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Implementing Capstan Friction in MuJoCo Spatial Tendons #3405
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The The [friction-loss docs](https://mujoco.readthedocs.io/en/stable/computation/index.html#friction-loss) suggest a more detailed alternative: small bodies connected by tendons, with actual contact against the surrounding surfaces. That gives load-dependent friction, but costs more to simulate. Keeping the lightweight routed tendon would require a custom force model. A passive-force plugin could contain that calculation, but you'd still need to model the segment tensions and stick/slip behavior yourself. |
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Intro
Hi!
My setup
My current setup is implemented in Python using MuJoCo. The model consists of a spatial tendon routed through multiple sites, where each site represents a cable guide or pulley.
My question
Hello, I would like to model capstan friction in a MuJoCo tendon that passes through multiple routing sites or pulleys.
At each contact point (i), I would like the tendon tensions to satisfy the capstan equation
[
\frac{T_{\max,i}}{T_{\min,i}}
e^{\mu_i \theta_i},
]
where:
For a tendon passing through (N) routing sites, the overall tension ratio becomes
[
\frac{T_{\max}}{T_{\min}}
\prod_{i=1}^{N} e^{\mu_i\theta_i}
e^{\sum_{i=1}^{N}\mu_i\theta_i}.
]
The direction of cable motion determines which side is (T_{\max}) and which is (T_{\min}), so these quantities swap during loading and unloading.
Does MuJoCo provide a simple built-in way to model this behavior directly within a spatial tendon? Alternatively, is there a recommended way to implement this using tendon parameters, equality constraints, or a MuJoCo plugin, rather than computing and applying the corresponding friction forces externally at every simulation step?
Minimal model and/or code that explain my question
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