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

Morphology--control co-design jointly optimizes an agent's body structure and control policy as an integrated embodied system. However, existing methods typically model morphology design and control with separate networks coupled only indirectly through a shared task objective, limiting explicit high-level coordination. Inspired by natural genes that coordinate biological development, we introduce Morphogene, a compact latent blueprint that bridges an agent's body and brain. Through AdaConcat, Morphogene jointly conditions morphology and control generation at the limb level, allowing its variations to induce coordinated changes in both components. Building on this representation, we propose GeCode, which formulates co-design as exploration in the compact Morphogene space. Each Morphogene anchors a local design region in which nearby body--brain designs are explored, while performance-guided updates move these anchors toward promising regions for more efficient exploration of the broader design space. This process combines local refinement with global exploration while preserving body--brain compatibility. Extensive experiments across diverse 2D and 3D co-design tasks demonstrate that GeCode consistently outperforms existing state-of-the-art methods, achieving substantially faster convergence and higher final performance.

The intelligent behavior of robots does not emerge solely from control systems, but from the tight coupling between body and brain, a principle known as embodied intelligence. Designing soft robots that leverage this interaction remains a significant challenge, particularly when morphology and control require simultaneous optimization. A significant obstacle in this co-design process is that morphological evolution can disrupt learned control strategies, making it difficult to reuse or adapt existing knowledge. We address this by develop a Graph Neural Network-based approach for the co-design of morphology and controller. Each robot is represented as a graph, with a graph attention network (GAT) encoding node features and a pooled representation passed through a multilayer perceptron (MLP) head to produce actuator commands or value estimates. During evolution, inheritance follows a topology-consistent mapping: shared GAT layers are reused, MLP hidden layers are transferred intact, matched actuator outputs are copied, and unmatched ones are randomly initialized and fine-tuned. This morphology-aware policy class lets the controller adapt when the body mutates. On the benchmark, our GAT-based approach achieves higher final fitness and stronger adaptability to morphological variations compared to traditional MLP-only co-design methods. These results indicate that graph-structured policies provide a more effective interface between evolving morphologies and control for embodied intelligence.

Robot co-design via bi-level optimization couples within-lifetime controller learning for fitness evaluation with cross-generational morphological evolution. Prior work has established that well-adapted morphology facilitates faster control learning, a property termed morphological intelligence. Yet how control learning reciprocally shapes morphological evolution remains unexplored. This paper examines both directions for a holistic account of brain-body interplay. We first show that morphological contributions to control learning decouple into two orthogonal dimensions. We formalize the convergence speed as morphological intelligence and identify the performance ceiling as a complementary quantity termed true potential. A concise functional relation is then established to jointly characterize both quantities from individual learning curves, which, when aggregated at the population level, capture evolutionary profiles. Through extensive experiments on simulated voxel-based soft robots, we reveal that premature fitness evaluation systematically underestimates true potential and biases selection towards fast learners. This restricts design space exploration, compromising both optimization efficiency and morphological diversity. Notably, the widely recognized morphological Baldwin effect emerges as an artifact of this bias rather than a general evolutionary tendency. We therefore propose AdaControl, which monitors disproportionate selection for morphological intelligence during evolution and allocates minimally sufficient control learning for unbiased fitness evaluation. With AdaControl, a simple genetic algorithm rivals state-of-the-art generative-model-based co-design methods in discovering diverse high-performing designs while cutting computation by up to 80% versus exhaustive control.