SDRS: Shape-Differentiable Robot Simulator
xiaohan ye, Xifeng Gao, Kui Wu, Zherong Pan, Taku Komura
AI summary
Problem
Current differentiable robot simulators suffer from non-differentiable singularities during substantial geometric or topological changes, restricting gradient-based co-design to minor, localized adjustments.
Approach
The method parameterizes robot links as unions of convex polyhedrons and models contact mechanics using separating hyperplanes as zero-mass auxiliary entities, eliminating explicit contact detection and ensuring global differentiability.
Key results
- Novel convex polyhedron-based shape parameterization enabling topology changes
- Penalty-based contact mechanics using separating hyperplanes as zero-mass entities
- Provable global differentiability under significant geometric and topological changes
- Successful gradient-based robot co-design optimizing shape and control simultaneously
Why it matters
It allows researchers and engineers to jointly optimize complex robot hardware and controllers at scale, overcoming the curse of dimensionality in traditional sampling-based design methods.
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 substan- tial shape changes. To address this, we present the Shape- Differentiable Robot Simulator (SDRS), designed to be differen- tiable 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 be- tween 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.