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Redesign the dcmotor controller: setpoint inputs, torque-space gains.

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The dcmotor input block is any subset of the canonical list [pos, vel,
ff, voltage], selected with input="pos vel ff voltage" and recorded as
mjtCtrlInput bits in actuator_ctrlspec like pid. Tokens are required in
canonical order: the attribute denotes a set, the block always packs
canonically, and accepting permutations invites reading the string as a
layout choice. The mode flag in gainprm[8] is retired (reserved,
written 0).

Controller gains are now in torque space, as for pid: the controller
commands tau = kp*(q*-l) + kd*(v*-ldot) + ki*x_I + tau_ff over the
present inputs (absent setpoints frozen at zero) and converts to drive
voltage V = R/K * tau + K*ldot. The second term compensates back-EMF,
as the current loop of a real torque-mode driver does (torque commands
are current commands): commanded torque is delivered exactly until a
limit binds, and the torque-speed envelope emerges from the Vmax clamp.
The map uses the nameplate R: thermal resistance growth is not
compensated, so a hot motor under-delivers by R/R(T). A stateless
setpoint dcmotor now matches <pid> exactly, for any K and R; the old
back-EMF droop remains available as the physical behavior of the raw
voltage path. Voltage-space datasheet gains convert by K/R. Controller
inputs require a positive motor constant (the map divides by K), and
controller gains require a controller input.

ff and voltage are distinct inputs, different in kind: ff is a torque
feedforward added to the controller output, uniform with pid's ff
(feedforward in the actuator's output space), while voltage is the raw
terminal voltage of the physical device, injected downstream of the
controller and its Vmax clamp, unclamped (ctrlrange bounds it if
desired). input="voltage" is the default: the plain voltage-commanded
motor, whose behavior is unchanged by this commit. The integrator
always accumulates position error; the old velocity mode's integral
term, ki*(int(u)dt - theta), which tracked the integral of the velocity
command, is retired without replacement, keeping ki mode-independent --
commanded integrated velocity belongs to an integrator activation
state, not to controller gains. slewmax rate-limits the first controller
input -- position setpoint (rad/s), velocity setpoint (rad/s^2) or torque
feedforward (N*m/s), each a real driver feature (reference ramping,
ramped-velocity and ramped-torque input modes); the raw voltage input
is never rate-limited and slewmax requires a controller input.

input="none" selects the empty signature: the actuator owns no controls
at all (nu = 0 is now legal with actuators present) and is purely
passive -- LuGre friction, cogging and back-EMF braking as passive
joint forces. This exists because auxiliary dynamic states (the LuGre
bristle) attach to actuators, not joints. The terminal voltage is
identically zero, i.e. a shorted motor (dynamic braking); motorconst=0
decouples the electrical branch. mjINPUT_NONE is a distinct enum value
because ctrlspec = 0 means "unset, use the type default". History and
delay require an input; the controller voltage override and input read
in mj_fwdActuation are gated on a nonempty block.

The analytic velocity derivative of the controller becomes
dV/dw = -kd*R/K + K, whose second term cancels the back-EMF bias
exactly: the net damping of an unclipped torque-mode motor is -kd, and
of a voltage-mode or passive motor -K^2/R. Viewers label inputs via
mj_actuatorInputName: pos, vel, ff, voltage.

The dcmotor LaTeX design doc is updated accordingly: torque-space
units, the tau->V map and its saturation-generated envelope, the
input-block pipeline figure, and a Passive Operation section.

PiperOrigin-RevId: 965795351
Change-Id: Ibc308ca21bd6bad014e77f950ee08feaad449b73
This commit is contained in:
Yuval Tassa
2026-08-17 00:42:47 -07:00
committed by Copybara-Service
parent 11fa4a5b45
commit 2f1843f4a7
29 changed files with 574 additions and 350 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/XMLreference.rst
+40 -19
View File
@@ -5691,7 +5691,7 @@ specify them independently.
.. _actuator-general-dyntype:
:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, muscle, user], "none"`
:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, dcmotor, muscle, user], "none"`
Activation dynamics type for the actuator. The available dynamics types were already described in the :ref:`Actuation
model <geActuation>` section. Repeating that description in somewhat different notation (corresponding to the mjModel
and mjData fields involved) we have:
@@ -5711,7 +5711,7 @@ specify them independently.
