Added optional smoothing to muscle dynamics:
- `muscle` actuators take a new `tausmooth` attribute (defaults to 0) which when positive, smooths the transition between activation and deactivation timescales. - `mju_muscleDynamics` takes 3 parameters, adding width of smoothing sigmoid. PiperOrigin-RevId: 531473354 Change-Id: I8ab6c0289ff04437e798c3ca6edda132a30fcc31
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Yuval Tassa
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Copybara-Service
Copybara-Service
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@@ -2944,7 +2944,7 @@ mju_muscleDynamics
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.. mujoco-include:: mju_muscleDynamics
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Muscle activation dynamics, prm = (tau_act, tau_deact).
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Muscle activation dynamics, prm = (tau_act, tau_deact, smoothing_width).
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.. _mju_encodePyramid:
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@@ -5535,7 +5535,7 @@ section. The underlying :el:`general` attributes are set as follows:
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========= ======= ========= ======================================================
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Attribute Setting Attribute Setting
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========= ======= ========= ======================================================
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dyntype muscle dynprm timeconst(2)
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dyntype muscle dynprm timeconst(2) tausmooth
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gaintype muscle gainprm range(2), force, scale, lmin, lmax, vmax, fpmax, fvmax
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biastype muscle biasprm same as gainprm
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========= ======= ========= ======================================================
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@@ -5589,6 +5589,12 @@ This element has nine custom attributes in addition to the common attributes:
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:at:`timeconst`: :at-val:`real(2), "0.01 0.04"`
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Time constants for activation and de-activation dynamics.
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.. _actuator-muscle-tausmooth:
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:at:`tausmooth`: :at-val:`real, "0"`
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Width of smooth transition between activation and deactivation time constants. Units of ctrl, must be
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nonegative.
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.. _actuator-muscle-range:
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:at:`range`: :at-val:`real(2), "0.75 1.05"`
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+4
-4
@@ -1105,13 +1105,13 @@
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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| | | | :ref:`jointinparent<actuator-muscle-jointinparent>` | :ref:`tendon<actuator-muscle-tendon>` | :ref:`slidersite<actuator-muscle-slidersite>` | |
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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| | | | :ref:`cranksite<actuator-muscle-cranksite>` | :ref:`timeconst<actuator-muscle-timeconst>` | :ref:`range<actuator-muscle-range>` | |
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| | | | :ref:`cranksite<actuator-muscle-cranksite>` | :ref:`timeconst<actuator-muscle-timeconst>` | :ref:`tausmooth<actuator-muscle-tausmooth>` | |
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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| | | | :ref:`force<actuator-muscle-force>` | :ref:`scale<actuator-muscle-scale>` | :ref:`lmin<actuator-muscle-lmin>` | |
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| | | | :ref:`range<actuator-muscle-range>` | :ref:`force<actuator-muscle-force>` | :ref:`scale<actuator-muscle-scale>` | |
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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| | | | :ref:`lmax<actuator-muscle-lmax>` | :ref:`vmax<actuator-muscle-vmax>` | :ref:`fpmax<actuator-muscle-fpmax>` | |
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| | | | :ref:`lmin<actuator-muscle-lmin>` | :ref:`lmax<actuator-muscle-lmax>` | :ref:`vmax<actuator-muscle-vmax>` | |
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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| | | | :ref:`fvmax<actuator-muscle-fvmax>` | | | |
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| | | | :ref:`fpmax<actuator-muscle-fpmax>` | :ref:`fvmax<actuator-muscle-fvmax>` | | |
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| | | +-----------------------------------------------------------------+-----------------------------------------------------------------+-----------------------------------------------------------------+ |
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+------------------------------------+----+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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| |_| actuator |br| |_| |L| | | .. table:: |
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@@ -45,6 +45,11 @@ General
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6x^5 - 15x^4 + 10x^3, & 0 \lt & x \lt 1 \\
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1, & 1 \le & x \qquad
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\end{cases}
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- Added optional :ref:`tausmooth<actuator-muscle-tausmooth>` attribute to muscle actuators. When positive, the
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time-constant :math:`\tau` of muscle activation/deactivation uses :ref:`mju_sigmoid` to transition smoothly
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between the two extremal values given by the `Millard et al. (2013) <https://doi.org/10.1115/1.4023390>`__ muscle
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model, within a range of width tausmooth. See :ref:`Muscle actuators<CMuscle>` for more details.
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Relatedly, :ref:`mju_muscleDynamics` now takes 3 parameters instead of 2, adding the new smoothing-width parameter.
