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arxiv: 2604.12855 · v1 · submitted 2026-04-14 · 💻 cs.RO

Evolving the Complete Muscle: Efficient Morphology-Control Co-design for Musculoskeletal Locomotion

Lidong Sun , Wentao Zhao , Ye Wang , Huaping Liu , Fuchun Sun This is my paper

Pith reviewed 2026-05-10 14:33 UTC · model grok-4.3

classification 💻 cs.RO
keywords musculoskeletal robotsmorphology control co-designevolutionary optimizationlocomotionmuscle parametersspectral manifoldmyosuite
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The pith

Evolving muscle strength, velocity and stiffness together via a low-dimensional manifold improves musculoskeletal robot locomotion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to demonstrate that fixing muscle physiological parameters caps the performance of musculoskeletal robots on complex locomotion tasks, while jointly evolving strength, velocity and stiffness alongside control policies can raise that upper bound. To make the resulting high-dimensional search feasible, the authors introduce Spectral Design Evolution, which reduces the parameter space using symmetry and principal-component projection. If this holds, robots could adapt their physical properties more effectively to varied environments without exhaustive trial-and-error. Readers should care because the approach directly targets the morphology-control coupling that limits compliant robotic systems today.

Core claim

The authors introduce a Complete Musculoskeletal Morphological Evolution Space in which muscle strength, velocity and stiffness are evolved simultaneously with control, and they show that Spectral Design Evolution projects these parameters onto a low-dimensional spectral manifold via bilateral symmetry and PCA. This enables efficient co-optimization that yields higher learning efficiency and greater locomotion stability than fixed-morphology or standard evolutionary baselines on four MyoSuite tasks covering walk, stair, hilly and rough terrains.

What carries the argument

Spectral Design Evolution (SDE), a reduction technique that combines a bilateral symmetry prior with PCA to embed the full set of muscle strength, velocity and stiffness values into a compact manifold for tractable evolutionary search.

If this is right

  • Evolving all three muscle attributes at once raises the achievable performance ceiling beyond what fixed-parameter or single-attribute optimization can reach.
  • The symmetry-plus-PCA reduction keeps exploration tractable even as the number of muscles grows.
  • The resulting policies exhibit improved stability and learning speed on flat, stair, hilly and rough terrain tasks.
  • Morphology and control can be co-optimized without separate sequential stages.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reduction strategy could be applied to other high-dimensional actuator spaces in legged or soft robots.
  • If the manifold generalizes across tasks, a single learned spectral basis might support rapid adaptation to new environments.
  • Hardware validation would test whether the simulated muscle-parameter gains survive sim-to-real gaps in actuator dynamics.

Load-bearing premise

The low-dimensional manifold produced by symmetry and PCA still contains enough task-relevant variation to reach near-optimal muscle configurations.

What would settle it

Running the same evolutionary search in the full unreduced parameter space and obtaining equal or superior performance with comparable compute would show the manifold projection is not necessary.

Figures

Figures reproduced from arXiv: 2604.12855 by Fuchun Sun, Huaping Liu, Lidong Sun, Wentao Zhao, Ye Wang.

Figure 1
Figure 1. Figure 1: Conceptual overview of Spectral Design Evolution [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The SDE framework architecture. The process consists of an offline dynamics-aware manifold construction phase [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Learning curves comparing full triad co-optimization [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Learning curves across four terrains. SDE demon [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison of evolved gaits: (Left) The [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Radar charts showing the distributions of evolved [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative explained variance of musculoskeletal [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 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. k = 9 eventually achieve slightly higher peak rewards, they exhibit slower initial convergence and higher variance across training seeds. Conversely, k = 3 suffers from under-fitting. Ultim… view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a Complete Musculoskeletal Morphological Evolution Space that jointly evolves muscle strength, velocity, and stiffness parameters for musculoskeletal robots. To address the resulting high-dimensional search space, it proposes Spectral Design Evolution (SDE), which applies a bilateral symmetry prior followed by PCA to project muscle parameters onto a low-dimensional spectral manifold for efficient morphology-control co-optimization. Empirical results on the MyoSuite framework across Walk, Stair, Hilly, and Rough locomotion tasks report improved learning efficiency and stability relative to fixed-morphology and standard evolutionary baselines.