.. _actuator-general-gaintype:
:at:`gaintype`: :at-val:`[fixed, affine, muscle, pid, so3, user], "fixed"`
:at:`gaintype`: :at-val:`[fixed, affine, muscle, dcmotor, pid, so3, user], "fixed"`
The gain and bias together determine the output of the force generation mechanism, which is currently assumed to be
affine. As already explained in :ref:`Actuation model <geActuation>`, the general formula is:
scalar_force = gain_term \* (act or ctrl) + bias_term.
@@ -5724,6 +5724,7 @@ specify them independently.
fixed gain_term = gainprm[0]
affine gain_term = gain_prm[0] + gain_prm[1]*length + gain_prm[2]*velocity
muscle gain_term = mju_muscleGain(...)
dcmotor DC motor gain (K or K/R), see :ref:`dcmotor<actuator-dcmotor>`
pid PID controller with setpoint inputs, see :ref:`pid<actuator-pid>`
so3 geodesic orientation servo, computed jointly over 3 force outputs, see :ref:`orientation<actuator-orientation>`
user gain_term = mjcb_act_gain(...)
@@ -5731,7 +5732,7 @@ specify them independently.
.. _actuator-general-biastype:
:at:`biastype`: :at-val:`[none, affine, muscle, so3, user], "none"`
:at:`biastype`: :at-val:`[none, affine, muscle, dcmotor, so3, user], "none"`
The keywords have the following meaning:
======= ================================================================
@@ -5740,6 +5741,7 @@ specify them independently.
none bias_term = 0
affine bias_term = biasprm[0] + biasprm[1]*length + biasprm[2]*velocity
muscle bias_term = mju_muscleBias(...)
dcmotor DC motor bias: back-EMF, cogging, LuGre friction, see :ref:`dcmotor<actuator-dcmotor>`
so3 damping term of the geodesic orientation servo, see :ref:`orientation<actuator-orientation>`
user bias_term = mjcb_act_bias(...)
======= ================================================================
@@ -5784,8 +5786,9 @@ specify them independently.
:at:`input`: :at-val:`string, optional`
Input signature of the actuator: which controls make up its control block, recorded in
``mjModel.actuator_ctrlspec``. For gaintype "so3" it selects the orientation chart: "expmap" (3 controls, the
default) or "quat" (4 controls); see :ref:`orientation/input<actuator-orientation-input>`. For gaintype "pid" it is
a token list selecting the input subset; see :ref:`pid/input<actuator-pid-input>`.
default) or "quat" (4 controls); see :ref:`orientation/input<actuator-orientation-input>`. For gaintypes "pid" and
"dcmotor" it is a token list selecting the input subset; see :ref:`pid/input<actuator-pid-input>` and
:ref:`dcmotor/input<actuator-dcmotor-input>`.
.. _actuator-general-actearly:
@@ -6806,8 +6809,11 @@ the stateless case.
- :ref:`resistance<actuator-dcmotor-resistance>`, :ref:`motorconst<actuator-dcmotor-motorconst>` and
:ref:`nominal<actuator-dcmotor-nominal>` are each optional, but some combination of them is required.
See Section 2.1 of the `technical note <_static/dcmotor.pdf>`__.
- The control :ref:`input<actuator-dcmotor-input>` semantic is either the voltage applied to the motor terminals (the
default), or a position or velocity target for a :ref:`PID controller<actuator-dcmotor-controller>`.
- The control block is selected by :ref:`input<actuator-dcmotor-input>`: any subset of ``[pos, vel, ff]``, where
``pos`` and ``vel`` are setpoint inputs to the on-board :ref:`PID controller<actuator-dcmotor-controller>` and
``ff`` is a torque feedforward added to its output; the ``voltage`` input is the raw terminal voltage. The
default is the plain voltage-commanded motor. With
``input="none"`` the actuator has no control inputs at all and acts as a purely passive device.
- Optional features include electrical dynamics (:ref:`inductance<actuator-dcmotor-inductance>`),
:ref:`cogging torque<actuator-dcmotor-cogging>`, :ref:`thermal resistance variation<actuator-dcmotor-thermal>`, and
:ref:`LuGre<actuator-dcmotor-lugre>` friction.
