Musculoskeletal robots combine compliant actuators with articulated skeletons, but exploring alternative configurations often requires repeated fabrication. We present MUSBRIC, a modular hardware platform and accompanying MuJoCo-based simulator for reconfigurable musculoskeletal robots. LEGO-compatible endcaps turn fiber-reinforced extensile pneumatic artificial muscles into reusable, plug-and-play muscle bricks that connect directly to standard LEGO components. Experimentally identified actuator behavior supports corresponding musculoskeletal simulations. An elbow-joint prototype validates load-dependent flexion and extension, showing that pulley-guided routing enables reversible motion and a mechanical stop stabilizes the straight posture. A robotic hand demonstrates compliant grasping and multi-joint construction. Matched hardware and simulation sweeps across 15 leg configurations demonstrate systematic exploration of attachment geometry, while a quadruped assembled from four legs demonstrates walking. Together, these demonstrations span mechanism analysis, configuration exploration, and functional robot construction within a single reconfigurable system. The hardware designs and simulation code will be released as open source soon to facilitate reproduction and further development.
Figures & tables
Fig. 2: Muscle-brick design and modeling. (a) Structure of the muscle brick, including the fiber-reinforced silicone tube and the inlet and sealed cap bricks. (b) Connection to LEGO beams using an axle and bushing (top) or a frictionless pin (bottom). (c) Tensile load–strain curves of an actuator at 0–500 kPa. (d) Simulation method coupling the actuator model with assembly dynamics in MuJoCo.
Quantity
Identified value
S0
12.56637mm2
α
3.03153×10−11m2/Pa
c0
0.095067N
c1
31.463491N
c2
−44.708056N
c3
30.779766N
TABLE I: Identified parameters of the PAM constitutive model.
Fig. 3: Single-joint mechanism and load response. (a) Elbow joint constructed using MUSBRIC. (b) Pulley-guided routing and comparison with direct attachment. (c) Experimental (solid) and simulated (dashed) joint angles under 0, 50, and 100 g added loads. The image sequences show flexion and extension at 0 and 100 g. Pressure commands alternate between (pbb,ptb)=(400,0) and (0,400) kPa.
Added load
Settled angle ( ∘ )
Trace RMSE
(g)
Experiment
Simulation
( ∘ )
0
110.6
110.9
7.09
50
93.6
92.8
5.26
100
78.7
79.7
5.95
TABLE II: Experimental and simulated joint responses.
Fig. 4: Joint stability and motion range (a) with and (b) without a mechanical stop. The diagrams compare the straight configurations, and the image sequences show the corresponding pressure-limited motion.
Symbol
Definition
i ; j
Actuator index; pressure-command index
q
Joint angle
pi ; p ; pmax
Pressure of actuator i ; pressure vector; maximum pressure
xif ; xim
Vectors from the joint axis to actuator i ’s fixed- and moving-link attachment points, expressed in the corresponding link frames
R(q)
Rotation of the moving link from its straight configuration
rp
Pulley radius
TABLE III: Notation for joint stability and motion-range analysis.
Fig. 5: Robotic hand constructed using MUSBRIC. (a) Three-joint finger module and exploded assembly. (b) Two 1:1 gear stages enforcing equal relative rotations of the three joints. (c) Two-joint thumb constructed from the first two joints of the finger module with one gear stage. (d) Assembly of four fingers and the thumb. (e) Open and fist states. (f) Grasps of a bottle, tennis ball, tape roll, slipper, and toy kangaroo.
Fig. 6: Leg reconfiguration and quadruped locomotion. (a) Exploded assembly of the two-joint leg. (b) Four-posture motion cycle of the leg. (c) LEGO-grid attachment parameters and representative leg configurations. (d) Configurations with the maximum and minimum workspace areas and their corresponding workspaces. (e) Simulated and (f) experimental parameter maps of the workspace area across the 15 configurations. (g) A quadruped robot assembled from four leg modules. (h) Open-loop walking sequence of the quadruped assembled from four leg modules; the robot reaches 0.21 body lengths per second.
