Add the pid actuator: setpoint inputs, integral action, slew rate limiting.

<pid kp kv|dampratio [ki imax] [slewmax]> is a PID controller with real position and velocity setpoint inputs on a single force output, plus an optional feedforward input. With a zero velocity setpoint it reproduces <position> bit-exactly; the input signature is any subset of [pos, vel, ff], selected with input="..." and recorded as mjtCtrlInput bits in
actuator_ctrlspec; absent setpoint inputs are fixed at zero, so the control vector contains no inert entries.

kp and kv are single-sourced in the affine bias parameters (biasprm[1,2]) with no gainprm mirror: every consumer of the position-servo shape
(dampratio conversion, inheritrange, qDeriv) reads one location, which is what makes the bit-exact <position> parity possible. Controller state uses dyntype 'pid' with slot-gated activations in the order [slew, integral], following the dcmotor slot idiom: slewmax (dynprm[1]) rate limits the effective position setpoint through an activation holding it;
ki (gainprm[0]) integrates the position error -- wrapped on rotational transmissions -- with anti-windup clamping of the integrand at imax (dynprm[0]). Both features require the pos input. Servo input unpacking is shared with the dcmotor controller (unpackServoInputs); per-input ranges are exposed as posrange/velrange/ffrange.

This subsumes the functionality of the mujoco.pid plugin with proper activation state: correct under all integrators, visible to keyframes, act sensors and reset. Migration: kp/ki/kd map to kp/ki/kv, plugin imax is in force units (divide by ki), slewmax carries over; the single ctrl becomes input="pos".

PiperOrigin-RevId: 957588898
Change-Id: Id2786836ca6e76f58e5b5cc8323fc23be0a53784

doc/APIreference/APItypes.rst

@@ -357,6 +357,16 @@ Orientation input charts of so3 actuators. These values are used in ``m->actuato
 .. mujoco-include:: mjtCtrlChart
 
 
+.. _mjtCtrlInput:
+
+mjtCtrlInput
+~~~~~~~~~~~~
+
+Input bitflags of servo-family (pd, dcmotor) actuators. These values are used in ``m->actuator_ctrlspec``.
+
+.. mujoco-include:: mjtCtrlInput
+
+
 .. _mjtObj:
 
 mjtObj

doc/APIreference/functions.rst

@@ -5315,6 +5315,15 @@ Set actuator to velocity servo; return error if any.
 
 Set actuator to orientation servo.
 
+.. _mjs_setToPID:
+
+`mjs_setToPID <#mjs_setToPID>`__
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. mujoco-include:: mjs_setToPID
+
+Set actuator to PID controller.
+
 .. _mjs_setToDamper:
 
 `mjs_setToDamper <#mjs_setToDamper>`__

doc/XMLreference.rst

@@ -5664,25 +5664,27 @@ specify them independently.
 
 .. _actuator-general-dyntype:
 
-:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, muscle, user], "none"`
+:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, 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:
 
-   =========== ======================================
+   ============= ======================================
-   Keyword     Description
+   Keyword       Description
-   =========== ======================================
+   ============= ======================================
-   none        No internal state
+   none          No internal state
-   integrator  act_dot = ctrl
+   integrator    act_dot = ctrl
-   filter      act_dot = (ctrl - act) / dynprm[0]
+   filter        act_dot = (ctrl - act) / dynprm[0]
-   filterexact Like filter but with exact integration
+   filterexact   Like filter but with exact integration
-   muscle      act_dot = mju_muscleDynamics(...)
+   pid           act_dot = position error; see :ref:`pid<actuator-pid>`
-   user        act_dot = mjcb_act_dyn(...)
+   dcmotor       DC motor electrical dynamics, see :ref:`dcmotor<actuator-dcmotor>`
-   =========== ======================================
+   muscle        act_dot = mju_muscleDynamics(...)
+   user          act_dot = mjcb_act_dyn(...)
+   ============= ======================================
 
 .. _actuator-general-gaintype:
 
-:at:`gaintype`: :at-val:`[fixed, affine, muscle, so3, user], "fixed"`
+:at:`gaintype`: :at-val:`[fixed, affine, muscle, 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.
@@ -5695,6 +5697,7 @@ 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(...)
+   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(...)
    ======= ===============================
@@ -5739,12 +5742,23 @@ specify them independently.
    so the user can enter as many parameters as needed. These defaults are not compatible with muscle actuators; see
    :ref:`muscle <actuator-muscle>` below.
 