@@ -6946,22 +6952,37 @@ This element has the following custom attributes in addition to the common attri
.. _actuator-dcmotor-input:
:at:`input`: :at-val:`[voltage, position, velocity], "voltage"`
Specifies the input signal semantics. In "voltage" mode, the control directly sets applied motor voltage. In
"position" or "velocity" modes, the :ref:`PID controller<actuator-dcmotor-controller>` uses the control as a
reference setpoint relative to the joint trajectory. (see `tech note <_static/dcmotor.pdf>`__, Section 2.5)
:at:`input`: :at-val:`string, "voltage"`
Input signature: a space-separated subset of the tokens "pos", "vel", "ff" and "voltage", required in this
canonical order. The ``pos`` and ``vel`` inputs are setpoints for the on-board
:ref:`controller<actuator-dcmotor-controller>`, and ``ff`` is a torque feedforward added to its output, as for
:ref:`pid/input<actuator-pid-input>`. The ``voltage`` input is different in kind: it is the raw terminal voltage
of the physical device, applied downstream of the controller and its :at-val:`Vmax` clamp.
``input="voltage"`` (the default) is the plain voltage-commanded motor. Absent setpoint inputs are fixed at zero.
The keyword "none" selects the empty signature: the actuator has no control inputs and is purely
passive, useful for modeling :ref:`friction<actuator-dcmotor-lugre>` and :ref:`cogging<actuator-dcmotor-cogging>`
as passive joint forces. The terminal voltage is zero, so back-EMF drives current through the (shorted) motor and
brakes the joint; setting :ref:`motorconst<actuator-dcmotor-motorconst>` to zero disables the electrical branch.
(see `tech note <_static/dcmotor.pdf>`__, Section 2.5)
.. _actuator-dcmotor-controller:
:at:`controller`: :at-val:`real(6), "0 0 0 0 0 0"`
PID controller parameters, defined as :at:`controller` = ":at-val:`kp` :at-val:`ki` :at-val:`kd`
:at-val:`slewmax` :at-val:`Imax` :at-val:`Vmax`". Depending on the :at:`input` mode, the controller stabilizes
either position or velocity. If the :at:`input` mode is voltage, :at-val:`kp`, :at-val:`ki`, :at-val:`kd` are
ignored. :at-val:`Vmax` sets the maximum drive voltage :math:`v_{\max}` (Volt); in position/velocity modes it clamps
the controller output, in voltage mode it clamps the control signal (if :at:`ctrlrange` is also set, the tighter
limit wins). A value of 0 (the default) disables the respective feature. When positive, :at-val:`slewmax` limits the
setpoint rate-of-change, :at-val:`Imax` clamps the integrator state (anti-windup), and :at-val:`Vmax` clamps the
drive voltage. (see `tech note <_static/dcmotor.pdf>`__, Section 2.5)
:at-val:`slewmax` :at-val:`Imax` :at-val:`Vmax`". The gains are in torque space, as for
:ref:`pid<actuator-pid>`: the controller commands the torque
:math:`\tau = k_p (u_{pos} - l) + k_d (u_{vel} - \dot{l}) + k_i x_I + u_{f\!f}` over the inputs present in the
:ref:`input<actuator-dcmotor-input>` signature, absent setpoints being fixed at zero, and drives the voltage
:math:`v = (R/K)\,\tau + K \dot{l}`, the second term compensating back-EMF as in a current-controlled driver:
commanded torque is delivered exactly until a limit is reached. Torque-space gains from datasheet voltage-space
values are obtained by multiplying by :math:`K/R`. The integrator state
:math:`x_I` accumulates position error and requires the ``pos`` input; controller gains require a controller
input and a positive :ref:`motorconst<actuator-dcmotor-motorconst>`.
A value of 0 (the default) disables the respective feature. When positive, :at-val:`slewmax` limits the
rate-of-change of the first input (position setpoint in rad/s, or with signatures lacking ``pos``, velocity
setpoint or torque feedforward), :at-val:`Imax` clamps the integrator state (anti-windup), and :at-val:`Vmax`
clamps the drive voltage :math:`v_{\max}` (Volt), upstream of the raw ``voltage`` input.
