Motion Control of High-Dimensional Musculoskeletal Systems with Hierarchical Model-Based Planning

Shanning Zhuang; Vincent Zhuang; Yanan Sui; Yunyue Wei

REVIEW 4 major objections 7 minor 21 references

Motion Control of High-Dimensional Musculoskeletal Systems with Hierarchical Model-Based Planning

T0 review · 4 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Zero-shot MPC controls a 700-muscle whole-body human model without any training.

desk verdict A real zero-shot MPC result for 700-muscle control, but the low-level inverse law is under-derived and the speed claim overstates. read the letter →

arxiv 2505.08238 v1 pith:YXEEHNSG submitted 2025-05-13 cs.RO

Yunyue Wei , Shanning Zhuang , Vincent Zhuang , Yanan Sui This is my paper · ORCID

classification cs.RO

keywords modelpredictivecontrolmusculoskeletalsystemszero-shothierarchicalsampling-basedMPCwhole-bodyhumanoidcostfunctionoptimizationoveractuated

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that high-dimensional musculoskeletal control does not require reinforcement learning: a hierarchical, model-based planner can achieve stable whole-body motion in minutes instead of days. The proposed $MPC^{2}$ splits the problem into high-level posture planning and low-level muscle coordination. A sampling-based model predictive controller plans a 37-dimensional target posture, and a morphology-aware proportional controller translates that posture into 700 individual muscle commands. The authors demonstrate stable zero-shot standing, walking on flat, rough, sloped, and stair terrain, and sports imitation on a whole-body human model, where state-of-the-art DRL baselines need at least a day to train. The fast planning loop also enables automatic cost-function tuning by black-box optimization, reducing human reward engineering.

What carries the argument

The load-bearing mechanism is the two-level hierarchy: a model predictive position controller that samples and optimizes a 37-dimensional target posture (the major joint coordinates), and a morphology-aware proportional controller that computes target muscle lengths, converts them to actuator forces, and inverts the first-order activation dynamics to produce neural-excitation commands. The proportional gains are not constant; they are scaled by the absolute value of the Jacobian columns relating each actuator to the planned posture change, as in Eq. (11). This Jacobian-based gain schedule lets the low level automatically prioritize the muscles most relevant to the current posture and motion phase, which the paper identifies as the reason the high-level planner can operate in a drastically reduced action space.

What would settle it

Replace the one-step inverse law (Eq. (10)) with a numerically stable inversion of the first-order activation ODE (for example an implicit Euler solve), keeping every other component fixed. If walking distance collapses toward the MPPI baseline or stand time drops sharply, then the single-step inversion is load-bearing. A direct check is to log per-muscle activation error over a ten-second stand: if most actuators miss their target activation by more than a few percent each step, the one-step inversion is not actually holding.

Watch

Extended reading notes

Core claim

$MPC^{2}$ achieves stable zero-shot control of the 700-actuator MS-Human-700 whole-body musculoskeletal model across standing, terrain walking, and sports imitation, without any training procedure. The method plans only a low-dimensional target posture, then uses a proportional controller whose per-muscle gains are set from the muscle Jacobian, so that 700 actuators are coordinated implicitly rather than individually commanded. The paper further shows that this controller continues to walk when major muscles in one leg are suddenly disabled, tolerates large external perturbations, transfers zero-shot to an ostrich musculoskeletal model with the same cost function, and produces a walking gait with over 75% lower summed muscle activation than a DRL baseline. The central empirical claim is that hierarchical model-based planning can replace day-scale learning with minute-scale, near-real-time control in over-actuated systems.

Load-bearing premise

The controller can reliably compute, in a single control step, the neural excitation that makes each muscle produce the commanded force, even though the printed inverse formula in Eq. (10) is dimensionally inconsistent and no derivation is shown.

