Source-linked AI summary
MuJoCable: Reduced-Order Surface-Routed Cable Transmission for Tendon-Driven Robots
Yi Zhang, Qi Shao, Yicong Lin, Muyuan Ma, Tao Sun, Yue Xie
TL;DR
Tendon-driven robots need transmission models that capture how moving routes, unilateral tension, and segment friction jointly affect motion and force transfer, which existing rigid-body simulation does not provide. MuJoCable adds a reduced-order, configuration-dependent surface-routed transmission to MuJoCo and combines route optimization with friction-aware force transfer. It reproduces pulley relations, reveals friction-driven load and motion redistribution in SpiRobs, and connects simulation states to hardware motion and route design.
Problem
Existing rigid-body simulation does not jointly resolve moving noncircular cable contact, unilateral tension, and segment-wise friction for tendon transmissions.
Method
MuJoCable optimizes a configuration-dependent route over moving surfaces, applies a unilateral axial law with directional Capstan propagation, and maps nodal virtual work to rigid-body loads.
Results
MuJoCable reproduces pulley mechanics, reveals friction-driven load growth and proximal joint-rotation redistribution in 18-joint SpiRobs, and matches observed motion sequences in hardware tests.
Takeaways & Limitations
The model exposes geometry, take-up, and guide-loss contributions to transmission discrepancies and can direct physical route revisions before fabrication.
Takeaways & Limitations
The route solver assumes a known route topology and does not switch topology when cables detach, leave guides, or select another wrap.
Abstract
from arXiv · showhide
Tendon transmissions reduce distal inertia and add compliance, yet routing, slack, and friction govern motion and force transfer. Mainstream rigid-body robotics simulators such as MuJoCo do not jointly resolve moving noncircular contact, unilateral tension, and segment friction. We present MuJoCable, which adds a reduced-order, configuration-dependent cable transmission to MuJoCo. Its routing algorithm jointly optimizes an ordered path across moving analytic and mesh surfaces. A unilateral axial law, directional Capstan propagation, and nodal virtual work map this path to segment tensions and body forces. The warm-started engine plugin applies these forces during simulation and exposes route and load states for design. Pulley benchmarks recover analytical transmission relations with a Capstan-ratio error below 0.5%. On the underactuated 18-joint SpiRobs, MuJoCable reveals friction-driven load growth and proximal redistribution of joint rotation that the native tendon does not represent. Hardware tests on SpiRobs and a tendon-route-coupled finger reproduce observed motion sequences. By making physical threading executable, MuJoCable brings transmission sources of the simulation-to-reality gap into route, cable, and actuator design before fabrication.
1 Introduction
Tendon routing couples geometry, friction, slack, and tension to robot motion and force transfer, but standard reduced-order and native MuJoCo models do not jointly resolve these effects. MuJoCable addresses this gap with configuration-dependent surface routing, unilateral friction-aware transmission, and an engine-plugin implementation.
- Motivation: Cable routing, friction, and migrating contact points determine how motor retraction becomes joint torque, robot shape, and force transmission.Underactuation distributes these effects across several joints, making routing part of both the mechanism and its control interface.
- Limitations of existing models: Native MuJoCo tendons use body-fixed sites and spherical or cylindrical wraps, so adjacent noncircular contact migration cannot emerge.Their Hookean force law can also produce pushing generalized forces rather than enforcing a unilateral cable state.
- MuJoCable approach: MuJoCable jointly optimizes an ordered cable path across adjacent moving analytic and mesh surfaces, allowing stroke and moment arms to emerge from noncircular rolling geometry.The route is configuration-dependent and follows physical threading over moving surfaces.
- MuJoCable approach: A pull-only axial law, directional Capstan propagation, and nodal virtual work resolve slack, unequal segment tensions, actuator demand, and joint-level motion redistribution.These mechanisms map the solved route to cable loads and rigid-body dynamics.