(see `tech note <_static/dcmotor.pdf>`__, Section 2.5)
.. _actuator-plugin:
@@ -6982,7 +7003,7 @@ Associate this actuator with an :ref:`engine plugin<exPlugin>`. Either :at:`plug
.. _actuator-plugin-dyntype:
:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, muscle, user], "none"`
:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, dcmotor, muscle, user], "none"`
Activation dynamics type for the actuator. The available dynamics types were already described in the :ref:`Actuation
model <geActuation>` section. If :ref:`dyntype<actuator-general-dyntype>` is not "none", an activation variable will
be added to the actuator. This variable will be added after any activation state computed by the plugin (see
doc/_static/dcmotor.pdf
Vendored
BIN
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doc/changelog.rst
+22
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@@ -31,6 +31,28 @@ Actuation
identical to :ref:`position<actuator-position>`. The input signature is any subset of ``[pos, vel, ff]``, selected
by :ref:`input<actuator-pid-input>`; absent setpoint inputs are fixed at zero, so the control vector contains no
inert entries.
- The :ref:`dcmotor<actuator-dcmotor>` on-board controller is redesigned: the
:ref:`input<actuator-dcmotor-input>` attribute selects any subset of ``[pos, vel, ff, voltage]``, where ``pos``
and ``vel`` are setpoints for the controller, ``ff`` is a torque feedforward, and ``voltage`` is the raw terminal
voltage (the default, a plain voltage-commanded motor). Controller gains are in torque space, as for
:ref:`pid<actuator-pid>`, and the drive voltage compensates back-EMF as in a current-controlled driver: commanded
torque is delivered exactly until a limit is reached. The keyword ``input="none"`` selects the empty signature:
the actuator has no control inputs and is purely passive, so friction, cogging and back-EMF braking can be used
as passive joint forces.
.. admonition:: Breaking API changes
:class: attention
- The mode-flag semantics of :ref:`dcmotor/input<actuator-dcmotor-input>` ("voltage", "position", "velocity",
selecting the interpretation of a single control) are replaced by input signatures, and the controller gains
changed from voltage space to torque space. The old velocity mode's integral term (integrated-velocity
tracking) is retired without replacement; the integrator always accumulates position error.
**Migration:** Voltage-commanded motors (the default) are unchanged. Replace ``input="position"`` with
``input="pos"`` and ``input="velocity"`` with ``input="vel"``, and multiply the controller gains by
:math:`K/R` (torque per volt). The motor's back-EMF damping, previously felt in addition to the controller's
damping, is now compensated: to preserve behavior when the velocity setpoint is zero, add :math:`K^2/R` to the
converted :at-val:`kd`.
Engine
^^^^^^
doc/dcmotor/dcmotor.tex
+69 -112
View File
@@ -543,6 +543,7 @@ where $t_T = R_T C$ is the thermal time constant. This produces exponential rise
\begin{figure}[ht]
\centering
\resizebox{\columnwidth}{!}{%
\begin{tikzpicture}
\pgfmathsetmacro{\Tss}{1.0}
\pgfmathsetmacro{\ttau}{1.0}
@@ -568,7 +569,7 @@ where $t_T = R_T C$ is the thermal time constant. This produces exponential rise
\node[font=\scriptsize, anchor=south] at (axis cs:\xmax*0.5, \Tss)
{$T_{ss} = T_a + R_T P$};
\end{axis}
\end{tikzpicture}
\end{tikzpicture}}%
\caption{Temperature rise under constant power dissipation $P$.
At $t = t_T$, it reaches $(1-1/e) \approx 63\%$ of its steady-state value.}
\label{fig:thermal_response}
@@ -810,7 +811,7 @@ Attribute & Size & Description \\
\texttt{damping} & 3 & Viscous damping coefficients \\
\texttt{armature} & 1 & Armature inertia \\
\midrule
\texttt{input} & keyword & Mode (voltage/position/velocity) \\
\texttt{input} & string & Input block: subset of \texttt{pos vel ff voltage}, or \texttt{none} \\
\texttt{controller} & 6 & Gains, slew, and voltage saturation ($k_p, k_i, k_d, s, I_{\max}, v_{\max}$) \\
\bottomrule
\end{tabular}
@@ -1066,25 +1067,26 @@ Many actuators embed an on-board controller computing drive voltage from positio
\begin{table}[H]
\centering
\small
\begin{tabular}{@{}lll@{}}
\footnotesize
\begin{tabular}{@{}llp{4.2cm}@{}}
\toprule
Attribute & Type & Description \\
\midrule
\texttt{input} & keyword & \texttt{voltage}, \texttt{position}, \texttt{velocity} \\
\texttt{controller} & vector & Gains (mode-dependent) \\
\texttt{input} & string & subset of \texttt{pos vel ff voltage}, in canonical order; \texttt{none} (passive) \\
\texttt{controller} & vector & Gains, slew, and voltage saturation ($k_p, k_i, k_d, s, I_{\max}, v_{\max}$) \\
\bottomrule
\end{tabular}
\caption{Controller attributes. Default \texttt{input} is \texttt{voltage}.}
\label{tab:controller_attributes}
\end{table}
\noindent Unlike the motor parameters in Table~\ref{tab:datasheet}, controller gains are user-specified firmware settings with units that vary by manufacturer. MuJoCo uses direct {\em voltage-space} units (e.g., $k_p$ in V/rad). Torque-space (N$\cdot$m/rad) gains can be converted by multiplying by $R/K$, though empirical calibration is often necessary due to unknown internal units on real hardware.
