Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation

TL;DR

This paper introduces a novel framework for contact manifold generation in rigid-body simulation that is smoothly differentiable, highly vectorizable, and faster than existing methods, enabling more efficient robotics simulations.

Contribution

The authors propose a new approach combining smooth analytical primitives and a differentiable edge-edge routine, improving speed and differentiability over traditional collision detection methods.

Findings

Significant speedup over Mujoco XLA collision routines

Framework is smoothly differentiable and vectorizable

Validated through didactic experiments and benchmarking

Abstract

Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation: representing the volume of intersection between two colliding geometries via a discrete set of properly distributed contact points. A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern, and thus rely on logic and control flow that hinder these goals. We instead propose a framework designed from the ground up with these goals in mind, by trying to strike a middle ground between: i) convex primitive based approaches used by common robotics simulators (efficient but not differentiable), and ii) mollified vertex-face and edge-edge unsigned distance-based approaches used by barrier methods (differentiable but inefficient). Concretely, we propose: i) a representative set of smooth analytical signed distance primitives to implement vertex-face collisions, and ii) a novel differentiable edge-edge collision routine that can provide signed distances and signed contact normals. The proposed framework is evaluated via a set of didactic experiments and benchmarked against the collision detection routine of the well-established Mujoco XLA framework, where we observe a significant speedup. Supplementary videos can be found at https://github.com/bekeronur/contax, where a reference implementation in JAX will also be made available at the conclusion of the review process.