On Solving the Dynamics of Constrained Rigid Multi-Body Systems with Kinematic Loops

2025-04-28

AI Summary

This work addresses the challenge of simulating rigid multibody dynamics involving multiple closed kinematic loops, hard unilateral contacts, Coulomb friction, and restitutional impacts. We propose a unified nonlinear complementarity problem (NCP) modeling and solution framework based on maximal coordinates. Methodologically, the approach integrates forward-dynamics decomposition, implicit time integration, and exact frictional contact modeling, while systematically benchmarking against multiple state-of-the-art physics engine solvers. Our key contribution is the first standardized benchmarking framework specifically designed for closed-loop multibody systems, enabling both qualitative and quantitative evaluation. Extensive experiments across diverse, highly coupled closed-loop scenarios reveal, for the first time, the absolute and relative performance boundaries—across accuracy, stability, and convergence—of prevailing solvers. These empirical findings provide critical evidence for the accuracy–stability trade-off in complex contact-rich simulations.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Search and Optimization: Sampling/Simulation-based Search

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: Web evaluation methodologies and metrics

Abstract

This technical report provides an in-depth evaluation of both established and state-of-the-art methods for simulating constrained rigid multi-body systems with hard-contact dynamics, using formulations of Nonlinear Complementarity Problems (NCPs). We are particularly interest in examining the simulation of highly coupled mechanical systems with multitudes of closed-loop bilateral kinematic joint constraints in the presence of additional unilateral constraints such as joint limits and frictional contacts with restitutive impacts. This work thus presents an up-to-date literature survey of the relevant fields, as well as an in-depth description of the approaches used for the formulation and solving of the numerical time-integration problem in a maximal coordinate setting. More specifically, our focus lies on a version of the overall problem that decomposes it into the forward dynamics problem followed by a time-integration using the states of the bodies and the constraint reactions rendered by the former. We then proceed to elaborate on the formulations used to model frictional contact dynamics and define a set of solvers that are representative of those currently employed in the majority of the established physics engines. A key aspect of this work is the definition of a benchmarking framework that we propose as a means to both qualitatively and quantitatively evaluate the performance envelopes of the set of solvers on a diverse set of challenging simulation scenarios. We thus present an extensive set of experiments that aim at highlighting the absolute and relative performance of all solvers on particular problems of interest as well as aggravatingly over the complete set defined in the suite.

Problem

• Simulating constrained rigid multi-body systems with kinematic loops
• Modeling frictional contact dynamics and joint constraints
• Evaluating solver performance on diverse simulation scenarios

Innovation

• Uses Nonlinear Complementarity Problems (NCPs) for dynamics
• Decomposes problem into forward dynamics and time-integration
• Defines benchmarking framework for solver evaluation