Beker, O., Gürtler, N., Shi, J., Geist, A.R., Razmjoo, A., Martius, G. and Calinon, S. (2025)
A Smooth Analytical Formulation of Collision Detection and Rigid Body Dynamics With Contact
arXiv:2503.11736.
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.
Bibtex reference
@article{Beker25arXiv,
author={Beker, O. and G{\"u}rtler, N. and Shi, J. and Geist, A. R. and Razmjoo, A. and Martius, G. and Calinon, S.},
title={A Smooth Analytical Formulation of Collision Detection and Rigid Body Dynamics With Contact},
journal={arXiv:2503.11736},
year={2025}
}