Using `mjcb_act_dyn` to model a custom actuator with non-linear dynamics/kinematics given a state-space model? #3183

ralphieraccoon · 2026-03-17T11:11:18Z

ralphieraccoon
Mar 17, 2026

Intro

Hello, I'm a postdoc looking to move a model from Simscape to Mujoco.

My setup

Mujoco 3.6.0, Python 3.12, Ubuntu 24.04 Noble Numbat

My question

I'm trying to model an actuator in Mujoco using the state space model below:

$$\begin{aligned} h\left(\theta_{s}\right) & = \frac{\theta_{s} r_{s}^{2}}{\sqrt{l_{u}^{2} - \theta_{s}^{2}r_{s}^{2}}} \\\ k\left(\theta_{s}, \lambda \right) & = \lambda - \sqrt{l_{u}^{2} - \theta_{s}^{2}r_{s}^{2}} \\\ \boldsymbol{\dot{x}} & = \begin{bmatrix}x_{2}\\ -\frac{K_{L}}{J}h\left(x_{1}\right)k\left(x_{1}, \lambda\right) - \frac{B}{J}x_{2}\\ \end{bmatrix} + \begin{bmatrix}0\\ \frac{K_{t}}{J}\\\end{bmatrix}u \\\ y & = K_{L}\text{sat}_{0}^{\infty}k\left(x_{1}, \lambda\right) \\\ \boldsymbol{\dot{x}{\prime}} & = \begin{bmatrix}\text{sat}_{-\omega_{s}}^{\omega_{s}} \dot{x}_{1} \\\ \text{sat}_{-\alpha_{s}}^{\alpha_{s}} \dot{x}_{2}\end{bmatrix} \end{aligned}$$

where $\lambda$ is the actuator length, $u$ is the input, and $K_t, K_L, J, B, l_u, r_s, \omega_{s}, \alpha_{s}$ are all constants. $y$ is the actuator force.

Here it is in block diagram form in Simulink:

I was wondering exactly how this would be modelled in Mujoco, would you use mjcb_act_dyn or would a more complex solution be needed? Apologies, I'm very new to this.

Minimal model and/or code that explain my question

Model:

minimal XML

<mujoco>
  <visual>
    <map force="0.1" zfar="30"/>
    <rgba haze="0.15 0.25 0.35 1"/>
    <global offwidth="2560" offheight="1440" elevation="-20" azimuth="120"/>
  </visual>

  <asset>
    <texture type="skybox" builtin="gradient" rgb1=".3 .5 .7" rgb2="0 0 0" width="32" height="512"/>
    <texture name="grid" type="2d" builtin="checker" width="512" height="512" rgb1=".1 .2 .3" rgb2=".2 .3 .4"/>
    <material name="grid" texture="grid" texrepeat="1 1" texuniform="true" reflectance=".2"/>
  </asset>

  
  <worldbody>
    <geom name="floor" size="0 0 .05" type="plane" material="grid" condim="3"/>
    <light name="spotlight" mode="targetbodycom" target="b1" diffuse=".8 .8 .8" specular="0.3 0.3 0.3" pos="0 -6 4" cutoff="30"/>
    
    <body name="b1" pos="0 0 0">
      <site name="bt" pos="0 0 0.01"/>
      <geom type="cylinder" size="0.13 0.01" rgba="1 0 0 1"/>

        <body name="f1" pos="0 0 0.22">
          <site name="ft" pos="0 0 -0.01"/>
          <geom type="cylinder" size="0.13 0.01" rgba="1 0 0 1"/>
        </body>

    </body>  
  </worldbody>

  <contact>
    <exclude body1="b1" body2="f1"/>
  </contact>

  <tendon>
    <spatial name="tt" damping="1">
    <site site="bt"/>
    <site site="ft"/>
    </spatial>
  </tendon>
  
  <actuator>
    <general dyntype="user" tendon="tt" gear="1" forcerange="-10 0"/>
  </actuator>

</mujoco>

Code:

import mujoco
import mediapy as media

def my_act_dyn(model, data, id):
    
    return 0.0

model = mujoco.MjModel.from_xml_string(xml)
data = mujoco.MjData(model)

mujoco.set_mjcb_act_dyn(my_act_dyn)

mujoco.viewer.launch(model, data)

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Using `mjcb_act_dyn` to model a custom actuator with non-linear dynamics/kinematics given a state-space model? #3183

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Using mjcb_act_dyn to model a custom actuator with non-linear dynamics/kinematics given a state-space model? #3183

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ralphieraccoon Mar 17, 2026

Intro

My setup

My question

Minimal model and/or code that explain my question

Confirmations

Replies: 0 comments

Using `mjcb_act_dyn` to model a custom actuator with non-linear dynamics/kinematics given a state-space model? #3183

ralphieraccoon
Mar 17, 2026