Editorial extensions

If this is right

Control generation for new tasks drops from at least a day of DRL training to about two minutes, so cost functions can be iterated automatically via Bayesian optimization within hours.
The same controller and cost function transfer zero-shot across morphologies, demonstrated on the ostrich model, suggesting that the hierarchy captures something morphology-invariant.
Over-actuation becomes a robustness feature: sudden loss of key muscles is absorbed by the remaining actuators without retraining.
Because the planner is training-free, the method could be deployed in settings where tasks and cost functions change frequently, where DRL's training cost would be prohibitive.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 37-dimensional posture abstraction suggests a general recipe for other high-dimensional over-actuated systems: find a task-relevant low-dimensional manifold (not necessarily joint positions) and a Jacobian-style map from actuators to that manifold.
If the Jacobian-based gain schedule is the core ingredient, a cheaper approximation using only posture-dependent muscle moment arms might suffice on physical hardware where exact muscle Jacobians are uncertain.
The near-real-time claim depends on fast parallel rollouts in simulation; transferring to real hardware would likely require replacing the exact dynamics with a learned model, and robustness under model error could degrade.
The large reduction in summed muscle activation compared with the DRL baseline hints that learned muscle coordination may be over-activating; this is testable experimentally by comparing EMG-like activation sums in the produced gaits.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: MPC^2 is a genuine empirical advance — training-free MPC controlling a 700-muscle human model for standing, walking, slopes, stairs, and sports imitation — but the paper's low-level actuator inversion (Eq. 10) is un-derived and poorly presented, and the speed claims are overstated. I'd take the zero-shot results seriously, but I'd want the low-level law clarified and validated before citing the mechanism as fact.

What's actually new: the hierarchical recipe — sampling-based MPC over 37 posture dimensions plus a Jacobian-scaled proportional controller that maps posture error to 700 muscle commands — looks sensible, and the ablations earn their keep. Instant rollouts help in the lean-back recovery test, and morphology-aware gains beat constant-gain and PD variants. The terrain, perturbation, muscle-failure, ostrich, and arm results are a broad empirical package, and the 2-minute versus day-long comparison with DynSyn is a real advantage for reward-function iteration.

The soft spots are concentrated around Eq. (10). As printed, it is dimensionally ambiguous; the intended expression is almost certainly u* = a + τ2(a*-a)/(Δt − τ1(a*-a)), and the paper gives no derivation. More substantively, the derivation uses the simplified activation dynamics of Eq. (2), not the MuJoCo muscle model in Appendix A, which has a sign-dependent time constant. The paper never reports activation-tracking error, so the one bridge from planned posture to 700 muscle activations is unverified. That is a genuine gap, not a nitpick. The near-real-time language is also optimistic given the main thread runs at 20% real-time speed (1% for soccer), and the 'no previous methods' claim would need a more systematic comparison to back. No code or data accompanies the paper.

The central empirical claim — that this controller stabilizes a high-dimensional musculoskeletal model zero-shot — is plausible and consistent with the videos and quantitative walk distances. The missing derivation and tracking validation are addressable. This paper deserves serious peer review; I would send it out, and ask the authors to derive Eq. (10) properly, show activation tracking, and recalibrate the speed claims.

If you're deciding whether to engage: if you work in musculoskeletal control or model-based RL, yes, read it and probably cite the empirical result. Just don't rely on the low-level inverse law as stated.

Referee Report

4 major / 7 minor

Summary. The paper proposes MPC^2, a hierarchical model-based controller for high-dimensional musculoskeletal systems. A high-level sampling-based MPC (MPPI with 'instant rollouts') plans a sequence of target postures in a low-dimensional joint space (37 dimensions for the 700-muscle human model), while a morphology-aware proportional controller maps the target posture to per-muscle activation commands using Jacobian-scaled gains. The authors report zero-shot standing, walking over flat/rough/sloped/stair terrains, sports imitation, and control of an ostrich and an arm model, all without training, plus automated cost-function tuning via Bayesian optimization. Ablations support the instant-rollout and morphology-aware-gain components, and comparisons are made against DRL (DynSyn) and various MPC baselines.