- Implementation and evaluation: The MuJoCo engine plugin warm-starts route solving and reports route validity, take-up, slack, segment tension, and actuator load for simulation and diagnostics.Evaluation includes pulley mechanics, robot comparisons, and runtime measurements.
2 Related Work
Prior work supports tendon-driven robots and models paths or frictional transmission, but generally fixes the route representation or omits direction-dependent, segment-wise losses across moving cable contacts. MuJoCable targets this missing combination within rigid-body robot simulation.
- Robot applications: Tendon models support underactuated hands, tendon-driven manipulators, continuum robots, rolling-contact mechanisms, and morphology–actuation mappings.Open parametric hands coordinate morphology and actuation through tendon-length and pulley mappings.
- Path representations: General-purpose simulators and OpenSim-style methods compute transmission or muscle paths from sites, points, and analytic wrap objects.Specialized methods extend path construction to arbitrary surfaces and provide lengths or moment arms.
- Remaining gap: These path methods do not provide direction-dependent losses and unequal tensions across robot guides, while native MuJoCo lacks moving noncircular cable contact.MyoSim adds musculoskeletal force parameters to MuJoCo but does not add a moving noncircular cable-contact model.
- Friction models: Analytical, complementarity, and learned models address sheath, disk, pulley, or measured-input friction after selecting a centerline, disk sequence, or learned representation.They cover effects including elasticity, backlash, presliding, hysteresis, static contact, and residual dynamics.
3 Method
MuJoCable solves a reduced-order transmission problem coupling configuration-dependent surface routing, unilateral tension, frictional propagation, and rigid-body loading at each simulation step. Its plugin preserves physical constraints, exposes route and load diagnostics, and extends MuJoCo tendons to moving noncircular contacts and segment-wise friction.
- Scope and formulation: MuJoCable targets short, tension-dominated transmissions with quasi-static routes over known rigid surfaces, retaining routing and force transfer without distributed cable degrees of freedom.The model carries tension only, may go slack, and applies when routing and tension transmission dominate free-cable sag, bending, and wave motion.
- Scope and formulation: At every rigid-body step, the method solves a valid moving-surface path, unilateral friction-dependent segment tensions, and loads applied to connected bodies.This coupling closes the loop as MuJoCo integrates the cable load and updates the moving surfaces.
- Cable representation: An MJCF cable specification separates endpoints, hard guides, routing surfaces, physical parameters, friction, and tension limits from an ordered topology seed used only to initialize the route class.Endpoint sites define cable ends, hard-guide sites impose physical constraints, and routing sites supply surface order, wrapping side, and mesh corridor without carrying cable force.
- Transmission mechanics: The solved route provides length, length-rate, tangents, wrap angles, and point Jacobians that drive the unilateral axial law and map nodal forces to generalized loads.The formulation includes free length, effective extension, source tension, taut state, stiffness, damping, transition width, and tension limits.
- Surface routing: Joint optimization across adjacent analytic and mesh surfaces lets runtime contact migrate while preserving hard guides, surface nonpenetration, and the initialized route class.Cylinder segments are handled through analytic tangencies and unrolling, while closed meshes use an initialized triangle corridor optimized under nonpenetration.
- Transmission mechanics: Directional Capstan propagation resolves unequal segment tensions, so local friction changes actuator demand and the force delivered to each body rather than producing one scalar tendon force.For zero friction, equal tension recovers the native scalar length-gradient mapping; with friction, unbalanced guide and wrap loads reach their owning bodies through nodal assembly.
- MuJoCo integration: The plugin applies nodal forces to associated bodies, supports spool reaction torque through virtual work, and reports route validity, slack, take-up, tensions, actuator load, solver iterations, and residuals.Penetration or topology failure sets the cable generalized load to zero while retaining the warm start.
4 Experiments and Results
The experiments validate MuJoCable against analytical pulley relations, then show how moving-surface routing and guide friction alter robot motion, loads, and transmission states. Simulation-hardware comparisons reproduce overall bending sequences on two underactuated robots.
