Evolving the Complete Muscle: Efficient Morphology-Control Co-design for Musculoskeletal Locomotion
Authors: Lidong Sun, Wentao Zhao, Ye Wang, Huaping Liu, Fuchun Sun
Organizations: Naval University of Engineering, Wuhan 430033, China · Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China · Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Musculoskeletal robots offer intrinsic compliance and flexibility, providing a promising paradigm for versatile locomotion. However, existing research typically relies on models with fixed muscle physiological parameters. This static physical setting fails to accommodate the diverse dynamic demands of complex tasks, inherently limiting the robot's performance upper bound. In this work, we focus on the morphology and control co-design of musculoskeletal systems. Unlike previous studies that optimize single physiological attributes such as stiffness, we introduce a Complete Musculoskeletal Morphological Evolution Space that simultaneously evolves muscle strength, velocity, and stiffness. To overcome the exponential expansion of the exploration space caused by this comprehensive evolution, we propose Spectral Design Evolution (SDE), a high-efficiency co-optimization framework. By integrating a bilateral symmetry prior with Principal Component Analysis (PCA), SDE projects complex muscle parameters onto a low-dimensional spectral manifold, enabling efficient morphological exploration. Evaluated on the MyoSuite framework across four tasks (Walk, Stair, Hilly, and Rough terrains), our method demonstrates superior learning efficiency and locomotion stability compared to fixed-morphology and standard evolutionary baselines.
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Fig. 1: Conceptual overview of Spectral Design Evolution (SDE). (Left) Fixed-morphology agent fails on challenging terrains due to physical limits. (Right) SDE optimizes muscle triad parameters ( σ,ν,κ ) on a low-dimensional spectral manifold, enabling the robot to adapt its physical capacity for superior locomotion stability.
Fig. 2: The SDE framework architecture. The process consists of an offline dynamics-aware manifold construction phase and an online two-stage co-optimization phase where the design policy πθ and control policy πϕ are optimized via shared reward signals.
Fig. 3: Experimental setup and task environments in MyoSuite: (a) The MyoLeg model used for spectral analysis and co-optimization; (b) Walk terrain; (c) Rough terrain with stochastic debris; (d) Hilly terrain with undulating slopes; (e) Stair terrain with vertical obstacles.
Fig. 4: Learning curves across four terrains. SDE demonstrates superior adaptability, particularly in high-impedance tasks like Stair , Hilly and Rough .
Fig. 5: Learning curves comparing full triad co-optimization against single-parameter evolution. The synergy between parameters contributes to adaptation across diverse terrains.
Fig. 6: Qualitative comparison of evolved gaits: (Left) The full SDE framework emerges a stable, alternating bipedal gait with natural leg-swing phases. (Right) The SDE- σ (Strength-only) variant falls into a sub-optimal “scissor-gait”, where the limbs remain in a crossed configuration and the agent moves via hopping.
Fig. 7: Radar charts showing the distributions of evolved muscle parameters across different muscle groups. (a-c) depict the evolution of individual parameters: strength ( σ ), velocity ( ν ), and stiffness ( κ ), which exhibit fragmented and inconsistent adaptation across muscles. (d) shows the SDE-evolved full triad, highlighting a coordinated synergy where muscle parameters co-adapt in a physiologically plausible manner, enabling efficient and stable locomotion.
Fig. 8: Ablation study on bilateral symmetry. While SDE-Asym has higher degrees of freedom, the symmetry prior in SDE ensures more stable and physically plausible gait patterns.
Fig. 9: Cumulative explained variance of musculoskeletal dynamical response across different k . A distinct “elbow” is observed at k=5 , capturing over 98% of the morphological variance.
Fig. 10: Learning curves on the Rough task for different latent dimensions k . Although k=7 and k=9 offer higher theoretical expressivity, k=5 achieves the most efficient balance between convergence speed and final reward.
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.
Junru Song, Yang Yang, Yaqing Xu +5
Shanghai Jiao Tong University, Shanghai 200240, China · Intelligent Game and Decision Laboratory, Beijing 100048, China · Renmin University of China, Beijing 100872, China +1
Co-design is a high-dimensional search problem in the robot morphology and control design space. Efficient search requires exploiting the structure shaped by their interaction. To understand this structure, we analyze the landscapes of soft locomotion and manipulation tasks. We identify three patterns consistent across regions of their co-design spaces: 1) Within a region, quality varies along a low-dimensional manifold, with minimal variation orthogonal to it, reducing the effective search space dimensionality. 2) In higher-quality regions, the variance in quality is spread across more dimensions, necessitating search to expand dimensionality as quality improves. 3) In higher-quality regions, quality varies along joint morphology-control dimensions, requiring search along them. Using these insights, we devise an efficient co-design algorithm that yields 36% better co-designs than state-of-the-art baselines. We examine their exploration patterns and show that these baselines required an order of magnitude more function evaluations to find co-designs of comparable quality. Finally, we ablate our algorithm to verify that exploiting the identified structure was the key to efficient co-design.
Apoorv Vaish, Oliver Brock
Robotics and Biology Laboratory, Technische Universität Berlin · Science of Intelligence (SCIoI), Cluster of Excellence, Berlin · Robotics Institute Germany (RIG)
In the automated co-design of soft robots, precisely adapting the material stiffness field to task environments is crucial for unlocking their full physical potential. However, mainstream platforms (e.g., EvoGym) strictly discretize the material dimension, artificially restricting the design space and performance of soft robots. To address this, we propose EvoGymCM (EvoGym with Continuous Materials), a benchmark suite formally establishing continuous material stiffness as a first-class design variable alongside morphology and control. Aligning with real-world material mechanisms, EvoGymCM introduces two settings: (i) EvoGymCM-R (Reactive), motivated by programmable materials with dynamically tunable stiffness; and (ii) EvoGymCM-I (Invariant), motivated by traditional materials with invariant stiffness fields. To tackle the resulting high-dimensional coupling, we formulate two Morphology-Material-Control co-design paradigms: (i) Reactive-Material Co-Design, which learns real-time stiffness tuning policies to guide programmable materials; and (ii) Invariant-Material Co-Design, which jointly optimizes morphology and fixed material fields to guide traditional material fabrication. Systematic experiments across diverse tasks demonstrate that continuous material optimization boosts performance and unlocks synergy across morphology, material, and control.
Le Shen, Kangyao Huang, Wentao Zhao +1
College of Control Science and Engineering, Zhejiang University. · Department of Computer Science and Technology, Tsinghua University.