Significance. If the central empirical claims hold after addressing the noted gaps, the work would advance morphology-control co-design for compliant robotic systems by demonstrating a scalable way to explore comprehensive muscle parameter spaces without exhaustive search. The multi-terrain evaluation and direct comparison to relevant baselines provide a practical foundation; the symmetry-plus-PCA reduction is a pragmatic engineering choice that could influence future musculoskeletal robot design pipelines.

major comments (2)
  1. [§3.2] §3.2 (Spectral Design Evolution): The claim that the bilateral-symmetry-plus-PCA projection preserves sufficient expressivity for near-optimal morphologies rests on the unverified assumption that retained principal components capture terrain-specific and asymmetric adaptations. No ablation, explained-variance breakdown, or reconstruction-error analysis for task-critical parameters (e.g., on Stair or Rough terrains) is provided; without it, reported gains may simply reflect the reduced search space rather than genuine co-design superiority.
  2. [§5] §5 (Experimental Evaluation): Performance improvements are stated without reporting the number of independent runs, statistical significance tests, variance across seeds, or full baseline implementation and hyperparameter details. These omissions are load-bearing for the central claim of superior learning efficiency and locomotion stability.
minor comments (2)
  1. The definition of the spectral manifold projection operator could be stated as an explicit equation to improve reproducibility.
  2. Figure captions for the evolved morphologies would benefit from quantitative comparison metrics (e.g., parameter deviation from baseline) rather than qualitative description alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and commit to revisions that strengthen the empirical support and reproducibility of our claims.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Spectral Design Evolution): The claim that the bilateral-symmetry-plus-PCA projection preserves sufficient expressivity for near-optimal morphologies rests on the unverified assumption that retained principal components capture terrain-specific and asymmetric adaptations. No ablation, explained-variance breakdown, or reconstruction-error analysis for task-critical parameters (e.g., on Stair or Rough terrains) is provided; without it, reported gains may simply reflect the reduced search space rather than genuine co-design superiority.

    Authors: We agree that additional analysis is needed to substantiate the expressivity of the spectral manifold. In the revised manuscript we will add: (1) an explained-variance breakdown of the retained principal components for each terrain, (2) reconstruction-error metrics focused on task-critical muscle parameters (e.g., stiffness and velocity on Stair and Rough), and (3) an ablation comparing full SDE against a version that disables the PCA projection while retaining symmetry. These additions will demonstrate that performance gains arise from effective morphology-control co-design rather than search-space reduction alone. revision: yes

  2. Referee: [§5] §5 (Experimental Evaluation): Performance improvements are stated without reporting the number of independent runs, statistical significance tests, variance across seeds, or full baseline implementation and hyperparameter details. These omissions are load-bearing for the central claim of superior learning efficiency and locomotion stability.

    Authors: We acknowledge these omissions weaken the strength of the empirical claims. The revised manuscript will report the exact number of independent runs (with seed values), include statistical significance tests (e.g., paired t-tests or Wilcoxon rank-sum with p-values and effect sizes), provide mean ± standard deviation across seeds for all metrics, and supply complete hyperparameter tables plus implementation details for every baseline in the main text or supplementary material. These changes will enable full assessment of reproducibility and reliability. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparisons rest on independent baselines.

full rationale

The paper defines a Complete Musculoskeletal Morphological Evolution Space and reduces it via Spectral Design Evolution (SDE) that applies a bilateral symmetry prior followed by PCA projection onto a low-dimensional manifold. Performance claims rest on direct empirical runs inside the MyoSuite simulator across Walk/Stair/Hilly/Rough tasks, with explicit comparisons to fixed-morphology controllers and standard evolutionary baselines. No equation, parameter fit, or self-citation is shown to define the reported efficiency or stability gains by construction; the manifold is used only as a search-space reduction tool whose adequacy is tested by the same external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The method rests on domain assumptions about symmetry and dimensionality reduction to make the search tractable; no free parameters or invented entities with independent evidence are detailed in the abstract.