Significance. If the empirical claims hold, this is a substantial advance: a training-free, model-based controller matching or exceeding the task coverage of DRL methods that require days of training on a 700-actuator musculoskeletal model. The hierarchical decomposition is clean and the ablation study gives evidence for both main components. The black-box cost-function optimization is a practical and timely contribution. However, the paper's strongest claims rest on the low-level actuator inversion in Eq. (10), which is under-derived and untested against the actual MuJoCo muscle dynamics, and the flagship empirical results are not backed by quantitative metrics for most tasks. With the requested clarifications and added evidence, the contribution would merit publication.

major comments (4)

[§4.2, Eq. (10)] Equation (10) is the only mechanism that converts the planned high-level posture into muscle activations, yet it is introduced with 'we are able to derive' and no derivation is given. As printed, the expression is ambiguous: a literal reading of 'u* = a + τ2(a*−a) Δt − τ1(a*−a)' is dimensionally inconsistent (the first fractional term is dimensionless while τ1(a*−a) has units of time). If the intended formula is u* = a + τ2(a*−a)/(Δt − τ1(a*−a)), please derive it from Eq. (2) and state the assumptions. More substantively, the actual MuJoCo activation dynamics in Appendix A use τ(u,a) = τ_act(0.5+1.5a) for u>a and τ_deact/(0.5+1.5a) for u≤a, which is not the simplified form in Eq. (2); the paper does not report the values of τ1 and τ2, does not specify how u* is clipped to [0,1], and provides no activation-tracking error data. Because this inverse law is the sole bridge between the 37-dimensional posture plan and the 700 muscle controls, the central zero-shot claim depends on an untested and underspecified low-level law. Please add the derivation, the exact parameter values and clipping, and a one-step tracking experiment, or show that residual tracking errors are absorbed by the high-level MPC loop.
[§4.2, Eq. (11)] The definition of the gain vector K is ambiguous. In the text K is described as a per-actuator vector (k1,...,k_du), but the right-hand side of Eq. (11) as written appears to be a scalar (a sum over joints of a product involving the Jacobian column). If col_i(J_m) is a vector over actuators, then the notation 'col_i(J_m) · [z*_i − M_pos(s_t)_i]' mixes a vector with a scalar; please make explicit how each per-actuator gain k_j is extracted from the Jacobian. In addition, the scalar k̄ is the only free low-level controller parameter, but its value is never reported. The paper should state the chosen k̄ and provide a sensitivity analysis to show that the results do not hinge on a narrow range of this parameter.
[§5.1 and Table 1] The central empirical claim is stable zero-shot control across Stand, Walk, Rough, Slope, and Stair, but only qualitative statements and videos are provided for most tasks. No numerical success criteria, failure counts, or distance/speed metrics are reported for the terrain tasks, and the performance metric plotted in Figure 5 is not defined in the text. Table 1 reports walking distance for MPC^2 and six MPC baselines, but this table is not analyzed in the main text. Please define the evaluation metrics, report means and standard errors over multiple seeds for every task, and state whether 'stable control' is a thresholded criterion. Without this, the flagship claim cannot be verified quantitatively.
[§5.1 and Abstract] The abstract and contribution list describe the method as achieving 'near-real-time' control, but the reported simulation conditions are 20% of real-time speed in the main thread (10% for Stair and 1% for soccer), meaning the method is 5–100 times slower than real time depending on the task. The claim that 'control sequences to complete the task can be generated within 2 minutes' is not equivalent to near-real-time if the simulated task itself takes 50 seconds or more at 20% speed. Please either revise the wording to reflect the actual wall-clock latency per control step or report the per-step planning latency separately from the simulation speed.

minor comments (7)

