Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation

2026-02-23

AI Summary

This work addresses the inefficiency of existing differentiable simulation frameworks in generating contact manifolds due to conventional collision-handling logic, which hinders both differentiability and parallel computation. The authors propose a novel contact manifold generation method that balances efficiency and differentiability by bridging convex primitives and distance-barrier approaches. Specifically, they introduce smooth, analytically defined signed distance primitives for vertex–face collisions and, for the first time, present a differentiable edge–edge collision routine that simultaneously outputs signed distances and contact normals. Implemented within a JAX-based, massively vectorized framework, the method demonstrates significantly faster collision detection than Mujoco XLA on benchmark tasks, thereby validating its dual advantages in computational efficiency and end-to-end differentiability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• contact manifold generation
• differentiable simulation
• vectorization
• rigid-body dynamics
• collision detection

Innovation

• differentiable simulation
• contact manifold
• signed distance function
• vectorization
• rigid-body dynamics