mujoco

<mujoco model="Polynomial Stiffness">
<!--
  Four boxes hanging from spatial tendons, demonstrating polynomial stiffness.
  Each tendon has a different stiffness profile:
    1. Linear:       k(q) = a*q                 (stiffness="100  0    0")
    2. Quadratic:    k(q) = b*q^2               (stiffness="0    200  0")
    3. Cubic:        k(q) = c*q^3               (stiffness="0    0    300")
    4. Combination:  k(q) = a*q + b*q^2 + c*q^3 (stiffness="100 -400  400")
-->

  <visual>
    <map force="0.1" zfar="30"/>
    <rgba haze="0.15 0.25 0.35 1"/>
    <global offwidth="1280" offheight="720" elevation="-10"/>
  </visual>

  <asset>
    <texture type="skybox" builtin="gradient" rgb1="0.3 0.5 0.7" rgb2="0 0 0" width="32" height="32"/>
    <texture name="grid" type="2d" builtin="checker" rgb1=".2 .3 .4" rgb2=".1 .15 .2" width="512" height="512"/>
    <material name="grid" reflectance="0.3" texture="grid" texrepeat="5 5" texuniform="true"/>
  </asset>

  <default>
    <geom condim="3"/>
    <site rgba="0 .8 0 .5" size=".03"/>
    <tendon width=".01" rgba=".9 .9 .9 1" springlength="0 .3"/>
    <default class="box">
      <geom type="box" size=".2 .2 .2" mass="5"/>
    </default>
  </default>

  <worldbody>
    <geom type="plane" size="3 3 .01" material="grid"/>
    <light directional="true" diffuse=".4 .4 .4" specular="0 0 0" pos="0 0 5" dir="0 0 -1" castshadow="false"/>
    <light directional="false" diffuse=".8 .8 .8" specular=".3 .3 .3" pos="0 -2 4" dir="0 .5 -1"/>

    <!-- anchor sites -->
    <site name="anchor_linear"    pos="-1.5 0 2"/>
    <site name="anchor_quadratic" pos="-.5  0 2"/>
    <site name="anchor_cubic"     pos=".5   0 2"/>
    <site name="anchor_combi"     pos="1.5  0 2"/>

    <body name="linear" pos="-1.5 0 1.5">
      <freejoint/>
      <geom class="box" rgba=".2 .6 1 1"/>
      <site name="hook_linear" pos="0 0 .2"/>
    </body>

    <body name="quadratic" pos="-.5 0 1.5">
      <freejoint/>
      <geom class="box" rgba="1 .4 .1 1"/>
      <site name="hook_quadratic" pos="0 0 .2"/>
    </body>

    <body name="cubic" pos=".5 0 1.5">
      <freejoint/>
      <geom class="box" rgba=".2 .8 .2 1"/>
      <site name="hook_cubic" pos="0 0 .2"/>
    </body>

    <body name="combi" pos="1.5 0 1.5">
      <freejoint/>
      <geom class="box" rgba=".8 .2 .8 1"/>
      <site name="hook_combi" pos="0 0 .2"/>
    </body>
  </worldbody>

  <tendon>
    <spatial name="linear" stiffness="100">
      <site site="anchor_linear"/>
      <site site="hook_linear"/>
    </spatial>

    <spatial name="quadratic" stiffness="0 200">
      <site site="anchor_quadratic"/>
      <site site="hook_quadratic"/>
    </spatial>

    <spatial name="cubic" stiffness="0 0 300">
      <site site="anchor_cubic"/>
      <site site="hook_cubic"/>
    </spatial>

    <spatial name="combination" stiffness="100 -400 400">
      <site site="anchor_combi"/>
      <site site="hook_combi"/>
    </spatial>
  </tendon>
</mujoco>