IEEE Transactions on Robotics, 2025

SDRS: Shape-Differentiable Robot Simulator

Xiaohan Ye1, Xifeng Gao2, Kui Wu2, Zherong Pan2,†, and Taku Komura1,†
1The University of Hong Kong    2LightSpeed Studios, Tencent    †Corresponding authors
Paper (TRO) arXiv Code
Gripper shape optimization teaser Differentiable robot co-design pipeline with annotations
SDRS overview: differentiable robot simulation with shape optimization

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 representing robot shapes using a set of convex polyhedrons. This representation allows 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 and treats it as a zero-mass auxiliary entity whose state is determined by the principle of least action. This setup enables global differentiability even as robot shapes undergo significant geometric and topological changes.

Results

Task 1: Spider Leg Shape Optimization

Initial spider leg design Optimized spider leg shapes comparison
Shape optimization of a spider-inspired robot leg. Left: Initial leg geometry. Right: Comparison of optimized shapes from SDRS (left) and mesh-based method (right).

Task 2: Bipedal Robot Foot Optimization

Bipedal robot walking render Original bipedal foot design Foot optimized with fine mesh cage Foot optimized with SDRS
Comparative foot shape optimization for bipedal locomotion. From left to right: Robot walking visualization, original foot shape, fine mesh cage result, and SDRS optimization result.

Task 3: Single-Jaw Gripper Topology Optimization

Single-jaw gripper initial design SDRS gripper simulation scene Mesh-based gripper simulation scene
Single-jaw gripper topology optimization. Left: Initial gripper design. Middle: SDRS simulation enabling topology changes. Right: Mesh-based simulation with fixed topology.

Citation

@article{ye2025sdrs,
  title={SDRS: Shape-Differentiable Robot Simulator},
  author={Ye, Xiaohan and Gao, Xifeng and Wu, Kui and Pan, Zherong and Komura, Taku},
  journal={IEEE Transactions on Robotics},
  year={2025}
}