Shaping the Evolutionary Dynamics of Robot Morphology via Adaptive Control Learning
Authors: Junru Song, Yang Yang, Yaqing Xu, Ying Wen, Wei Peng, Guozhen Li, Wei'en Zhou, Wen Yao
Organizations: Shanghai Jiao Tong University, Shanghai 200240, China · Intelligent Game and Decision Laboratory, Beijing 100048, China · Renmin University of China, Beijing 100872, China · Shanghai Innovation Institute, Shanghai 200232, China
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.
Figures & tables
Figure 1: (a) Task environments used for benchmarking. (b) Two-dimensional VSR representation in EvoGym ( Bhatia et al. 2021 ) . (c) Two representative morphologies from preliminary experiments, illustrating the distinction between fast and good learners.
Figure 2: Robot co-design.
Figure 3: Morphological intelligence versus true potential for 250 high-performing morphologies (top 5% of 1,000 evaluated solutions × five independent trials). No significant correlation is observed (Spearman’s ρ=0.05 , p=0.23 ), though the variance of morphological intelligence narrows at higher true potential.
Figure 4: Overview of robot co-design with AdaControl. In each generation, the population undergoes progressive control learning with iteratively increased iterations until the morphological intelligence of survivors is sufficiently close to the population average. In each pseudo step of natural selection, only the observed segments of learning curves (unshaded areas) are used for estimating morphological intelligence.
Task
Control Complexity
200
500
1000
2000
3000
Carrier
2086.40 ± 743.67
1995.46 ± 802.65
2064.89 ± 768.64
2116.82 ± 735.35
2200.78 ± 674.62
Pusher
2094.57 ± 685.21
2080.44 ± 708.53
2141.01 ± 679.03
2145.09 ± 646.19
2216.28 ± 634.45
BridgeWalker
1633.38 ± 855.06
1481.07 ± 852.35
1589.40 ± 843.95
1691.15 ± 820.79
1731.16 ± 819.92
Table 1: Mean and standard deviation of PPO convergence iterations under different control complexities.
Figure 5: True potential versus weak-control-evaluated fitness under varying control complexities in Carrier. Annotated p -values are from two-tailed t -tests.
Figure 6: Average ranking of survivors when re-sorted by true potential rather than weak-control fitness. Lower rankings indicate greater deviation from true-potential-based selection.
Figure 7: Learning curves of high-performing morphologies evolved under different control complexities. Individual curves in gray; colored curves show the average per complexity.
Figure 8: Average MI of all evaluated morphologies throughout evolution under different control complexities.
Figure 9: Population-average MI of survivors per generation. Shaded areas indicate standard deviation. Weak control produces a rising MI trend, signaling accumulating bias; strong control and AdaControl maintain stable MI.
Task
AdaControl
FitControl
Carrier
1063.62 ± 194.48
1631.64 ± 324.59
Pusher
609.82 ± 124.62
1959.40 ± 211.11
BridgeWalker
584.00 ± 62.29
1443.45 ± 81.24
Table 2: Average PPO iterations per evaluation for AdaControl and FitControl (mean ± std). AdaControl reduces control learning cost by 65–81% relative to strong control (3000 iterations) while achieving comparable or superior optimization efficiency and morphological diversity.
Figure 10: Optimization efficiency measured by number of robot evaluations. Numbers in parentheses denote average PPO iterations. Insets magnify the later stages of evolution.
Figure 11: Optimization efficiency measured by cumulative PPO iterations (log scale). “equiv.” denotes the fixed complexity approximately matching AdaControl’s average iterations (1000 for Carrier, 500 for Pusher and BridgeWalker).
Figure 12: Diversity of high-performing morphologies under different control schemes. Left: GA with fixed complexities and AdaControl, positioned by average PPO iterations, with dashed regression line from fixed-complexity results. Right: FitControl, LASeR, and MorphVAE. FitControl is absent in (c) as it did not produce any high-performing morphology in BridgeWalker.
Figure 13: Diversity of high-performing morphologies versus total PPO iterations (log scale) for different MI ratio thresholds rthr . Each point is labeled with its threshold value.
Figure 14: Relationship between MI and morphological attributes in Carrier. (a) Each point represents one morphology. (b)–(c) Morphologies with the same voxel count are aggregated; only the mean MI is shown.
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.
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.
Yanning Dai, Yuhui Wang, Dylan R. Ashley +1
Center of Excellence for Generative AI, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. · Dalle Molle Institute for Artificial Intelligence Research (IDSIA), Lugano, Switzerland. · Università della Svizzera italiana (USI), Lugano, Switzerland. +1
In this paper, we introduce a model of evolution and learning in robots that co-optimizes a distribution of latent design vectors (genotypes) and a mixture of control experts (neural modules), which are gated by the latent coordinates of each decoded design (phenotype). This provides a scalable alternative to co-design algorithms that either train an individual policy for every robot, which is inefficient, or a monolithic universal controller for all robots, which results in overly conservative structures and behaviors. Our approach lies somewhere between these two extremes, preserving ancestral knowledge in a unified yet modular framework in which different body plans activate and deactivate different combinations of learned sensorimotor circuits for goal-directed behavior. This allows one part of the controller to be overhauled to better suit new species of designs as they emerge without disrupting the hard-earned knowledge contained within other expert modules. It also allows pretrained expert policies to be directly plugged into the mixture, which can steer evolution into otherwise unexplored areas of latent space containing desired morphological traits. We refer to this process as "evo by demo" and explore how it may be used to guide freeform evolution toward canonical structures defined by the pretrained model. Videos and code can be found at: https://eco-moe.github.io.