+.. _actuator-general-velrange:
+
+:at:`velrange`: :at-val:`real(2), "0 0"`
+   Range of the velocity-setpoint input of a :ref:`pid<actuator-pid>` actuator.
+
+.. _actuator-general-ffrange:
+
+:at:`ffrange`: :at-val:`real(2), "0 0"`
+   Range of the feedforward input of a :ref:`pid<actuator-pid>` actuator.
+
 .. _actuator-general-input:
 
 :at:`input`: :at-val:`string, optional`
    Input signature of the actuator: which controls make up its control block, recorded in
-   ``mjModel.actuator_ctrlspec``. Available for gaintype "so3", where it selects the orientation chart: "expmap"
+   ``mjModel.actuator_ctrlspec``. For gaintype "so3" it selects the orientation chart: "expmap" (3 controls, the
-   (3 controls, the default) or "quat" (4 controls); see :ref:`orientation/input<actuator-orientation-input>`.
+   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>`.
 
 .. _actuator-general-actearly:
 
@@ -5954,6 +5968,146 @@ This element has one custom attribute in addition to the common attributes:
    :ref:`position<actuator-position>` attribute and in the :ref:`default class<default-position-inheritrange>`,
    saved XMLs always convert it to explicit :at:`ctrlrange` at the actuator.
 
+.. _actuator-pid:
+
+:el-prefix:`actuator/` |-| **pid** |*|
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This element creates a PID controller with position and velocity setpoint inputs on a single force output, with optional
+integral action and feedforward. With the default input signature ``[pos, vel]`` the force is
+:math:`k_p (u_{pos} - l) + k_v (u_{vel} - v)` where :math:`l, v` are the actuator length and velocity; with a zero
+velocity setpoint this is identical to :ref:`position<actuator-position>`. The input signature is any subset of
+``[pos, vel, ff]``, selected by :ref:`input<actuator-pid-input>`: an absent setpoint input is fixed at zero, and the
+``ff`` input adds a feedforward force. Integral action is enabled by :ref:`ki<actuator-pid-ki>`: the position error is integrated in
+:ref:`act<siPhysicsState>` and contributes :math:`k_i \cdot act` to the force, with anti-windup clamping by
+:ref:`imax<actuator-pid-imax>`.
+:ref:`slewmax<actuator-pid-slewmax>` limits the rate of change of the effective position setpoint. Each of these
+features, when enabled, adds one activation state, in the order [slew, integral]. The underlying
+:ref:`general<actuator-general>` attributes are set as follows:
+
+========= ===================== ========= =========
+Attribute Setting               Attribute Setting
+========= ===================== ========= =========
+dyntype   none or pid dynprm    imax 0 0
+gaintype  pid                   gainprm   ki 0 0
+biastype  affine                biasprm   0 -kp -kv
+========= ===================== ========= =========
+
+This element has custom attributes in addition to the common attributes:
+
+.. _actuator-pid-name:
+
+.. _actuator-pid-class:
+
+.. _actuator-pid-group:
+
+.. _actuator-pid-nsample:
+
+.. _actuator-pid-interp:
+
+.. _actuator-pid-delay:
+
+.. _actuator-pid-ctrllimited:
+
+.. _actuator-pid-forcelimited:
+
+.. _actuator-pid-ctrlrange:
+
+.. _actuator-pid-forcerange:
+
+.. _actuator-pid-lengthrange:
+
+.. _actuator-pid-gear:
+
+.. _actuator-pid-damping:
+
+.. _actuator-pid-armature:
+
+.. _actuator-pid-cranklength:
+
+.. _actuator-pid-user:
+
+.. _actuator-pid-joint:
+
+.. _actuator-pid-jointinparent:
+
+.. _actuator-pid-tendon:
+
+.. _actuator-pid-slidersite:
+
+.. _actuator-pid-cranksite:
+
+.. _actuator-pid-site:
+
+.. _actuator-pid-refsite:
+
+.. _actuator-pid-kp:
+
+:at:`kp`: :at-val:`real, "1"`
+   Position feedback gain.
+
+.. _actuator-pid-kv:
+
+:at:`kv`: :at-val:`real, "0"`
+   Velocity feedback gain: applied to the velocity error when the ``vel`` input is present, and as pure damping
+   otherwise. When using this attribute, it is recommended to use the implicitfast or implicit
+   :ref:`integrators<geIntegration>`.
+
+.. _actuator-pid-dampratio:
+
+:at:`dampratio`: :at-val:`real, "0"`
+   Damping applied by the actuator, using damping ratio units, as for
+   :ref:`position/dampratio<actuator-position-dampratio>`. This attribute is exclusive with :at:`kv`.
+
+.. _actuator-pid-ki:
+
+:at:`ki`: :at-val:`real, "0"`
+   Integral gain. A nonzero value enables integral action: the position error is integrated in
+   :ref:`act<siPhysicsState>` (:ref:`dyntype<actuator-general-dyntype>` "pid") and contributes :math:`k_i \cdot act`
+   to the force.
+   Requires the ``pos`` input.
+
+.. _actuator-pid-imax:
+
+:at:`imax`: :at-val:`real, "0"`
+   Anti-windup limit on the integral state: accumulation stops beyond ±\ :at:`imax`. The default value 0 means
+   "unclamped".
+
+.. _actuator-pid-slewmax:
+
+:at:`slewmax`: :at-val:`real, "0"`
+   Maximum rate of change of the effective position setpoint. When positive, the commanded setpoint is rate-limited
+   through an activation state holding the effective setpoint, as for the
+   :ref:`dcmotor controller<actuator-dcmotor-controller>`. The default value 0 means "unlimited".
+
+.. _actuator-pid-input:
+
+:at:`input`: :at-val:`string, "pos vel"`
+   Input signature: a space-separated subset of the tokens "pos", "vel" and "ff", packed in this canonical order.
+   Absent setpoint inputs are fixed at zero, so the control vector contains no inert entries.
+
+.. _actuator-pid-posrange:
+
+:at:`posrange`: :at-val:`real(2), "0 0"`
+   Range of the position-setpoint input; an alias of :ref:`ctrlrange<actuator-general-ctrlrange>` (the first
+   input).
+
+.. _actuator-pid-velrange:
+
+:at:`velrange`: :at-val:`real(2), "0 0"`
+   Range of the velocity-setpoint input.
+
+.. _actuator-pid-ffrange:
+
+:at:`ffrange`: :at-val:`real(2), "0 0"`
+   Range of the feedforward input.
+
+.. _actuator-pid-inheritrange:
+
+:at:`inheritrange`: :at-val:`real, "0"`
+   Identical to :ref:`position/inheritrange<actuator-position-inheritrange>`, setting :at:`posrange` from the
+   transmission target's :at:`range`.
+
 .. _actuator-orientation:
 
