A Smooth Analytical Formulation of Collision Detection and Rigid Body Dynamics With Contact
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Beker, Onur, Gürtler, Nico, Shi, Ji, Geist, A. René, Razmjoo, Amirreza, Martius, Georg, Calinon, Sylvain
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979298205
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