Differentiable Collision Detection: a Randomized Smoothing Approach

Collision detection is an important component of many robotics applications, from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only recently that the question of properly differentiating collision detection has emerged as a central issue, thanks notably to the ongoing and various efforts made by the scientific community around the topic of differentiable physics. Yet, very few solutions have been suggested so far, and only with a strong assumption on the nature of the shapes involved. In this work, we introduce a generic and efficient approach to compute the derivatives of collision detection for any pair of convex shapes, by notably leveraging randomized smoothing techniques which have shown to be particularly adapted to capture the derivatives of non-smooth problems. This approach is implemented in the HPP-FCL and Pinocchio ecosystems, and evaluated on classic datasets and problems of the robotics literature, demonstrating few micro-second timings to compute informative derivatives directly exploitable by many real robotic applications, including differentiable simulation.

Authors

• Louis Montaut
• Quentin Le Lidec
• Antoine Bambade
• Vladimír Petrík
• Josef Sivic
• Justin Carpentier

Keywords

• Smoothing methods
• Shape
• Computational modeling
• Ecosystems
• Robot control
• Estimation
• Timing
• Collision Detection
• General Approach
• Robotic Applications
• Convex Shape
• Normal Distribution
• Computational Efficiency
• Ellipsoid
• General Case
• Finite Difference
• Minimization Problem
• Functional Support
• Convex Hull
• Relative Configuration
• Hessian Matrix
• Gradient-based Optimization
• Trajectory Optimization
• Contact Interaction
• Calculation Of Derivatives
• Physical Simulation
• Machine Learning Community
• Gumbel Distribution
• Separate Vectors
• Relative Pose
• Problem In Robotics