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.. youtube:: ZppeDArq6AU
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@@ -2434,7 +2434,7 @@ mjtNum mju_muscleGain(mjtNum len, mjtNum vel, const mjtNum lengthrange[2],
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mjtNum acc0, const mjtNum prm[9]);
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mjtNum mju_muscleBias(mjtNum len, const mjtNum lengthrange[2],
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mjtNum acc0, const mjtNum prm[9]);
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mjtNum mju_muscleDynamics(mjtNum ctrl, mjtNum act, const mjtNum prm[2]);
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mjtNum mju_muscleDynamics(mjtNum ctrl, mjtNum act, const mjtNum prm[3]);
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void mju_encodePyramid(mjtNum* pyramid, const mjtNum* force, const mjtNum* mu, int dim);
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void mju_decodePyramid(mjtNum* force, const mjtNum* pyramid, const mjtNum* mu, int dim);
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mjtNum mju_springDamper(mjtNum pos0, mjtNum vel0, mjtNum Kp, mjtNum Kv, mjtNum dt);
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+15
-7
@@ -754,13 +754,12 @@ ascending portion of the :math:`\text{FL}` curve, or the descending portion, or
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model with 50 muscles. Do you believe that someone did careful experiments and measured the operating range for every
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muscle in your model, taking into account all the joints that the muscle spans? If not, then it is better to think of
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musculo-skeletal models as having the same general behavior as the biological system, while being different in various
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details - including details that are of great interest to some research community. For most muscle properties which
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details -- including details that are of great interest to some research community. For most muscle properties which
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modelers consider constant and known, there is an experimental paper showing that they vary under some conditions. This
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is not to discourage people from building accurate models, but rather to discourage people from believing too strongly
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in their models. Modeling in biology is quite different from modeling in physics and engineering... which is why we find
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it ironic when people in Robotics complain that building accurate robot models is hard.
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in their models.
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Coming back to our muscle model, there is the muscle activation act. This is the state of a first-order nonlinear
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Coming back to our muscle model, there is the muscle activation ``act``. This is the state of a first-order nonlinear
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filter whose input is the control signal. The filter dynamics are:
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@@ -773,12 +772,17 @@ are two time constants specified with the attribute timeconst, namely :math:`\te
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<https://doi.org/10.1115/1.4023390>`__, the effective time constant :math:`\tau` is then computed at runtime as:
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.. math::
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\tau(\texttt{ctrl}, \texttt{act}) =
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\tau(\texttt{ctrl}-\texttt{act}) =
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\begin{cases}
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\tau_\text{act} \cdot (0.5 + 1.5\cdot\texttt{act}) & \texttt{ctrl} \gt \texttt{act} \\
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\tau_\text{deact} / (0.5 + 1.5\cdot\texttt{act}) & \texttt{ctrl} \leq \texttt{act}
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\tau_\text{act} \cdot (0.5 + 1.5\cdot\texttt{act}) & \texttt{ctrl}-\texttt{act} \gt 0 \\
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\tau_\text{deact} / (0.5 + 1.5\cdot\texttt{act}) & \texttt{ctrl} - \texttt{act} \leq 0
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\end{cases}
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Since the above equation describes discontinuous switching, which can be undesirable when using derivative-based
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optimization, we introduce the optional smoothing parameter :ref:`tausmooth<actuator-muscle-tausmooth>`. When greater
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than 0, the switching is replaced by :ref:`mju_sigmoid`, which will smoothly interpolate between the two values within
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the range :math:`(\texttt{ctrl}-\texttt{act}) \pm \text{tausmooth}/2`.
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Now we summarize the attributes of element :ref:`muscle <actuator-muscle>` which users may want to adjust,
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depending on their familiarity with the biomechanics literature and availability of detailed measurements with regard
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to a particular model:
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@@ -801,6 +805,10 @@ timeconst
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Muscles are composed of slow-twitch and fast-twitch fibers. The typical muscle is mixed, but some muscles have a
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higher proportion of one or the other fiber type, making them faster or slower. This can be modeled by adjusting the
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time constants. The vmax parameter of the :math:`\text{\small FLV}` function should also be adjusted accordingly.
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tausmooth
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When positive, smooths the transition between activation and de-activation time-constants. While a single
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`motor unit <https://en.wikipedia.org/wiki/Motor_unit>`__ is either activating or de-activating, an entire muscle
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will have a mixture of many units, leading to a corresponding mixture of timescales.
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lmin, lmax, vmax, fpmax, fvmax
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These are the parameters controlling the shape of the :math:`\text{\small FLV}` function. Advanced users can
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experiment with them; see MATLAB function `FLV.m <_static/FLV.m>`__. Similar to the scale setting, if you want to
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