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.
Designing high-performance legged robots requires jointly optimizing morphology and control. Model-free Reinforcement Learning (RL) offers an alternative to model-predictive control for developing robust controllers without explicitly specifying robot dynamics. Thus, we have seen theuse of RL to train controllers and evaluate designs for robot morphology optimization. While RL has shown success inlocomotion, using it in the co-design inner loop is expensive due to repeated policy training. Universal policies conditioned on morphology offer a promising alternative, but suffer from behavioral diversity collapse, converging to a single strategy that performs sub-optimally across designs. On the other hand, end-to-end Mixture-of-Experts (MoE) architectures fail due to a collapse in its representation. We propose Gaussian Evolutionary Specialists (GES), a framework that decouples design-space partitioning from policy learning to capture diverse behaviors explicitly. GES assigns specialist policies to evolving Gaussian regions and iteratively refines them via training, probing, and territory expansion. The resulting specialists are integrated into a design sampling loop, replacing costly re-training with direct evaluation. When tested on the Buoyancy-Assisted Light Legged Unit (BALLU), GES discovers designs with 5 - 25% higher performance than naive universal policies. On hardware, a GES optimized design overcomes a 24 cm tall obstacle - 3x improvement over the baseline BALLU design. Moreover, GES curtails design optimization time by 37%.
Replicating and surpassing the autonomy of natural organisms remains a long-standing goal in robotics. Yet most robotic systems have their structure, materials, and control designed separately, in sharp contrast to the co-evolution in nature. This separation often leads to suboptimal designs, and we still have a limited understanding of the individual and collective contributions of these design entities. In this work, we propose a gradient-based co-design framework that simultaneously optimizes the topology, material distribution, and control policy of a truss-lattice robot. The framework embeds mixed-type topological and material variables into a continuous design space and integrates a neural network controller within a differentiable simulator, capturing their interactions and enabling efficient gradient calculation via automatic differentiation. Furthermore, we develop a constrained optimization to navigate the highly non-convex design landscape and jointly optimize all design entities. Case studies demonstrate that the proposed framework consistently discovers diverse locomotion strategies that outperform baselines obtained through separated design. The framework is also flexible to accommodate different functional requirements and boundary conditions. Using this framework, we further extract design insights that reveal the individual and collective effects of different entities on robotic performance. The proposed framework provides a computational foundation for the autonomous co-design of robotic systems, capable of reconfiguration, locomotion, and other complex autonomous behaviors.
We propose to turn generalist multi-embodiment value functions into reusable models for robot design. Instead of running a new reinforcement learning co-design loop for each robot, we first train an embodiment-aware policy and value function across many robot designs. After training, the frozen value function is used as a differentiable surrogate to optimize candidate embodiments through value gradients. We evaluate our approach across different robot design settings, from perturbed single robots to held-out robots across morphology classes, with single models trained on up to 50 robots and design spaces of over 1100 continuous embodiment parameters. Beyond optimizing complete embodiments, we show that value gradients can identify performance-limiting design and control parameters, enabling both the optimization and the analysis of new robot designs.