MUSBRIC: LEGO-Compatible Pneumatic Muscle Bricks for Reconfigurable Musculoskeletal Robots

Qiyao Wang; Yinglei Zhu; Liang Zhou; Wenzhe Gong; Xin-Jun Liu; Huichan Zhao

cs.ROOct 29, 2026

MUSBRIC: LEGO-Compatible Pneumatic Muscle Bricks for Reconfigurable Musculoskeletal Robots

Authors: Qiyao Wang, Yinglei Zhu, Liang Zhou, Wenzhe Gong, Xin-Jun Liu, Huichan Zhao

Organizations: Department of Mechanical Engineering, State Key Laboratory of Tribology in Advanced Equipment, Beijing Key Laboratory of Transformative High-end Manufacturing Equipment and Technology, Tsinghua University, Beijing 100084, China. · Tsinghua Medicine, Tsinghua University, Beijing 100084, China.

Abstract

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
$S_{0}$	$12.56637~\mathrm{mm}^{2}$
$\alpha$	$3.03153\times 10^{-11}~\mathrm{m}^{2}/\mathrm{Pa}$
$c_{0}$	$0.095067~\mathrm{N}$
$c_{1}$	$31.463491~\mathrm{N}$
$c_{2}$	$-44.708056~\mathrm{N}$
$c_{3}$	$30.779766~\mathrm{N}$

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 $(p_{\mathrm{bb}},p_{\mathrm{tb}})=(400,0)$ 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
$p_{i}$ ; $\mathbf{p}$ ; $p_{\max}$	Pressure of actuator $i$ ; pressure vector; maximum pressure
$\mathbf{x}_{i}^{\mathrm{f}}$ ; $\mathbf{x}_{i}^{\mathrm{m}}$	Vectors from the joint axis to actuator $i$ ’s fixed- and moving-link attachment points, expressed in the corresponding link frames
$\mathbf{R}(q)$	Rotation of the moving link from its straight configuration
$r_{p}$	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.

Modular Robotics

Modular robotics studies robots built from interchangeable or self-reconfiguring parts that adapt their shape, capabilities, and tasks.

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Diff-Muscle: Efficient Learning for Musculoskeletal Robotic Table Tennis

Wentao Zhao, Jun Guo, Kangyao Huang, Xin Liu+1

Department of Computer Science and Technology, Tsinghua University, China.

Robotic Table Tennis Differential Flatness Robotics Robotic Control

Open paper AskPDF arXiv

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.

Abstract

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