\noindent Unlike the motor parameters in Table~\ref{tab:datasheet}, controller gains are user-specified firmware settings. MuJoCo uses {\em torque-space} units (e.g., $k_p$ in N$\cdot$m/rad), matching the \texttt{pid} actuator. Voltage-space datasheet gains (V/rad) convert by multiplying by $K/R$, though empirical calibration is often necessary due to unknown internal units on real hardware.
The controller computes a target voltage $v$ from the \texttt{ctrl} command. All motor physics --- cogging, saturation, friction, etc. --- apply identically downstream of $v$. The \texttt{input} attribute selects the controller:
\begin{figure}[H]
\centering
\resizebox{\columnwidth}{!}{%
\begin{tikzpicture}[
block/.style={draw, rounded corners=2pt, minimum height=1.6em,
font=\scriptsize, fill=blue!5},
@@ -1093,20 +1095,20 @@ The controller computes a target voltage $v$ from the \texttt{ctrl} command. All
every node/.style={inner sep=2pt},
]
% ctrl input
\node[font=\small] (ctrl) at (0, 3.5) {Input $u = {}$\texttt{ctrl}};
\node[font=\small] (ctrl) at (0, 3.8) {\texttt{ctrl} $=$ Input block $(\theta^*, \dot\theta^*, \tau_{f\!f}, v_{\text{raw}})$ \; (present members only)};
% Mode selector box
\node[block, minimum width=5.5cm, minimum height=6.5em, align=center]
% Controller box
\node[block, minimum width=7.2cm, minimum height=6.5em, align=center]
(sel) at (0, 1.8) {};
\node[font=\footnotesize\bfseries, anchor=north] at (0, 2.7)
{Controller mode};
{Controller};
\node[mode] at (0, 1.45) {$\begin{aligned}
\texttt{voltage:}\quad v &= u \\[2pt]
\texttt{position:}\quad v &= k_p(u\!-\!\theta) + k_i x_I - k_d\dot\theta \\[2pt]
\texttt{velocity:}\quad v &= k_p(u\!-\!\dot\theta) + k_i(x_I\!-\!\theta)
\tau &= k_p(\theta^*\!-\!\theta) + k_d(\dot\theta^*\!-\!\dot\theta) + k_i x_I + \tau_{f\!f} \\[2pt]
v &= \text{clip}(\tfrac{R}{K}\tau + K\dot\theta,\, \pm v_{\max}) + v_{\text{raw}} \\[2pt]
&\phantom{=}\ \text{absent inputs are zero;}\quad \text{\texttt{input=\textquotedbl none\textquotedbl:}}\ v = 0
\end{aligned}$};
% arrow ctrl to mode
% arrow ctrl to controller
\draw[arr] (ctrl.south) -- (sel.north);
% Motor block
@@ -1121,101 +1123,52 @@ The controller computes a target voltage $v$ from the \texttt{ctrl} command. All
\node[font=\small] (tau) at (0, -1.8) {Torque $\tau$};
\draw[arr] (motor.south) -- (tau.north);
\end{tikzpicture}
\caption{Controller pipeline. The \texttt{input} attribute selects how $v$ is derived from \texttt{ctrl}; motor physics is identical downstream.}
\end{tikzpicture}}%
\caption{Controller pipeline. The \texttt{input} attribute selects which members of the control block are present; motor physics is identical downstream.}
\label{fig:controller_pipeline}
\end{figure}
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Position Mode}
\label{sec:position_mode}
\subsubsection{Setpoint Mode}
\label{sec:setpoint_mode}
When \texttt{input="position"}, the user command $u = {}$\texttt{ctrl} is a target position, yielding voltage:
\begin{equation}
v = k_p \, (u - \theta) + k_i \, x_I - k_d \, \dot\theta
\label{eq:position_mode}
\end{equation}
where $\theta$ is the actuator length, $\dot\theta \equiv \omega$ is the actuator velocity, $x_I$ is the integral of position error, and $k_p$, $k_i$, $k_d$ are the proportional, integral, and derivative gains.
