Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

翻译：形态-控制协同设计关注智能体身体结构与控制策略的耦合优化。该问题呈现双层结构，其中控制策略会动态适应形态以最大化性能。现有方法通常采用单层公式，在优化形态时将控制策略视为固定，从而忽略了控制的适应动态。这可能导致优化效率低下，因为形态更新可能与控制适应不匹配。本文从博弈论视角重新审视协同设计问题，将形态与控制之间的内在耦合建模为Stackelberg博弈的一种新变体。我们提出了Stackelberg近端策略优化（Stackelberg PPO），该方法将控制的适应动态显式地纳入形态优化过程。通过对这种内在耦合进行建模，我们的方法使形态更新与控制适应保持一致，从而稳定训练并提高学习效率。在多种协同设计任务上的实验表明，Stackelberg PPO在稳定性和最终性能上均优于标准PPO，为显著提升机器人设计效率开辟了新途径。