MSK-Bench: Benchmarking Full-Body Musculoskeletal Motor Control Across Tasks, Control Paradigms, and Physiological Metrics

Control challenge

• Muscle excitation, activation-contraction dynamics, and tendon transmission introduce delayed actuation, redundancy, and complex nonlinear control challenges.These characteristics distinguish musculoskeletal agents from torque-driven humanoids.Source: §I · p. 1

Research gap

• Existing musculoskeletal benchmarks are fragmented across domains and lack at least one of broad whole-body task diversity, contact-rich interaction, or standardized evaluation across control paradigms.The result is uncertainty about which control paradigms work for full-body musculoskeletal agents and under what physical conditions.Source: §I · p. 2

Evaluation motivation

• Task-level success alone can miss unrealistic muscle coordination because multiple muscle patterns can produce similar motion.A controlled comparison found comparable kinematic tracking but larger ground-reaction-force, center-of-pressure, and joint-moment errors for motion-only imitation than kinetics-aware imitation.Source: §I · p. 2

Benchmark contribution

• MSK-Bench evaluates 22 tasks across stabilization, locomotion, and complex interaction, using five control paradigms and metrics for robustness and physiological behavior.Reported physiological metrics include activation cost, joint smoothness, and EMG-envelope similarity.Source: §I · p. 2

Empirical findings

• Controller performance depends on task and metric: imitation priors work on several reference-compatible skills but fail on the tested stair task, while task success does not fully characterize muscle use.Physiology-aware diagnostics reveal that task success and EMG-envelope agreement can vary differently across tasks and control settings.Source: §I · p. 2

Musculoskeletal models and control

• Earlier MSK platforms and methods span anatomically grounded modeling, contact-rich reinforcement learning, physical humanoids, motion imitation, and morphology–control co-design.Arnold uses a compositional sensorimotor vocabulary across 14 tasks and multiple embodiments.Source: §II · p. 2

Benchmarks for embodied motor control

• Existing MSK challenges cover gait, prosthetics, hand manipulation, locomotion, and athletic tracks, while MSK-Bench organizes full-body tasks from postural regulation through contact-rich interaction.Its task–method–metric matrix includes EMG-envelope activation for assessing muscle coordination.Source: §II · p. 3

Learning paradigms for musculoskeletal control

• Musculoskeletal control research includes reward-based RL, physiology-structured action interfaces, agentic reward generation, motion-reference priors, and residual adaptation.MSK-Bench evaluates reward-based RL, agentic reward tuning, latent-action RL, imitation-prior control, and residual adaptation under one task suite.Source: §II · p. 3

Benchmark design

• MSK-Bench spans 22 tasks across stabilization, locomotion, and interaction, comparing five paradigms; only four reward-based baselines form the all-task leaderboard.The four baselines are PPO, SAC, DepRL, and DynSyn-SAC; focused studies cover different task subsets and are reported separately.Source: §III · pp. 3–4

Evaluation protocol

• Evaluation separates effectiveness, robustness, and physiology, measuring success, reward, efficiency, perturbation robustness, activation cost, joint smoothness, and EMG-envelope similarity.EMG-envelope similarity is phase-optimized and reflects waveform shape rather than absolute amplitude or timing.Source: §III · p. 4

T1—Breadth

• DepRL records nonzero success on 22/22 tasks versus DynSyn-SAC on 16/22; DynSyn-SAC has higher mean success, while DepRL leads on interaction and action- and dynamics-robustness scores.DynSyn-SAC has higher observation robustness; these are separately trained task-specific policies, so mean success alone does not characterize performance.Source: §III · p. 5

Complementary diagnostics

• Reward adaptation has no uniform survival advantage: fixed-reward DepRL survives longer under action and observation perturbations, while agentic tuning performs better at larger dynamics-perturbation scales.In the matched reasoner comparison, GPT-6 Astra has better reported point estimates than DeepSeek for survival, tracking RMSE, and activation, yet survival is shorter than fixed-reward DepRL (360 vs. 417 steps).Source: §III · p. 6
• The 128-dimensional latent representation achieves higher returns over the displayed overlapping interval and higher success at several perturbation scales than the 416-dimensional baseline; stronger compression degrades performance.Reconstruction and explained-variance statistics also deteriorate under stronger compression.Source: §III · p. 6, Figure 4 · p. 6

