Novel Algorithms for Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Construction

TL;DR

This paper introduces a new method for collision detection in robotics that is smoothly differentiable and highly vectorizable, improving the efficiency of contact manifold construction using advanced geometric representations.

Contribution

It presents a novel collision detection approach with analytical SDF primitives and a contact manifold generation routine, enhancing differentiability and computational efficiency.

Findings

Enables smooth differentiation in collision detection pipelines.

Uses expressive analytical SDF primitives for complex surface representation.

Provides a vectorizable routine for contact manifold generation.

Abstract

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about the dynamics holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining useful gradients and Hessians, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that can address the collision detection part of the puzzle in a manner that is smoothly differentiable and massively vectorizable. This is achieved via two contributions: i) a highly expressive class of analytical SDF primitives that can efficiently represent complex 3D surfaces, ii) a novel contact manifold generation routine that makes use of this geometry representation.