[§4.2] The statement that the target actuator length l* 'can be computed with model forward dynamics' is imprecise; actuator length is a kinematic function of joint positions, not of forward dynamics. Please use the term 'forward kinematics' or 'muscle path geometry'.
[Appendix B] In the Walk task definition, the cost is labeled 'Cstand' rather than 'Cwalk', and the expression 'Cstand = 100(Cheight + Cupright + Cbalance + 10Cvf + 10Cvdir + 100Cbf + 5Cjp + 50Cfc' is missing a closing parenthesis; the same missing parenthesis appears in several other task definitions.
[Appendix A] The normalization 'a = 1/(1 + e^{−5(a−0.5)})' uses the symbol a on both sides; presumably the left-hand side is the normalized control input and the right-hand side uses the raw policy output. Please clarify the notation, since as written it is self-referential.
[Algorithm 1] The notation 'R_MP(z, H)' in Algorithm 1 and Eq. (8) is not explicitly defined; please state that it denotes the H-step cumulative cost under the low-level policy π_MP.
[§5.4] There is a typo in the opening sentence: 'morphology-aware proposition controller' should be 'morphology-aware proportional controller'.
[Figure 5] The axes of Figure 5(a) and 5(b) are not labeled in the text or caption; please specify what quantity is plotted against clock time (e.g., forward displacement, balance cost, or walking speed).
[Appendix C.1] The phrase 'Following the implementation in sh MPC' appears to reference a baseline or prior work without a citation; please provide the reference or remove the incomplete name.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the zero-shot control claim is an empirical benchmark result, and the author-overlapping references (model and DynSyn baseline) are not load-bearing for the derivation.

full rationale

MPC^2's core claim is an empirical, benchmarked control result rather than a derivation that collapses into its inputs. The high-level planner (Sec. 4.1, Eq. 8) optimizes a target posture z under a task cost, and the low-level law (Sec. 4.2, Eqs. 9-11) is a proportional inversion of the actuator model in Eq. 2; neither step is defined in terms of the quantities it is later said to predict. The scalar gain k-bar in Eq. 11 is a controller parameter, not a fitted target, and no fitted quantity is renamed as a prediction. The only author-overlapping references are the MS-Human-700 model (Zuo et al., 2024) and the DynSyn baseline (He et al., 2024); both enter as an experimental asset and a comparison baseline, and their correctness is not used to justify MPC^2's stability claim. The paper is self-contained against external baselines (MPPI, MJPC solvers, and DRL methods), so the standing/walking/sports-imitation claims stand or fall on the reported simulations rather than on a self-citation chain. I did flag Eq. (10) as a limitation: it is introduced with 'we are able to derive' but no derivation is shown, it is printed in a dimensionally ambiguous form, and its one-step activation tracking is not validated against the MuJoCo dynamics in Appendix A. That is a correctness and robustness gap, not circularity, because it does not make the empirical result equal to an input by construction. Overall, the paper falls in the non-circular 0-2 range; I assign 1 for the presence of minor non-load-bearing self-citations.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a handful of unverified controller-level choices: the hand-tuned gain scale k̄, per-task hand-designed cost weights, the correctness of the inverse actuator control law Eq (10), and the assumption that planning with the exact simulation model (f̂=f) transfers to the stated claims. No new physical entities are introduced.

free parameters (4)

k̄ (gain scaling parameter) = not reported
Eq (11) scales all per-actuator proportional gains by a single scalar. It determines overall muscle force magnitude and is critical for balance; the paper does not report its value or a sensitivity study.
Task cost weights = e.g., 100, 10, 0.01 in Appendix B
Each task in Appendix B uses hand-selected weights for height, upright, balance, velocity, and joint terms. These are design choices that the paper optimizes via Bayesian optimization only for soccer and walking speed.
MPC rollout hyperparameters = N=64, N̄=10, H=0.3s, r=1; λ, m, σ not specified
Algorithm 1 sets iteration 1 and 64 rollouts, but the MPPI temperature λ, elite count m, and initial sampling variance σ are required to reproduce the controller and are not reported.
Desired height and velocity targets = Htarget in {1.5, 1.55}, vtarget in {0, 0.5, 1}
These per-task parameters in Appendix B define the task objectives and are hand-specified.