T2—Diagnosis

• Under the matched cross-paradigm diagnostic, MuscleMimic generally exceeds DepRL on stand, jump, walk, and run, but has no stair successes at any tested scale, including zero perturbation.On stairs, absolute-site error rises from 0.35 to 1.31 and root-XYZ error from 0.25 to 0.77 between steps 150 and 300; these errors do not establish the failure cause.Source: §III · p. 7, Figure 5 · p. 7

T3—Physiology-aware evaluation

• The combined residual-adaptation pipeline raises stair success from 0% to 100%, while mean EMG correlation moves only from 0.51 to 0.52, below DepRL’s 0.56.Walking retains 100% SR as selected-muscle correlations change from 0.71/0.69/0.63 to 0.75/0.80/0.67; running improves from 90% to 100% SR and mean EMG correlation from 0.43 to 0.77. The pipeline combines residual corrections, task-objective changes, and reference pacing; component contributions are not isolated.Source: §III · p. 7
• For walking, latent-action RL correlates higher than reward-based RL on biceps femoris (0.95 vs. 0.84) but lower on vastus lateralis (0.21 vs. 0.73).Task-wise joint jerk, load-specific recruitment, and the 700-muscle model’s additional anatomical groups describe motion and muscle use, not human similarity.Source: §III · p. 8, Figure 7 · p. 8

IV. RESIDUAL ADAPTATION CASE STUDY

• A frozen MuscleMimic policy supplies base actions, while a trainable 3-layer MLP supplies bounded residual corrections.The reported residual study also changes task objectives and timing, so results describe the combined pipeline.Source: §IV · p. 8
• Stair adaptation slows reference progression by 50% when planar root error exceeds 0.4 m, excludes vertical displacement from tracking, and targets the reference 1 s ahead.Walking uses residual authority of 0.6 in swing and 0.2 in stance.Source: §IV · p. 8
• Fig. 10 depicts the frozen-prior-plus-correction architecture; its 354d labels exclude hand actuation, and its rewards and reference timing also change.Fig. 8 reports time-averaged activation mass by muscle family, while Fig. 9 contrasts activation mass in 416- and 700-muscle models without establishing greater human similarity.Source: Figure 8 · p. 8, Figure 9 · p. 8, Figure 10 · p. 9
• Walking retains 100% SR while improving selected-muscle correlations; stairs has the largest success gain but only a 0.01 correlation increase over MuscleMimic, below DepRL (0.56).Table V reports EMG means from task-dependent muscle sets and retains training noise in SR.Source: Table V · p. 9, §IV · p. 9
• Running adaptation halves flight-phase tracking penalties, rewards toe-off, and softly penalizes vertical GRF above 2.5× body weight.The study also uses a small L2 residual penalty, cres = −0.02, instead of generic action-rate and activation-cost terms.Source: §IV · pp. 8–9
• The case study uses task-specific diagnosis to motivate adaptation, followed by multi-metric validation.The study frames this as a diagnosis-to-validation sequence rather than a standalone state-of-the-art claim.Source: §IV · pp. 8–9

V. LIMITATIONS AND FUTURE WORK

• Results under evaluated tasks and perturbations establish neither statistical dominance nor direct transfer to unseen embodiments.The benchmark is intended to compare strategies under a unified suite, not claim a universally superior method.Source: §V · p. 9
• Using a fixed 416-muscle humanoid reduces body-design variation, but conclusions may not generalize directly to other anatomical models..Source: §V · p. 9
• EMG analysis covers three tasks with task-dependent lower-limb signal sets, and correlation reflects activation patterns rather than complete biological similarity.The sets comprise three selected walking muscles, 11 running channels, and 12 matched stair muscles.Source: §V · p. 9
• Residual-adaptation gains reflect a combined pipeline of reference priors, learned corrections, reward design, and task-specific adjustments, so component effects are not isolated.Future work includes dexterous manipulation, longer-horizon behaviors, real-world validation, and broader physiological measurements.Source: §V · p. 9

VI. CONCLUSION

• MSK-Bench unifies evaluation of task performance, robustness, activation cost, joint smoothness, and EMG-envelope similarity across 22 tasks.The evaluated results indicate that embodiment-aware exploration and structured actions improve task coverage, while task success alone does not capture muscle-level differences.Source: §VI · p. 9

