Novel Algorithms for Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Construction

2026-04-19

AI Summary

This work addresses the challenge of non-differentiability in contact-rich robotic simulation, where collision detection, contact dynamics, and time integration hinder the effective computation of gradients and Hessians. To overcome the differentiability bottleneck primarily at the collision detection stage, the paper proposes a novel approach for constructing smooth, differentiable contact manifolds using highly expressive analytical signed distance fields (SDFs). This method enables efficient representation of complex 3D geometries and supports highly vectorized parallel computation. The resulting differentiable contact model provides a scalable and computationally efficient foundation for gradient-based robot motion planning and control.

Technology Category

Intelligent Robots: Motion and Path PlanningSearch and Optimization: Sampling/Simulation-based SearchPlanning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systemsSystems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health

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.

Problem

• contact-rich robot behavior
• collision detection
• smooth differentiability
• gradient computation
• simulation pipeline

Innovation

• differentiable collision detection
• analytical SDF primitives
• contact manifold generation
• vectorizable simulation
• smoothly differentiable dynamics