Evolving Embodied Intelligence: Graph Neural Network--Driven Co-Design of Morphology and Control in Soft Robotics

Abstract

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.

Figures (5)

• Figure 1: Overview of the proposed GAT-based policy framework with DRL inheritance. The parent controller (top) represents the robot as a graph, where nodes denote position sensors and edges capture spatial relationships. A GAT encodes node features, which are pooled into a fixed-length vector and passed through a lightweight MLP head to generate actuator control signals. During inheritance (bottom), the trained controller is transferred to the child. When morphology changes, connections to removed actuators are discarded, and new ones are initialized for added actuators.
• Figure 2: Illustration of a soft robot designed for the Thrower-v0 task in the Evogym framework.
• Figure 3: Impact of inheritance on evolution. We examine the influence of inheritance on evolutionary progress by tracking the fitness of the top-performing robot across generations. Each curve shows the mean performance over three independent runs, with shaded regions representing the standard deviation. Our GAT-based inheritance methods achieve higher peak fitness than baselines, with reduced variance across runs. GA-GAT-PPO-Local-Transfer, which provides individualized node representations, outperforms on Pusher-v1, Thrower-v0, and Carrier-v1, where localized coordination is critical. In contrast, GA-GAT-PPO-Global-Transfer, which employs a shared mean representation, performs best on Catcher-v0, a task that requires broader system-level coordination.
• Figure 4: Visual comparison of four approaches applied to the Thrower-v0 task.
• Figure 5: Comparison of evolved morphologies. For each method and trial, we illustrate the robot structures that achieved the highest fitness.