- Theory-to-Simulation Validation: All seven pulley systems follow analytical references for cable travel, force multiplication, Capstan transmission, pulley torque, and radius conversion.The evaluation uses closed-form comparisons across the pulley cases.
- Theory-to-Simulation Validation: At µ = 0, the load-side tension in fixed-pulley cases matches the weight of the 0.2-kg payload.The fixed-pulley cases verify cable travel and Capstan scaling.
- Theory-to-Simulation Validation: At µ = 0.15, free-sheave tension differences produce torque and a peak speed of 0.605 rad/s, versus 3.74 × 10−15 rad/s at µ = 0.Equal segment tensions yield zero torque in the frictionless case; friction generates the tension difference driving motion.
- Simulation-to-Simulation Comparison: The rolling-joint model produces 52.481° from 10-mm shortening, compared with 49.994° from two prescribed 25° virtual hinges.The route remains valid for 99.92% of the trajectory, and the 2.487° difference reflects cable-stroke mapping over rolling surfaces.
- Simulation-to-Simulation Comparison: MuJoCable yields nearly the same steady SpiRobs bend as the native tendon while resolving peak cable tension nearly four times larger and cable take-up about 9% higher.Similar global motion therefore corresponds to different transmission states.
- Simulation-to-Simulation Comparison: At µ = 0.60, peak SpiRobs tension exceeds the frictionless value by more than four times while bending retains about three quarters of its magnitude.Higher friction also shifts rotation toward proximal joints as distal-joint motion falls markedly.
- Simulation-to-Simulation Comparison: Higher guide friction reduces finger final flexion from 269.3° to 214.3° and peak internal force from 0.395 to 0.183 N.The result connects local transmission losses with robot-level shape before fabrication.
- Implementation and Hardware Evaluation: MuJoCable adds 22.5% to matched 18-joint step time while running at 11.9 times real time with a 0.5-ms step.Median step times are 34.25 µs for the native tendon and 41.96 µs for MuJoCable.
5 Discussion
MuJoCable exposes routing, friction, slack, and tension as transmission states that explain and help diagnose motion discrepancies in underactuated robots. These states support component sizing and physical route refinement, while the current solver assumes a fixed route topology.
- Cable routing, slack, and friction determine how one actuator distributes cable stroke, tension, and motion across passive joints.MuJoCable helps separate discrepancies caused by geometry, take-up, or guide losses before controller changes or new fabrication.
- Predicted take-up, source tension, segment tensions, and route validity support actuator sizing, cable selection, and comparisons of threading and lubrication choices.These states move transmission-induced reality gaps into early design decisions and shorten mechanical iteration.
- Friction sweeps and route diagnostics identified critical guides in an underactuated finger, motivating reduced friction and lubrication for reliable tendon actuation.Simulation directed a physical route revision instead of treating the discrepancy as a controller-only problem.
- The route solver assumes known topology and does not yet switch routes when cables detach, leave guides, or select alternative wraps.Future work targets dynamic contact activation and topology transitions for derailment, re-engagement, and alternative threading-path design.
6 Conclusion
MuJoCable makes physical threading executable within general-purpose rigid-body simulation by combining moving-surface routing, unilateral tension, pulley transmission, and guide friction. Tests connect these transmission states to real underactuated motion and enable cable-route design before fabrication.
- MuJoCable combines moving multi-surface routing, unilateral cable tension, pulley transmission, and guide friction in one rigid-body robot model.The plugin turns physical threading into an executable transmission model for general-purpose robotics simulation.
- Hardware tests on the 18-joint SpiRobs platform and a tendon-route-coupled underactuated finger connect transmission states to observed underactuated motion.
- The interface exposes cable layout, pretension, material, and actuator choices before fabrication, supporting physics-informed cable-route design.It also opens cable-driven robot design to route optimization and reinforcement-learning-based control.