SurGE: Surrogate Gradient-guided Evolution for Co-design of Legged Robots with Parallel Elasticity

2026-06-20

AI Summary

This study addresses the optimization challenges in co-designing legged robots with compliant elements, where non-differentiable contact dynamics and mechanical meshing hinder gradient-based methods. To overcome this, the authors propose a novel framework that integrates a differentiable kinematics-dynamics single rigid-body model (Kino-SRB) with a design-aware control policy, introducing surrogate gradients into the otherwise non-differentiable co-design pipeline for the first time. They further enhance the CMA-ES optimizer with a mean-shift mechanism employing cosine-annealed step-size decay, significantly improving convergence stability and population concentration. Experimental validation on a 4-DoF hopping robot demonstrates a sixfold reduction in cross-seed standard deviation and an 18% increase in population concentration. Hardware tests in a 2D subspace achieve a 37.65% reduction in the objective function, with consistent performance between simulation and physical deployment.

Abstract

Co-design of legged robots with elastic elements is challenging due to the non-differentiability of contact dynamics and mechanism engagement. This paper presents SurGE, a framework that computes surrogate gradients of the design objective through a differentiable pipeline consisting of a kinodynamic single-rigid-body (Kino-SRB) model and a design-aware control policy, and injects them into CMA-ES via mean shift with cosine-annealed step decay. On a 4-DOF design space of a hopping robot with unidirectional parallel spring, SurGE achieves 6 times lower cross-seed standard deviation and 18% tighter population concentration compared to vanilla CMA-ES, while matching or improving the best objective. Hardware experiments on a 2D design subspace show that, starting from a hand-tuned initial design, SurGE reduces the design objective by 37.65% on hardware, with the improvement trend identified in simulation transferring consistently to the physical system. SurGE provides the potential to accelerate non-differentiable co-design problems in legged robots via surrogate model gradients.

Problem

• co-design
• legged robots
• elasticity
• non-differentiability
• contact dynamics

Innovation

• surrogate gradient
• co-design
• legged robots
• differentiable optimization
• CMA-ES