Robust Differentiable Collision Detection for General Objects
Jiayi Chen, Wei Zhao, Liangwang Ruan, Baoquan Chen, He Wang
AI summary
Problem
Traditional collision detection algorithms are inherently non-differentiable, blocking gradient flow and limiting optimization in contact-rich robotics. Prior differentiable methods are restricted to convex objects and lack robustness for complex, real-world geometries.
Approach
The method replaces direction-based smoothing with distance-based softmax relaxation, adaptive surface sampling, and equivalent gradient transport to compute stable derivatives for general object pairs.
Key results
- Median error below 0.1 mm on complex DexGraspNet and Objaverse meshes
- Over 40% accuracy improvement at millimeter precision versus existing baselines
- Memory- and time-efficient implementation with native GPU parallelization
- Demonstrated improvement in dexterous grasp synthesis quality
Why it matters
Empowers gradient-based planners and controllers to handle complex, contact-rich manipulation tasks that were previously intractable.
Abstract
Collision detection is a core component of robotics applications such as simulation, control, and planning. Tradi- tional algorithms like GJK+EPA compute witness points—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 effi- cient 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 configu- rations. Our method introduces distance-based first-order ran- domized smoothing, adaptive sampling, and equivalent gradient transport for robust and informative gradient computation. Experiments on complex meshes from DexGraspNet and Ob- javerse 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.