Robust Differentiable Collision Detection for General Objects

TL;DR

This paper presents a robust, differentiable collision detection framework capable of handling complex convex and concave objects, enabling improved gradient-based optimization in robotics tasks like grasping.

Contribution

It introduces a novel distance-based randomized smoothing method with adaptive sampling and gradient transport, enhancing robustness and applicability over existing convex-only approaches.

Findings

Significant improvements over baselines on DexGraspNet and Objaverse datasets.

Enables gradient-based optimization for complex object geometries.

Demonstrates application in dexterous grasp synthesis.

Abstract

Collision detection is a core component of robotics applications such as simulation, control, and planning. Traditional algorithms like GJK+EPA compute witness points (i.e., the closest or deepest-penetration pairs between two objects) but are inherently non-differentiable, preventing gradient flow and limiting gradient-based optimization in contact-rich tasks such as grasping and manipulation. Recent work introduced efficient first-order randomized smoothing to make witness points differentiable; however, their direction-based formulation is restricted to convex objects and lacks robustness for complex geometries. In this work, we propose a robust and efficient differentiable collision detection framework that supports both convex and concave objects across diverse scales and configurations. Our method introduces distance-based first-order randomized smoothing, adaptive sampling, and equivalent gradient transport for robust and informative gradient computation. Experiments on complex meshes from DexGraspNet and Objaverse show significant improvements over existing baselines. Finally, we demonstrate a direct application of our method for dexterous grasp synthesis to refine the grasp quality. The code is available at https://github.com/JYChen18/DiffCollision.