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

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.

8 pages, 7 figures. Accepted for publication at IROS 2026. Website at this https URL

Robotics (cs.RO)

arXiv:2606.21866 [cs.RO]

(or arXiv:2606.21866v2 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2606.21866 Focus to learn more arXiv-issued DOI via DataCite

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