When \texttt{input="pos vel ff"} (or subset thereof), the actuator owns a
block of controls $u = (\theta^*, \dot\theta^*, \tau_{f\!f})$: a position setpoint, a velocity
setpoint and a torque feedforward. Any subset may be selected, and the \texttt{dcmotor}'s \texttt{actuator\_ctrlnum} is variable.
An absent input corresponds to a setpoint frozen at
zero. The controller commands a torque and converts it to drive voltage:
\begin{align}
\tau &= k_p \, (\theta^* - \theta) + k_d \, (\dot\theta^* - \dot\theta)
+ k_i \, x_I \; + \, \tau_{f\!f}
\label{eq:setpoint_mode} \\
v &= \frac{R}{K} \, \tau + K \dot\theta
\label{eq:torque_to_voltage}
\end{align}
where the second term of \eqref{eq:torque_to_voltage} compensates back-EMF, as the
current loop of a real torque-mode driver does: commanded torque is delivered {\em
exactly} until a limit binds, and the torque-speed envelope emerges from voltage
saturation (\S\ref{sec:voltage_saturation}). The map uses the nameplate $R$; thermal
resistance growth (\S\ref{sec:resistance_temperature}) is not compensated. The
integrator state accumulates the position error, $\dot x_I = \theta^* - \theta$,
subject to anti-windup (\S\ref{sec:anti_windup}). When $k_i = 0$, no integral state
is added and the controller reduces to PD; when $k_p = k_i = 0$, it is a pure
velocity servo. The back-EMF compensation also cancels the motor's $-K^2/R$ damping
bias, so the net physical damping delivered by an unclipped torque-mode motor is
$-k_d$, matching \texttt{pid}. The separate \texttt{voltage} input is the raw
terminal voltage, added downstream of the controller and its saturation.
\noindent The signs in~\eqref{eq:position_mode} follow MuJoCo convention: $k_p > 0$ drives toward the target, $k_d > 0$ provides damping (opposing velocity), and $k_i > 0$ reduces steady-state error.
\subsubsection{Passive Operation}
\label{sec:passive}
\paragraph{Integral state.} When $k_i > 0$, one additional activation state $x_I$ is allocated, governed by:
\begin{equation*}
\dot{x}_I = u - \theta
\label{eq:position_integral}
\end{equation*}
When $k_i = 0$, no integral state is added and the controller reduces to PD.
\paragraph{Effective torque.} Substituting~\eqref{eq:position_mode} into the stateless torque equation~\eqref{eq:torque_speed}:
\begin{equation*}
\tau = \frac{K}{R} v - \frac{K^2}{R}\dot\theta
= \underbrace{\frac{K k_p}{R}}_{\text{stiffness}} (u - \theta)
+ \frac{K k_i}{R} x_I
- \underbrace{\frac{K(K + k_d)}{R}}_{\text{damping}} \dot\theta
\label{eq:position_torque}
\end{equation*}
Note that the motor's back-EMF term $K^2\dot\theta/R$ contributes {\em additional damping} beyond the controller $k_d$ term. Even with $k_d\!=\!0$, the motor provides natural damping $K^2/R$. The computed $v$ is subject to voltage saturation (\S\ref{sec:voltage_saturation}).
\begin{table}[H]
\centering
\small
\begin{tabular}{@{}lll@{}}
\toprule
Attribute & Symbol & Units \\
\midrule
\atKP{} & $k_p$ & V/rad \\
\atKI{} & $k_i$ & V/(rad$\cdot$s) \\
\atKD{} & $k_d$ & V$\cdot$s/rad \\
\bottomrule
\end{tabular}
\caption{Position mode controller gains.}
\label{tab:position_params}
\end{table}
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Velocity Mode}
\label{sec:velocity_mode}
When \texttt{input="velocity"}, the user command $u = {}$\texttt{ctrl} is a target velocity, and $k_p$, $k_i$ are the proportional and integral gains.
\begin{equation}
v = k_p \, (u - \dot\theta) + k_i \, (x_I - \theta)
\label{eq:velocity_mode}
\end{equation}
\paragraph{Integral state.} When $k_i > 0$, one additional activation state $x_I$ is allocated, governed by the integrator:
\begin{equation*}
\dot{x}_I = u
\label{eq:velocity_integral}
\end{equation*}
The term $k_i(x_I - \theta)$ then tracks a target position $x_I$ advancing at the commanded velocity $u$. This matches MuJoCo's \texttt{intvelocity} actuator behavior.