assumptions (5)

domain assumption The exact model dynamics are available, f̂ = f (Sec 4, item 1)
The paper explicitly relies on simulation with accessible exact dynamics. If model error is significant, the zero-shot claim is not established beyond the noise tests in Appendix C.1.
domain assumption The 37 major joint coordinates captured by M_pos fully characterize the relevant posture
The high-level planner optimizes only these 37 positions (Sec 4.1). If some task-critical degree of freedom is omitted, the planner cannot influence it.
ad hoc to paper The inverse actuator control law Eq (10) correctly drives muscle activation to the target in one control step
The formula is stated without derivation and appears dimensionally inconsistent as printed; the low-level controller depends on it.
standard math MPPI update rule (Eq 6) with elite samples yields good posture targets
Sampling-based MPC is a standard tool; the update is assumed to converge to a reasonable cost minimum within one iteration.
ad hoc to paper Proportional control on muscle length with Jacobian-scaled gains is sufficient for stable interaction with the ground and contacts
This is the core low-level design; it is validated empirically in Sec 5.4 but not derived from stability theory.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Motion Control of High-Dimensional Musculoskeletal Systems with Hierarchical Model-Based Planning." pith.science (2026). https://pith.science/paper/YXEEHNSG

@misc{pith2026250508238,
  author       = {Pith},
  title        = {Pith review of: Motion Control of High-Dimensional Musculoskeletal Systems with Hierarchical Model-Based Planning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YXEEHNSG}},
  note         = {Machine review of arXiv:2505.08238}
}

read the original abstract

Controlling high-dimensional nonlinear systems, such as those found in biological and robotic applications, is challenging due to large state and action spaces. While deep reinforcement learning has achieved a number of successes in these domains, it is computationally intensive and time consuming, and therefore not suitable for solving large collections of tasks that require significant manual tuning. In this work, we introduce Model Predictive Control with Morphology-aware Proportional Control (MPC^2), a hierarchical model-based learning algorithm for zero-shot and near-real-time control of high-dimensional complex dynamical systems. MPC^2 uses a sampling-based model predictive controller for target posture planning, and enables robust control for high-dimensional tasks by incorporating a morphology-aware proportional controller for actuator coordination. The algorithm enables motion control of a high-dimensional human musculoskeletal model in a variety of motion tasks, such as standing, walking on different terrains, and imitating sports activities. The reward function of MPC^2 can be tuned via black-box optimization, drastically reducing the need for human-intensive reward engineering.

Figures

Figures reproduced from arXiv: 2505.08238 by the authors.

**Figure 1.** Movement control of whole-body human musculoskeletal system over a diverse set of motion control tasks. The videos of the control performances are on the project page. 1 INTRODUCTION High-dimensional nonlinear dynamical systems are prevalent in the real world, with important examples including biological musculoskeletal systems. The system complexity laid the foundation of flexible motion due to their over-actuated… view at source ↗

**Figure 2.** Workflow of Model Predictive Control with Morphology-aware Proportional Control [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Control sequences of MPC2 in (a) Stand, (b) Rough, (c) Walk, (d) Slope and (e) Stair (f) Ostrich walk tasks. The simulation speed of Stair task is set to 10% due to slower contact computation. number r of MPC2 to 1 for rapid response to the changing states in the main thread, and sample 64 rollouts (containing N¯ = 10 instant rollouts) across a 0.3s horizon during each round of planning. Unless otherwise noted, the … view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Walking control under sudden muscle failure. (a) Illustration of muscle injury. (b) Control [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Control performance versus clock time of (a) Stand task, and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Dexterous manipulation sequences of MPC2 over arm musculoskeletal model. Comparison to RL and MPC baselines. In the Stand and Walk tasks, we compared the control performance of MPC2 with the current state-of-the-art DRL-based algorithms, DynSyn (He et al., 2024), wh…

