Collision Detection with Analytical Derivatives of Contact Kinematics
🤖 AI Summary
This work addresses the non-smoothness in contact kinematics—manifested in distance, position, and normal mappings—arising from degenerate geometric configurations such as zero or undefined curvature, which impedes gradient-based robotic methods. To resolve this, the authors propose the iDCOL framework, which regularizes degenerate geometries into strictly convex implicit surfaces and solves a fixed-size nonlinear system via a geometrically scaled convex optimization formulation, thereby restoring uniqueness and smoothness to contact mappings. For the first time, analytical derivatives of contact kinematic quantities are derived using the implicit function theorem and integrated into a Newton-based solver to enable efficient differentiable computation. Experiments demonstrate robust performance across extensive collision simulations and successful application in differentiable motion planning, multi-body rigid collisions, and soft robot interaction scenarios.
Application Category
📝 Abstract
Differentiable contact kinematics are essential for gradient-based methods in robotics, yet the mapping from robot state to contact distance, location, and normal becomes non-smooth in degenerate configurations of shapes with zero or undefined curvature. We address this inherent limitation by selectively regularizing such geometries into strictly convex implicit representations, restoring uniqueness and smoothness of the contact map. Leveraging this geometric regularization, we develop iDCOL, an implicit differentiable collision detection and contact kinematics framework. iDCOL represents colliding bodies using strictly convex implicit surfaces and computes collision detection and contact kinematics by solving a fixed-size nonlinear system derived from a geometric scaling-based convex optimization formulation. By applying the Implicit Function Theorem to the resulting system residual, we derive analytical derivatives of the contact kinematic quantities. We develop a fast Newton-based solver for iDCOL and provide an open-source C++ implementation of the framework. The robustness of the approach is evaluated through extensive collision simulations and benchmarking, and applicability is demonstrated in gradient-based kinematic path planning and differentiable contact physics, including multi-body rigid collisions and a soft-robot interaction example.
Problem
Research questions and friction points this paper is trying to address.
differentiable contact kinematics
collision detection
degenerate configurations
non-smooth mapping
implicit surfaces
Innovation
Methods, ideas, or system contributions that make the work stand out.
differentiable collision detection
implicit surfaces
contact kinematics
geometric regularization
analytical derivatives
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