Robust Differentiable Collision Detection for General Objects

2025-11-09

AI Summary

Existing differentiable collision detection methods (e.g., GJK+EPA) suffer from non-differentiability, hindering gradient-based optimization; directional random smoothing is limited to convex bodies and lacks robustness for non-convex geometries and complex contact configurations. This work proposes the first robust, differentiable collision detection framework supporting both convex and non-convex objects. We introduce distance-based first-order random smoothing—replacing directional sampling—with adaptive surface sampling and an equivalent gradient transmission mechanism, enabling stable and high-fidelity gradient propagation. Evaluated on DexGraspNet and Objaverse, our method significantly outperforms state-of-the-art approaches. Furthermore, it enables effective differentiable dexterous grasp generation, substantially improving grasp success rate and stability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Manipulation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Enabling differentiable collision detection for robotics simulation and control
• Overcoming non-differentiability limitations in contact-rich grasping tasks
• Supporting both convex and concave objects across diverse configurations

Innovation

• Distance-based randomized smoothing for differentiable collision detection
• Adaptive sampling and gradient transport for robust gradients
• Framework supports both convex and concave object geometries