SDRS: Shape-Differentiable Robot Simulator

TL;DR

SDRS is a novel robot simulator that maintains differentiability during large shape changes by representing robots with convex polyhedrons and using separating hyperplanes, enabling advanced co-design optimization.

Contribution

The paper introduces SDRS, a shape-differentiable robot simulator that handles significant shape changes using convex polyhedron representations and separating hyperplanes.

Findings

Ensures global differentiability during large shape changes.

Enables simultaneous optimization of robot shape and control.

Demonstrates practical co-design applications.

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.