When $k_i = 0$, no integral state is added and the controller provides pure velocity feedback. The computed $v$ is subject to voltage saturation (\S\ref{sec:voltage_saturation}).
\paragraph{Effective torque.} Substituting~\eqref{eq:velocity_mode} into~\eqref{eq:torque_speed}:
\begin{equation*}
\tau = \underbrace{\frac{K k_i}{R}}_{\text{stiffness}} (x_I - \theta)
- \underbrace{\frac{K(K + k_p)}{R}}_{\text{damping}} \dot\theta
+ \frac{K k_p}{R} u
\label{eq:velocity_torque}
\end{equation*}
Note the role swap compared to position mode: $k_i$ provides stiffness (position tracking to $x_I$) while $k_p$ adds damping alongside the motor's natural back-EMF damping $K^2/R$.
\begin{table}[H]
\centering
\small
\begin{tabular}{@{}lll@{}}
\toprule
Attribute & Symbol & Units \\
\midrule
\atKP{} & $k_p$ & V$\cdot$s/rad \\
\atKI{} & $k_i$ & V/rad \\
\bottomrule
\end{tabular}
\caption{Velocity mode controller gains.}
\label{tab:velocity_params}
\end{table}
\pagebreak
\texttt{input="none"} selects the {\em empty} input block: the actuator owns no
controls at all and acts as a purely passive device. The terminal voltage is
identically zero, so the motor operates with shorted terminals: back-EMF drives
current through $R$ and brakes the joint (dynamic braking), while cogging
\eqref{eq:cogging} and LuGre friction (\S\ref{sec:lugre}) act as passive joint
forces. Setting \texttt{motorconst} to zero decouples the electrical branch,
leaving pure friction and cogging. This exists because MuJoCo associates auxiliary
dynamic states (such as the LuGre bristle) with actuators, not joints: a passive
\texttt{dcmotor} is the idiomatic way to attach these passive phenomena to a joint.
Controller gains, slew rate limiting and integral gain require a controller input and are rejected.
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Setpoint Slew Rate}
@@ -1229,7 +1182,7 @@ where $u_{\text{prev}}$ is the previous effective setpoint and $\Delta t$ is the
\paragraph{State variable.} When $s > 0$, one activation state $u_{\text{prev}}$ is allocated, and updated each step to $u$ (post-clamping).
\paragraph{Units.} The slew rate $s$ has mode-dependent units: rad/s for position mode (limiting setpoint velocity), rad/s\textsuperscript{2} for velocity mode (limiting setpoint acceleration), and V/s for voltage mode.
\paragraph{Units.} The slew rate $s$ limits the first controller input, with corresponding units: position setpoint (rad/s), velocity setpoint (rad/s$^2$), or torque feedforward (N$\cdot$m/s). The raw \texttt{voltage} input is never rate-limited; \texttt{slewmax} requires a controller input.
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
\subsubsection{Anti-windup}
@@ -1245,12 +1198,12 @@ This prevents controller windup even when drive signals are saturated.
\subsubsection{Voltage Saturation}
\label{sec:voltage_saturation}
In \texttt{position} and \texttt{velocity} modes, the computed voltage $v$ can be arbitrarily large (proportional to the error). Real motor drivers are limited by their supply voltage. When \atVMAX{} is set ($v_{\max} > 0$), a voltage clamp is applied before the motor equations:
With setpoint inputs, the computed voltage $v$ can be arbitrarily large (proportional to the error). Real motor drivers are limited by their supply voltage. When \atVMAX{} is set ($v_{\max} > 0$), a voltage clamp is applied before the motor equations:
\begin{equation*}
v \leftarrow \text{clip}(v, \pm v_{\max})
\label{eq:vlimit}
\end{equation*}
This differs from \texttt{ctrlrange} (clamping user command $u$) and \texttt{forcerange} (clamping output torque). In position and velocity modes, \texttt{ctrlrange} limits the setpoint while \atVMAX{} limits the drive signal. In voltage mode ($v = u$), both clamp the voltage; if both are set, the tighter limit wins.