Musculoskeletal robots provide superior advantages in flexibility and dexterity, positioning them as a promising frontier towards embodied intelligence. However, current research is largely confined to relative simple tasks, restricting the exploration of their full potential in multi-segment coordination. Furthermore, efficient learning remains a challenge, primarily due to the high-dimensional action space and inherent overactuated structures. To address these challenges, we propose Diff-Muscle, a musculoskeletal robot control algorithm that leverages differential flatness to reformulate policy learning from the redundant muscle-activation space into a significantly lower-dimensional joint space. Furthermore, we utilize the highly dynamic robotic table tennis task to evaluate our algorithm. Specifically, we propose a hierarchical reinforcement learning framework that integrates a Kinematics-based Muscle Actuation Controller (K-MAC) with high-level trajectory planning, enabling a musculoskeletal robot to perform dexterous and precise rallies. Experimental results demonstrate that Diff-Muscle significantly outperforms state-of-the-art baselines in success rates while maintaining minimal muscle activation. Notably, the proposed framework successfully enables the musculoskeletal robots to achieve continuous rallies in a challenging dual-robot setting.
Wentao Zhao, Jun Guo, Kangyao Huang +2
Department of Computer Science and Technology, Tsinghua University, China.
Human locomotion emerges from high-dimensional neuromuscular control, making predictive musculoskeletal simulation challenging. We present a physiology-informed reinforcement-learning framework that constrains control using muscle synergies. We extracted a low-dimensional synergy basis from inverse musculoskeletal analyses of a small set of overground walking trials and used it as the action space for a muscle-driven three-dimensional model trained across variable speeds, slopes and uneven terrain. The resulting controller generated stable gait from 0.7-1.8 m/s and on ± 6∘ grades and reproduced condition-dependent modulation of joint angles, joint moments and ground reaction forces. Compared with an unconstrained controller, synergy-constrained control reduced non-physiological knee kinematics and kept knee moment profiles within the experimental envelope. Across conditions, simulated vertical ground reaction forces correlated strongly with human measurements, and muscle-activation timing largely fell within inter-subject variability. These results show that embedding neurophysiological structure into reinforcement learning can improve biomechanical fidelity and generalization in predictive human locomotion simulation with limited experimental data.
Ilseung Park, Eunsik Choi, Jangwhan Ahn +1
Carnegie Mellon University · Department of Physical Education, Seoul National University, Seoul, Republic of Korea · Seoul National University +2
The embodied learning of human motor control requires whole-body neuro-actuated musculoskeletal dynamics, while the internal muscle-driven processes underlying movement remain inaccessible to direct measurement. Computational modeling offers an alternative, but inverse dynamics methods struggled to resolve redundant control from observed kinematics in the high-dimensional, over-actuated system. Forward imitation approaches based on deep reinforcement learning exhibited inadequate tracking performance due to the curse of dimensionality in both control and reward design. Here we introduce a large-scale parallel musculoskeletal computation framework for biomechanically grounded whole-body motion reproduction. By integrating large-scale parallel GPU simulation with adversarial reward aggregation and value-guided flow exploration, the MS-Emulator framework overcomes key optimization bottlenecks in high-dimensional reinforcement learning for musculoskeletal control, which accurately reproduces a broad repertoire of motions in a whole-body human musculoskeletal system actuated by approximately 700 muscles. It achieved high joint angle accuracy and body position alignment for highly dynamic tasks such as dance, cartwheel, and backflip. The framework was also used to explore the musculoskeletal control solution space, identifying distinct musculoskeletal control policies that converge to nearly identical external kinematic and mechanical measurements. This work establishes a tractable computational route to analyzing the specificity and diversity underlying human embodied control of movement. Project page: https://lnsgroup.cc/research/MS-Emulator.