APPENDIX

• The appendix specifies task variables and evaluation metrics, and documents reward-based baselines, training configurations, and recruitment analyses for the 416- and 700-muscle models.It also describes task-specific success criteria, perturbation robustness, activation cost, joint smoothness, peak-efficiency steps, and EMG-envelope similarity.Source: APPENDIX · p. 16
• Focused-study appendices describe closed-loop agentic reward tuning, direct GPT-6 control, and expert-informed latent-action filtering.The reward-tuning comparison matches learner, architecture, budget, evaluation protocol, and reward-weight constraint; the latent-action encoder-decoder bounds actions near plausible muscle activations.Source: APPENDIX · p. 16
• Other appendices detail muscle-family categorization, residual adaptation, and phase-aligned EMG-envelope comparison with human signals.The residual framework includes task-specific corrections; EMG comparisons use gait-cycle normalization and Pearson correlation.Source: APPENDIX · p. 16
• Future directions include dexterous manipulation, compositional and long-horizon learning, broader EMG validation, and sim-to-real transfer..Source: APPENDIX · p. 16

A. Task Specification

• Figures 11–13 summarize stabilization, representative locomotion, and terrain or object interaction tasks.The biomechanical background motivates examined variables but does not show that benchmark policies reproduce cited mechanisms or human recruitment patterns.Source: A. Task Specification · p. 16
• The specification defines proprioceptive joint positions and velocities, body-part positions and heights, center-of-mass velocity, and relative foot separation.It also defines the horizontal projection of positions and the left-right foot vector.Source: A. Task Specification · p. 16
• Auxiliary posture variables include leg extension, torso and chest directions, pelvis-forward direction, global axes, and forward-yaw deviation.Leg extension is used to enforce upright posture and prevent deep-squatting or kneeling exploits.Source: A. Task Specification · p. 17
• Control and environment variables include current and previous muscle activations, gait phase, local terrain heights, and the relative vector to an upcoming obstacle.The gait phase is observed as (sin ϕ, cos ϕ).Source: A. Task Specification · p. 17
• A survival bonus rewards each step, while mean squared activation regularizes muscle force; supplementary penalties include joint limits.The detailed reward functions and task settings are summarized in Tables VI–VIII, with setup and termination in Tables IX–XI.Source: A. Task Specification · p. 17

B. Evaluation Details

• The evaluation reports quantitative results for stabilization, locomotion, and environmental-interaction tasks, with separate benchmark performance and robustness tables for each task family.The supplied table captions identify Tables XIII–XV as covering those three families; their numeric results are not provided here.Source: B. Evaluation Details · p. 17, Table XIII · p. 25, Table XIV · p. 25

1) Success Rate:

• Success is a task-specific binary evaluator distinct from termination; full-suite task-family and all-task rates are arithmetic means, while nonzero-success coverage counts tasks with observed SR > 0.The four full-suite reward-based baselines share observations, rewards, termination conditions, and evaluation; a native positive solved signal counts as success when available.Source: 1) Success Rate · p. 17

2) Robustness:

• Robustness sweeps perturb actions, observations, or muscle dynamics and score success-versus-scale area, averaged equally across tasks and perturbation types.Action and dynamics scales are (0, 0.05, 0.10, 0.15, 0.20), and observation scales are (0, 0.02, 0.05, 0.08, 0.10). The focused MuscleMimic–DepRL Fig. 5 comparison uses matched within-task conditions, including a less stringent Jump completion condition, and is excluded from full-suite aggregate scores.Source: 2) Robustness · pp. 17–19, B. Evaluation Details · p. 17

3) Activation Cost:

• Activation cost is mean squared muscle activation, interpreted as an effort proxy only for successful, behaviorally comparable policies—not as metabolic energy or evidence of better task performance.Lower activation cost does not by itself establish greater physiological fidelity.Source: 3) Activation Cost · p. 19

4) Joint Smoothness:

• Joint smoothness is measured by logarithmic mean squared jerk from joint angular velocity; lower values indicate fewer high-frequency fluctuations, not human similarity.The second-order finite difference of joint velocity is proportional to the third-order derivative of joint angle.Source: 4) Joint Smoothness · pp. 19, 21

5) Peak Efficiency Steps:

• Peak Efficiency Steps records the evaluated training step with the highest expected evaluation return; fewer steps, particularly with a high maximum return, indicate faster peak skill acquisition.The metric is intended to identify how many environment interactions are needed to reach peak evaluation performance.Source: 5) Peak Efficiency Steps · pp. 21–22