**Figure 7.** Figure 7: Control sequences of MPC2 in soccer sports imitation. The simulation speed is set to 1% for more frequent planning for rapidly changing motion, where the entire control sequence is learned within 4 minutes. reduces muscle activation by over 75% compared to DynSyn. We a…

**Figure 8.** Figure 8: Analysis of MPC2 . Results show the mean performances with one standard error over 20 trials. (a) Control performance of lean backward standing, with initial position shown on the left. Blue axis indicates the vertical direction. (b) Control performance of the Walk tas…

**Figure 9.** Figure 9: Performance of MPC2 under uncertain planning model from 0.79 m/s to 1.24m/s, and the walking speed of the ostrich from 0.90 m/s to 2.08m/s without manual tuning. (a) Soccer (b) Human Walk (c) Ostrich Walk [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

**Figure 10.** Figure 10: Cost function optimization C.4 CENTER OF MASS POLYGON SUPPORT In the Video W16-W17, we plot the centre of mass polygon support during walking for MPC2 and DynSyn. We observe that MPC2 is able to maintain larger polygon support compared to DynSyn, enhancing the stabili…

**Figure 11.** Figure 11: Automatic cost function design for improving the walking speed. (a) Optimized control [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

21 extracted references · 9 canonical work pages

[2]

Henri-Jacques Geiß, Firas Al-Hafez, Andre Seyfarth, Jan Peters, and Davide Tateo

URL https://arxiv.org/abs/2312.07340. Henri-Jacques Geiß, Firas Al-Hafez, Andre Seyfarth, Jan Peters, and Davide Tateo. Exciting ac- tion: Investigating efficient exploration for learning musculoskeletal humanoid locomotion.arXiv preprint arXiv:2407.11658,

arXiv
[4]

Taylor Howell, Nimrod Gileadi, Saran Tunyasuvunakool, Kevin Zakka, Tom Erez, and Yuval Tassa

URL https://arxiv.org/abs/2407.11472. Taylor Howell, Nimrod Gileadi, Saran Tunyasuvunakool, Kevin Zakka, Tom Erez, and Yuval Tassa. Predictive sampling: Real-time behaviour synthesis with mujoco,

arXiv
[7]

Ostrichrl: A musculoskeletal ostrich simulation to study bio- mechanical locomotion

Vittorio La Barbera, Fabio Pardo, Yuval Tassa, Monica Daley, Christopher Richards, Petar Kor- mushev, and John Hutchinson. Ostrichrl: A musculoskeletal ostrich simulation to study bio- mechanical locomotion. arXiv preprint arXiv:2112.06061,

arXiv
[10]

MuJoCo MPC for Humanoid Control: Evaluation on HumanoidBench

Moritz Meser, Aditya Bhatt, Boris Belousov, and Jan Peters. Mujoco mpc for humanoid control: Evaluation on humanoidbench. arXiv preprint arXiv:2408.00342,

work page Pith review arXiv
[12]

Yuval Tassa, Tom Erez, and Emanuel Todorov

URL https://arxiv.org/abs/2206.00484. Yuval Tassa, Tom Erez, and Emanuel Todorov. Synthesis and stabilization of complex behaviors through online trajectory optimization. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4906–4913. IEEE,

arXiv 2012
[14]

Caggiano Vittorio, Wang Huawei, Durandau Guillaume, Sartori Massimo, and Kumar Vikash

doi: 10.1109/IROS.2012.6386109. Caggiano Vittorio, Wang Huawei, Durandau Guillaume, Sartori Massimo, and Kumar Vikash. Myosuite – a contact-rich simulation suite for musculoskeletal motor control. https: //github.com/myohub/myosuite,

arXiv 2012
[15]

URL https://arxiv.org/abs/2205. 13600. Grady Williams, Paul Drews, Brian Goldfain, James M. Rehg, and Evangelos A. Theodorou. Ag- gressive driving with model predictive path integral control. In 2016 IEEE International Con- ference on Robotics and Automation (ICRA) , pp. 1433–1440,

work page 2016
[17]

