联牛顿法的增广拉格朗日（CANAL）与基于子系统交替方向乘子法（SubADMM）。结果表明，CANAL能以高精度与鲁棒性处理多接触问题；而SubADMM在高自由度多体系统中表现出更优的计算速度、可扩展性与并行能力。实验验证了该求解框架在多种机器人操作任务中的有效性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。