A Smooth Analytical Formulation of Collision Detection and Rigid Body Dynamics With Contact

2025-03-14

AI Summary

In contact-rich environments, existing zeroth-order optimization methods are robust but computationally inefficient, hindering gradient-based perception, planning, and control. Method: We propose the first fully analytical, twice continuously differentiable (C²) contact dynamics modeling framework that unifies contact detection and rigid-body dynamics. Our formulation ensures smooth differentiability throughout forward and inverse dynamics—without iterative solvers or convex decomposition—and achieves contact-count-independent computational complexity. The method integrates analytical geometry, implicit distance fields, Log-Sum-Exp smoothing, Lagrangian mechanics derivation, and automatic differentiation–friendly design, supporting collisions between arbitrary geometries. Results: Simulation experiments demonstrate that this “reasoning-friendly physics engine” significantly improves planning and control efficiency for both first- and second-order gradient-based methods, establishing a new paradigm for generating intelligent behaviors in highly contact-rich scenarios.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. A major contributor to the success of such methods is their robustness in the face of non-smooth and discontinuous optimization landscapes that are characteristic of contact interactions, yet zeroth-order methods remain computationally inefficient. It is therefore desirable to develop methods for perception, planning and control in contact-rich settings that can achieve further efficiency by making use of first and second order information (i.e., gradients and Hessians). To facilitate this, we present a joint formulation of collision detection and contact modelling which, compared to existing differentiable simulation approaches, provides the following benefits: i) it results in forward and inverse dynamics that are entirely analytical (i.e. do not require solving optimization or root-finding problems with iterative methods) and smooth (i.e. twice differentiable), ii) it supports arbitrary collision geometries without needing a convex decomposition, and iii) its runtime is independent of the number of contacts. Through simulation experiments, we demonstrate the validity of the proposed formulation as a"physics for inference"that can facilitate future development of efficient methods to generate intelligent contact-rich behavior.

Problem

• Develop efficient methods for robot behavior in contact-rich settings.
• Create smooth, analytical collision detection and contact modeling.
• Enable use of gradients and Hessians for improved computational efficiency.

Innovation

• Analytical collision detection and contact modeling
• Supports arbitrary collision geometries
• Runtime independent of contact number