Language to rewards for robotic skill synthesis

Wenhao Yu, Nimrod Gileadi, Chuyuan Fu, Sean Kirmani, Kuang-Huei Lee, Montse Gonzalez Are- nas, Hao-Tien Lewis Chiang, Tom Erez, Leonard Hasenclever, Jan Humplik, et al. Language to rewards for robotic skill synthesis. arXiv preprint arXiv:2306.08647,

arXiv

Show all 21 references

[18]

Self model for embodied intelligence: Mod- eling full-body human musculoskeletal system and locomotion control with hierarchical low- dimensional representation

Chenhui Zuo, Kaibo He, Jing Shao, and Yanan Sui. Self model for embodied intelligence: Mod- eling full-body human musculoskeletal system and locomotion control with hierarchical low- dimensional representation. In 2024 IEEE International Conference on Robotics and Automation (...

2024
[19]

The input control signal of muscle- tendon units is the neural excitation, denoted as u

12 Published as a conference paper at ICLR 2025 A N EURO -MUSCLE DYNAMICS We use the muscle-tendon units in MuJoCo as our actuator. The input control signal of muscle- tendon units is the neural excitation, denoted as u. The muscle activation, denoted as act, is calcu- lated b...

2025
[20]

As shown in Video W14-W15, starting with same cost function terms and weights as human walk- ing, we utilized Bayesian optimization in weight tuning, improving the walking speed of the human 1https://github.com/google-deepmind/mujoco_mpc/tree/main/mjpc/tasks/ allegro 2https://...

2023
[21]

2 Train frequency (steps) 1 Gradient steps 4 Target update interval 1 Environment number 112 Entropy coeff

17 Published as a conference paper at ICLR 2025 Algorithm Parameter Task Stand Walk SAC Learning rate linear schedule(0.001) Batch size 256 Buffer size 1e6 Warmup steps 100 Discount factor 0.98 Soft update coeff. 2 Train frequency (steps) 1 Gradient steps 4 Target update inter...

2025
[2012]

Mujoco: A physics engine for model-based control

Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems , pp. 5026–5033,

2012
[2013]

Genera- tive gaitnet

Jungnam Park, Sehee Min, Phil Sik Chang, Jaedong Lee, Moon Seok Park, and Jehee Lee. Genera- tive gaitnet. In ACM SIGGRAPH 2022 Conference Proceedings, pp. 1–9,

2022
[2016]

doi: 10.1109/ICRA.2016. 7487277. David A Winter. Biomechanics and motor control of human gait: normal, elderly and pathological

2016 doi
[2018]

Contact-implicit mpc: Controlling diverse quadruped motions without pre-planned contact modes or trajectories

Gijeong Kim, Dongyun Kang, Joon-Ha Kim, Seungwoo Hong, and Hae-Won Park. Contact-implicit mpc: Controlling diverse quadruped motions without pre-planned contact modes or trajectories. arXiv preprint arXiv:2312.08961,

arXiv
[2019]

Learning to learn faster from human feedback with language model predictive control.arXiv preprint arXiv:2402.11450,

11 Published as a conference paper at ICLR 2025 Jacky Liang, Fei Xia, Wenhao Yu, Andy Zeng, Montserrat Gonzalez Arenas, Maria Attarian, Maria Bauza, Matthew Bennice, Alex Bewley, Adil Dostmohamed, et al. Learning to learn faster from human feedback with language model predicti...