axioms (2)
  • domain assumption Bilateral symmetry prior is appropriate for the robot's muscle morphology
    Integrated with PCA to project parameters onto low-dimensional manifold
  • domain assumption Principal component analysis captures the dominant variations needed for task performance
    Enables efficient exploration of the complete muscle parameter space
invented entities (2)
  • Complete Musculoskeletal Morphological Evolution Space no independent evidence
    purpose: Simultaneous evolution of muscle strength, velocity, and stiffness
    New space defined to overcome limitations of single-attribute optimization
  • Spectral Design Evolution (SDE) no independent evidence
    purpose: High-efficiency co-optimization via spectral manifold projection
    Proposed framework to handle exponential growth in exploration space

pith-pipeline@v0.9.0 · 5494 in / 1359 out tokens · 49157 ms · 2026-05-10T14:33:18.258676+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 1 internal anchor

  1. [1]

    Muscle and tendon: properties, models, scaling, and application to biomechanics,

    F. E. Zajac, “Muscle and tendon: properties, models, scaling, and application to biomechanics,”Crit. Rev. Biomed. Eng., vol. 17, no. 4, pp. 359–411, 1989

    work page 1989

  2. [2]

    Optimal feedback control and the neural control of movement,

    S. H. Scott, “Optimal feedback control and the neural control of movement,”Nature Rev. Neurosci., vol. 5, pp. 532–546, 2004

    work page 2004

  3. [3]

    MyoSuite: A platform for biomechanics with deep reinforcement learning,

    V . Caggianoet al., “MyoSuite: A platform for biomechanics with deep reinforcement learning,” inProc. Int. Conf. Mach. Learn. (ICML), 2022

    work page 2022

  4. [4]

    Pfeifer and J

    R. Pfeifer and J. Bongard,How the Body Shapes the Way We Think. MIT Press, 2006

    work page 2006

  5. [5]

    Data-efficient co-adaptation of morphology and control with adaptive inference,

    K. S. Luck, J. Amor, and H. B. Amor, “Data-efficient co-adaptation of morphology and control with adaptive inference,” inProc. IEEE Int. Conf. Robot. Autom. (ICRA), 2020, pp. 2222–2228

    work page 2020

  6. [6]

    Bayesian morphology optimization for musculoskeletal systems,

    J. Zhao, Y . Yang, and H. Liu, “Bayesian morphology optimization for musculoskeletal systems,” inProc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), 2023

    work page 2023

  7. [7]

    Dep-rl: Embodied exploration for reinforcement learning in overactu- ated and musculoskeletal systems,

    P. Schumacher, D. H ¨aufle, D. B ¨uchler, S. Schmitt, and G. Martius, “Dep-rl: Embodied exploration for reinforcement learning in overactu- ated and musculoskeletal systems,”arXiv preprint arXiv:2206.00484, 2022

    work page arXiv 2022

  8. [8]

    Data-driven spectral submanifold reduction for nonlinear optimal control of high- dimensional robots,

    T. Simpson, M. Cenedese, I. Axas, and G. Haller, “Data-driven spectral submanifold reduction for nonlinear optimal control of high- dimensional robots,”IEEE Robot. Autom. Lett., vol. 6, no. 3, pp. 5304– 5311, 2021

    work page 2021

  9. [9]

    Acquiring musculoskeletal skills with a hierar- chical reinforcement learning framework,

    A. S. Chiappaet al., “Acquiring musculoskeletal skills with a hierar- chical reinforcement learning framework,”Neuron, 2024

    work page 2024

  10. [10]

    DynSyn: Dynamical synergistic repre- sentation for efficient learning and control,

    K. He, C. Zuo, and Y . Sui, “DynSyn: Dynamical synergistic repre- sentation for efficient learning and control,” inProc. 41st Int. Conf. Mach. Learn. (ICML), 2024

    work page 2024

  11. [11]