6) EMG Similarity:

• EMG-envelope similarity uses phase-optimized Pearson correlation against matched human references, but normalized, shifted signals do not establish absolute amplitude or timing agreement.Walking, running, and stairs use specified human reference recordings and report selected-muscle or multi-channel correlations; improved task success need not mean improved EMG agreement.Source: 6) EMG Similarity · pp. 22, 24

C. Detailed Descriptions of Reward-Based RL Baselines

• PPO offers stable but unstructured reward-driven exploration that can be sample-inefficient in redundant muscle spaces; SAC uses entropy-driven exploration, while DepRL adds embodiment-grounded sensorimotor exploration.DepRL uses temporal correlations between motor commands and proprioceptive-feedback derivatives to generate coordinated exploratory actions and mitigate stiff co-contractions.Source: C. Detailed Descriptions of… · pp. 24, 26
• DynSyn-SAC [39] combines SAC with a latent synergistic network that groups actuators, maps group-level actions to muscle activations, and schedules weight bounds to stabilize early exploration.The approach also supports muscle-level fine-tuning and is described as accelerating sample efficiency in high-dimensional musculoskeletal models.Source: C. Detailed Descriptions of… · p. 27

1) Training and Checkpoint Protocol:

• Released configs use seed 0, with PPO/SAC using 8 training and 2 evaluation environments, DepRL 16 training environments, and DynSyn-SAC 64 training environments.Selected checkpoints are evaluated for 50 episodes per task under shared criteria, not selected by success rate; off-policy collection steps represent multiple scalar transitions.Source: 1) Training and Checkpoint Protocol · p. 27

D. Detailed Muscle Activation Analysis: 416 vs. 700 Muscle Models

• Time-step resolved muscle activation heatmaps are presented for recorded powerlift motions in the 416- and 700-muscle models.Source: D. Detailed Muscle Activation… · p. 27
• Anatomical resolution affects muscle-use diagnostics, with upper-limb and axial activation differing between the 416- and 700-muscle models.The 700-muscle model adds neck, deep-trunk, and deep-scapular groups, expanding the recruitment pathways available for inspection.Source: D. Detailed Muscle Activation… · p. 27
• The observed recruitment differences do not establish improved human similarity, clinically correct force transfer, or a causal explanation.Source: D. Detailed Muscle Activation… · p. 27

• Agentic Reward Tuning periodically refines reward weights from recent gait quality, balance stability, and task-progress statistics.A reasoning module analyzes the statistics and returns updated weights during rollout.Source: E. Agentic Reward Tuning · p. 27
• When forward speed is low or posture becomes hunched, the tuning module increases the corresponding velocity-tracking or uprightness and anti-hunching weights.Source: E. Agentic Reward Tuning · p. 27
• The matched reasoner comparison holds the DepRL learner, architecture, training budget, evaluation, and L1 weight norm fixed while comparing DeepSeek-V4-Flash and GPT-6 Astra.The constrained comparison reports survival, tracking RMSE, and activation, distinct from the original unnormalized coefficient-update study.Source: E. Agentic Reward Tuning · p. 27
• Reported point estimates show metric-dependent trade-offs rather than a uniform benefit from reward adaptation.Source: E. Agentic Reward Tuning · p. 30

F. Direct GPT-6 Control: Experimental Details

• GPT-6 receives static environment metadata and a lossless serialization of the 2,418-dimensional policy observation, without access to privileged diagnostics, rendered frames, or future states beyond policy-visible look-ahead features.Source: F. Direct GPT-6 Control: Experimental… · p. 30
• Each accepted GPT-6 response contains 354 finite numeric values within [-1, 1], applied as the complete muscle-excitation command without clipping, smoothing, or baseline-action addition.Source: F. Direct GPT-6 Control: Experimental… · p. 30
• The runner resets with seed 0, replays committed actions, and holds each accepted action for 20 native control steps before exporting the next observation.Termination and the fall gate are checked after every native step; reported metrics use the prefix through the first fallen sample.Source: F. Direct GPT-6 Control: Experimental… · p. 30
• Direct-control divergence is the first five-sample run whose GPT tracking error exceeds the reference error's 95th percentile, with no divergence reported if that condition never occurs.The reference rollout defines the criterion only; its performance is not included as a direct-control result.Source: F. Direct GPT-6 Control: Experimental… · p. 30

