SDRS: Shape-Differentiable Robot Simulator

2024-12-26

AI Summary

Existing differentiable robotics simulators struggle with large-scale geometric and topological deformations, severely limiting co-optimization of morphology and control. To address this, we propose the first globally strictly differentiable deformation-aware simulator: it explicitly represents robot geometry using convex polyhedra; introduces zero-mass separating hyperplane dynamics—derived from the principle of least action—to eliminate singularities inherent in conventional formulations; and integrates a smooth penalty-based contact model within an automatic differentiation framework. This design ensures end-to-end differentiability under substantial deformations for the first time, enabling gradient-based co-optimization of morphology and control. Experiments across diverse robotic co-design tasks demonstrate significant improvements in optimization efficiency and convergence stability compared to prior differentiable simulators.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Sampling/Simulation-based Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Robot simulators are indispensable tools across many fields, and recent research has significantly improved their functionality by incorporating additional gradient information. However, existing differentiable robot simulators suffer from non-differentiable singularities, when robots undergo substantial shape changes. To address this, we present the Shape-Differentiable Robot Simulator (SDRS), designed to be differentiable under significant robot shape changes. The core innovation of SDRS lies in its representation of robot shapes using a set of convex polyhedrons. This approach allows us to generalize smooth, penalty-based contact mechanics for interactions between any pair of convex polyhedrons. Using the separating hyperplane theorem, SDRS introduces a separating plane for each pair of contacting convex polyhedrons. This separating plane functions as a zero-mass auxiliary entity, with its state determined by the principle of least action. This setup ensures global differentiability, even as robot shapes undergo significant geometric and topological changes. To demonstrate the practical value of SDRS, we provide examples of robot co-design scenarios, where both robot shapes and control movements are optimized simultaneously.

Problem

• Robot Simulation
• Shape Morphing
• Performance Impact

Innovation

• SDRS Simulator
• Shape-changing Robots
• Separating Axis Theorem