This differs from \texttt{ctrlrange} (clamping user commands $u$) and \texttt{forcerange} (clamping output torque). The clamp applies to the controller output only: the raw \texttt{voltage} input is added downstream, unclamped (use \texttt{ctrlrange} to bound it). Because the torque-to-voltage map \eqref{eq:torque_to_voltage} compensates back-EMF, the achievable torque under \atVMAX{} shrinks with speed: the torque-speed envelope of \S\ref{sec:electromagnetics}.
\begin{table}[H]
\centering
@@ -1259,11 +1212,11 @@ This differs from \texttt{ctrlrange} (clamping user command $u$) and \texttt{for
\toprule
Attribute & Symbol & Units \\
\midrule
\atKP{} & $k_p$ & mode-dependent \\
\atKI{} & $k_i$ & mode-dependent \\
\atKD{} & $k_d$ & V$\cdot$s/rad \\
\atKP{} & $k_p$ & N$\cdot$m/rad \\
\atKI{} & $k_i$ & N$\cdot$m/(rad$\cdot$s) \\
\atKD{} & $k_d$ & N$\cdot$m$\cdot$s/rad \\
\atSLEW{} & $s$ & ctrl-units/s \\
\atIMAXINT{} & $I_{\max}$ & mode-dependent \\
\atIMAXINT{} & $I_{\max}$ & rad$\cdot$s \\
\atVMAX{} & $v_{\max}$ & Volt \\
\bottomrule
\end{tabular}
@@ -1272,6 +1225,8 @@ Attribute & Symbol & Units \\
\end{table}
% ---------------------------------------------------------------------------
\vfill\newpage
% Low-Level Semantics
% ---------------------------------------------------------------------------
\subsection{Low-Level Semantics}
@@ -1294,7 +1249,7 @@ Array & Index & Symbol & Description \\
& 5 & $k_i$ & Controller integral gain \\
& 6 & $k_d$ & Controller derivative gain \\
& 7 & $v_{\max}$ & Voltage saturation (V) \\
& 8 & --- & Input mode (0:\ $v$, 1:\ $\theta$, 2:\ $\dot\theta$) \\
& 8 & --- & Reserved \\
\midrule
\texttt{dynprm} & 0 & $t_e$ & Electrical time constant (s) \\
& 1 & $(di{/}dt)_{\max}$ & Current rate limit (A/s) \\
@@ -1323,6 +1278,8 @@ Array & Index & Symbol & Description \\
\texttt{armature} & 0 & $J_r$ & Actuator armature \\
\midrule
\texttt{gear} & 0 & $N$ & Gear ratio \\
\midrule
\texttt{ctrlspec} & 0 & --- & Input signature (\texttt{mjtCtrlInput} bitmask) \\
\bottomrule
\end{tabular}
\caption{\texttt{mjModel} array semantics for the \texttt{dcmotor} actuator.}
doc/includes/references.h
+4 -2
View File
@@ -2548,7 +2548,9 @@ typedef enum mjtCtrlChart { // so3 input signature (actuator_ctrlspec): or
typedef enum mjtCtrlInput { // servo input signature (actuator_ctrlspec): present-input bits
mjINPUT_POS = 1, // position setpoint input
mjINPUT_VEL = 2, // velocity setpoint input
mjINPUT_FF = 4 // feedforward input
mjINPUT_FF = 4, // feedforward input, in the actuator's output space
mjINPUT_VOLTAGE = 8, // raw terminal voltage input (dcmotor)
mjINPUT_NONE = 16 // explicitly no inputs: purely passive (dcmotor)
} mjtCtrlInput;
typedef enum mjtObj { // type of MujoCo object
mjOBJ_UNKNOWN = 0, // unknown object type
@@ -4018,7 +4020,7 @@ const char* mjs_setToAdhesion(mjsActuator* actuator, double gain);
const char* mjs_setToDCMotor(mjsActuator* actuator, double motorconst[2], double resistance,
double nominal[3], double saturation[3], double inductance[2],
double cogging[3], double controller[6], double thermal[6],
double lugre[5], int input_mode);
double lugre[5], int ctrlspec);
mjsMesh* mjs_addMesh(mjSpec* s, const mjsDefault* def);
mjsHField* mjs_addHField(mjSpec* s);
mjsSkin* mjs_addSkin(mjSpec* s);