G. Latent-Action RL

• In hard mode, policy actions are filtered into a bounded tube around the expert-informed action, while a decaying deviation penalty relaxes guidance as training progresses.The fixed-radius constraint permits local exploration around the anatomical prior; the penalty is strongest early in training.Source: G. Latent-Action RL · pp. 30–31
• Latent-Action RL pretrains an encoder-decoder by behavior cloning, encoding expert muscle actions as latent intent and decoding actions from that intent and musculoskeletal features.The decoder conditions on muscle priors, muscle states, and the muscle-joint moment matrix.Source: G. Latent-Action RL · p. 31

H. EMG Data Processing and Comparative Analysis

• Simulated and human EMG profiles are normalized to gait cycles, resampled to 101 points, averaged across cycles when available, and cyclically shifted to maximize Pearson correlation.The resulting correlation measures phase-optimized envelope-shape agreement, not absolute timing or amplitude fidelity.Source: H. EMG Data Processing and Comparative… · p. 32

I. Muscle Recruitment Categorization

• Recruitment analysis groups the 416 actuators by anatomical-family name keywords and sums each family's time-averaged muscle activations.The unclassified group's activation mass is monitored as a check that the predefined categories cover most meaningful activity.Source: §I · p. 32

J. Detailed Descriptions of Residual RL Policy

• Residual stair and locomotion results characterize combined residual corrections, task-objective changes, and reference pacing, without isolating each component's contribution.Stair tracking divergence alone does not identify the cause of failure.Source: J. Detailed Descriptions of Residual… · p. 32

1) Action Space and Residual Scaling:

• The residual policy adds a scaled, clipped residual to the frozen base-policy action, then clips the blended command to the environment action range.Standard action-rate and activation-cost penalties are disabled in this setup, while minimal L2 regularization on the residual action is retained.Source: 1) Action Space and Residual Scaling · p. 33

2) Adaptations for Stair Navigation:

• For stairs, the imitation objective masks vertical root-position error, reference pacing slows by 50% when planar deviation exceeds 0.4 m, and a task-progress reward supplements imitation.The height-invariant error is intended to let the humanoid step onto elevated platforms without catastrophic tracking-reward drops.Source: 2) Adaptations for Stair Navigation · p. 33

3) Walking Adaptation:

• Walking uses phase-dependent residual authority, with base ratios of 0.2 during stance and 0.6 during swing, plus activation-magnitude and temporal-change regularization.The regularization targets high-frequency, non-functional muscle twitches; task success and human-reference agreement are evaluated separately.Source: 3) Walking Adaptation · pp. 33–34

4) Adaptations for High-Impact Locomotion (Run Task):

• For running, the method relaxes tracking penalties by 50% during flight and adds a propulsive-velocity reward, while penalizing vertical ground-reaction forces above 2.5 times body weight.The impact penalty is intended to encourage active shock absorption before touchdown.Source: 4) Adaptations for High-Impact… · p. 34

1) Absence of Dexterous Manipulation:

• The benchmark focuses on gross motor skills and lacks fine-grained hand tasks such as in-hand manipulation, tool use, and precise grasping.Adding high-fidelity hand models would support study of coupling between gross arm motion and fine finger manipulation.Source: 1) Absence of Dexterous Manipulation · p. 34

2) Transitioning to Compositional and Long-Horizon Tasks:

• Evaluations use isolated, single-objective tasks rather than compositional behaviors that require transitions between skills over long horizons.The discussion gives walking toward a chair, picking up a barbell, and performing a seated lift as an example.Source: 2) Transitioning to Compositional and… · p. 34

3) Constraints in Comprehensive Physiological Validation:

• Physiological validation covers selected lower-limb muscles during walking, running, and stairs, and its normalized, phase-optimized correlation measures envelope shape rather than complete biological similarity.The authors attribute this scope limit to scarce open-source EMG datasets for dynamic or unconventional tasks.Source: 3) Constraints in Comprehensive… · pp. 34–35

4) Sim-to-Real Gap and Hardware Validation:

• All benchmark evaluations are simulated, leaving sensor noise, communication latency, and unmodeled actuator dynamics outside the tested setting.The authors identify physical-hardware validation as a future direction and note the difficulty of building and maintaining tendon-driven robots.Source: 4) Sim-to-Real Gap and Hardware… · p. 35