    Diff-muscle: Efficient learning for musculoskeletal robotic table tennis.arXiv preprint arXiv:2603.08617, 2026

    W. Zhao, J. Guo, K. Huang, X. Liu, and H. Liu, “Diff-muscle: Efficient learning for musculoskeletal robotic table tennis,”arXiv preprint arXiv:2603.08617, 2026

    work page arXiv 2026

  12. [12]

    OpenSim: Simulating musculoskeletal dynamics and neuromuscular control,

    A. Sethet al., “OpenSim: Simulating musculoskeletal dynamics and neuromuscular control,”PLoS Comput. Biol., vol. 14, 2018

    work page 2018

  13. [13]

    DeepMimic: Example-guided deep reinforcement learning of physics-based character skills,

    X. B. Penget al., “DeepMimic: Example-guided deep reinforcement learning of physics-based character skills,”ACM Trans. Graph., 2018

    work page 2018

  14. [14]

    Evolving 3D morphology and behavior by competition,

    K. Sims, “Evolving 3D morphology and behavior by competition,” in Artificial Life IV, 1994, pp. 28–39

    work page 1994

  15. [15]

    Embodied intelligence: A synergy of morphology, action, perception and learning,

    H. Liu, D. Guo, and A. Cangelosi, “Embodied intelligence: A synergy of morphology, action, perception and learning,”ACM Comput. Surv., vol. 57, no. 7, pp. 1–36, 2025

    work page 2025

  16. [16]

    Transform2Act: Learning a transform-and-control policy for efficient agent design,

    Y . Yuan, Y . Song, and K. Kitani, “Transform2Act: Learning a transform-and-control policy for efficient agent design,” inProc. 10th Int. Conf. Learn. Represent. (ICLR), 2022

    work page 2022

  17. [17]

    Symmetry-aware robot design with structured subgroups,

    H. Dong, J. Zhang, T. Wang, and C. Zhang, “Symmetry-aware robot design with structured subgroups,” inProc. 40th Int. Conf. Mach. Learn. (ICML), 2023

    work page 2023

  18. [18]

    Competevo: towards morphological evolution from competition,

    K. Huang, D. Guo, X. Zhang, X. Ji, and H. Liu, “Competevo: Towards morphological evolution from competition,”arXiv preprint arXiv:2405.18300, 2024

    work page arXiv 2024

  19. [19]

    BodyGen: Advancing towards efficient embodiment co-design,

    H. Lu, Z. Wu, J. Xing, J. Li, R. Li, Z. Li, and Y . Shi, “BodyGen: Advancing towards efficient embodiment co-design,” inProc. 13th Int. Conf. Learn. Represent. (ICLR), 2025

    work page 2025

  20. [20]

    Proximal Policy Optimization Algorithms

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,”arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Flexing computational muscle: Modeling and simulation of musculotendon dynamics,

    M. Millard, T. Uchida, A. Seth, and S. L. Delp, “Flexing computational muscle: Modeling and simulation of musculotendon dynamics,”J. Biomech. Eng., vol. 135, no. 2, p. 021005, 2013

    work page 2013

  22. [22]

    Combinations of muscle synergies in the construc- tion of a natural motor repertoire,

    G. d’Avellaet al., “Combinations of muscle synergies in the construc- tion of a natural motor repertoire,”Nature Neurosci., vol. 6, 2003

    work page 2003

  23. [23]

    Postural hand synergies for tool use,

    M. Santello, M. Flanders, and J. F. Soechting, “Postural hand synergies for tool use,”J. Neurosci., vol. 18, pp. 10 105–10 115, 1998

    work page 1998

  24. [24]

    MyoSuite: A contact-rich simulation suite for musculoskeletal motor control,

    A. Vittori, V . Caggiano,et al., “MyoSuite: A contact-rich simulation suite for musculoskeletal motor control,” inProc. 5th Conf. Robot Learning (CoRL), 2022

    work page 2022