Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization

2026-03-16

AI Summary

This work addresses the inefficiency in co-optimizing morphology and control that arises from neglecting the dynamic adaptation of control policies during morphological evolution. To this end, it formulates the co-design problem for the first time as a Stackelberg game and introduces Stackelberg PPO, a novel method that explicitly models the response dynamics of control policies to morphological changes through a bilevel optimization framework. By embedding the control adaptation process directly within morphology optimization, the approach achieves effective alignment between morphology and control. Experimental results across multiple co-design tasks demonstrate that the proposed method yields significantly improved training stability, faster convergence, and superior final performance compared to standard PPO, establishing a new paradigm for efficient robot design.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Evolutionary Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

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.

Problem

• morphology-control co-design
• bi-level optimization
• Stackelberg game
• policy adaptation
• robotics design

Innovation

• morphology-control co-design
• Stackelberg game
• Proximal Policy Optimization
• bi-level optimization
• robotics design