2025 arXiv
[2021]

Optimal weight adaptation of model predictive con- trol for connected and automated vehicles in mixed traffic with bayesian optimization

Viet-Anh Le and Andreas A Malikopoulos. Optimal weight adaptation of model predictive con- trol for connected and automated vehicles in mixed traffic with bayesian optimization. In 2023 American Control Conference (ACC), pp. 1183–1188. IEEE,

2023
[2022]

Ping Hsu, John Mauser, and Shankar Sastry

URL https: //arxiv.org/abs/2212.00541. Ping Hsu, John Mauser, and Shankar Sastry. Dynamic control of redundant manipulators. Journal of Robotic Systems, 6(2):133–148,

arXiv
[2023]

Sar: Generalization of physiological agility and dexterity via synergistic action representation

Cameron Berg, Vittorio Caggiano, and Vikash Kumar. Sar: Generalization of physiological agility and dexterity via synergistic action representation. arXiv preprint arXiv:2307.03716,

arXiv
[2024]

Td-mpc2: Scalable, robust world models for contin- uous control

Nicklas Hansen, Hao Su, and Xiaolong Wang. Td-mpc2: Scalable, robust world models for contin- uous control. arXiv preprint arXiv:2310.16828,

arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [2]

Henri-Jacques Geiß, Firas Al-Hafez, Andre Seyfarth, Jan Peters, and Davide Tateo

URL https://arxiv.org/abs/2312.07340. Henri-Jacques Geiß, Firas Al-Hafez, Andre Seyfarth, Jan Peters, and Davide Tateo. Exciting ac- tion: Investigating efficient exploration for learning musculoskeletal humanoid locomotion.arXiv preprint arXiv:2407.11658,

arXiv

[2] [4]

Taylor Howell, Nimrod Gileadi, Saran Tunyasuvunakool, Kevin Zakka, Tom Erez, and Yuval Tassa

URL https://arxiv.org/abs/2407.11472. Taylor Howell, Nimrod Gileadi, Saran Tunyasuvunakool, Kevin Zakka, Tom Erez, and Yuval Tassa. Predictive sampling: Real-time behaviour synthesis with mujoco,

arXiv

[3] [7]

Ostrichrl: A musculoskeletal ostrich simulation to study bio- mechanical locomotion

Vittorio La Barbera, Fabio Pardo, Yuval Tassa, Monica Daley, Christopher Richards, Petar Kor- mushev, and John Hutchinson. Ostrichrl: A musculoskeletal ostrich simulation to study bio- mechanical locomotion. arXiv preprint arXiv:2112.06061,

arXiv

[4] [10]

MuJoCo MPC for Humanoid Control: Evaluation on HumanoidBench

Moritz Meser, Aditya Bhatt, Boris Belousov, and Jan Peters. Mujoco mpc for humanoid control: Evaluation on humanoidbench. arXiv preprint arXiv:2408.00342,

work page Pith review arXiv

[5] [12]

Yuval Tassa, Tom Erez, and Emanuel Todorov

URL https://arxiv.org/abs/2206.00484. Yuval Tassa, Tom Erez, and Emanuel Todorov. Synthesis and stabilization of complex behaviors through online trajectory optimization. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4906–4913. IEEE,

arXiv 2012

[6] [14]

Caggiano Vittorio, Wang Huawei, Durandau Guillaume, Sartori Massimo, and Kumar Vikash

doi: 10.1109/IROS.2012.6386109. Caggiano Vittorio, Wang Huawei, Durandau Guillaume, Sartori Massimo, and Kumar Vikash. Myosuite – a contact-rich simulation suite for musculoskeletal motor control. https: //github.com/myohub/myosuite,

arXiv 2012

[7] [15]

URL https://arxiv.org/abs/2205. 13600. Grady Williams, Paul Drews, Brian Goldfain, James M. Rehg, and Evangelos A. Theodorou. Ag- gressive driving with model predictive path integral control. In 2016 IEEE International Con- ference on Robotics and Automation (ICRA) , pp. 1433–1440,

work page 2016

[8] [17]

Language to rewards for robotic skill synthesis

Wenhao Yu, Nimrod Gileadi, Chuyuan Fu, Sean Kirmani, Kuang-Huei Lee, Montse Gonzalez Are- nas, Hao-Tien Lewis Chiang, Tom Erez, Leonard Hasenclever, Jan Humplik, et al. Language to rewards for robotic skill synthesis. arXiv preprint arXiv:2306.08647,

arXiv