 :el-prefix:`actuator/` |-| **orientation** |*|
@@ -5976,7 +6130,7 @@ preserving its direction; the lower bound must be 0.
 :ref:`Actuator sensors<sensor-actuatorpos>` report one value per force output. The integrator variant, which
 stores the orientation setpoint in :ref:`act<siPhysicsState>`, is available via :ref:`general<actuator-general>` with
 :ref:`dyntype<actuator-general-dyntype>` "integrator" and is expmap-only. The video on the right shows this `example
-model <https://github.com/google-deepmind/mujoco/blob/main/test/engine/testdata/sensor/actuation/orientation.xml>`__.
+model <https://github.com/google-deepmind/mujoco/blob/main/test/engine/testdata/actuation/orientation.xml>`__.
 The underlying :el:`general` attributes are set as follows:
 
 ========= ======= ========= =========
@@ -6056,9 +6210,8 @@ This element has custom attributes in addition to the common attributes:
 :el-prefix:`actuator/` |-| **velocity** |*|
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-This element creates a velocity servo. Note that in order to create a PD controller, one has to define two actuators: a
+This element creates a velocity servo. Note that a PD controller with both position and velocity setpoint inputs is
-position servo and a velocity servo. This is because MuJoCo actuators are SISO while a PD controller takes two control
+provided by the :ref:`pid<actuator-pid>` actuator.
-inputs (reference position and reference velocity).
 When using this actuator, it is recommended to use the implicitfast or implicit :ref:`integrators<geIntegration>`.
 The underlying :el:`general` attributes are set as follows:
 
@@ -6802,7 +6955,7 @@ Associate this actuator with an :ref:`engine plugin<exPlugin>`. Either :at:`plug
 
 .. _actuator-plugin-dyntype:
 
-:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, muscle, user], "none"`
+:at:`dyntype`: :at-val:`[none, integrator, filter, filterexact, pid, 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
@@ -10020,6 +10173,10 @@ if omitted.
 
 .. _default-general-biasprm:
 
+.. _default-general-velrange:
+
+.. _default-general-ffrange:
+
 .. _default-general-input:
 
 .. _default-general-actearly:
@@ -10199,6 +10356,95 @@ All :ref:`intvelocity <actuator-intvelocity>` attributes are available here exce
 site, refsite, tendon, slidersite, cranksite.
 
 
+.. _default-pid:
+
+.. _default-pid-ctrllimited:
+
+.. _default-pid-forcelimited:
+
+.. _default-pid-ctrlrange:
+
+.. _default-pid-posrange:
+
+.. _default-pid-velrange:
+
+.. _default-pid-ffrange:
+
+.. _default-pid-forcerange:
+
+.. _default-pid-inheritrange:
+
+.. _default-pid-gear:
+
+.. _default-pid-damping:
+
+.. _default-pid-armature:
+
+.. _default-pid-cranklength:
+
+.. _default-pid-user:
+
+.. _default-pid-group:
+
+.. _default-pid-nsample:
+
+.. _default-pid-interp:
+
+.. _default-pid-delay:
+
+.. _default-pid-kp:
+
+.. _default-pid-kv:
+
+.. _default-pid-dampratio:
+
+.. _default-pid-ki:
+
+.. _default-pid-imax:
+
+.. _default-pid-slewmax:
+
+.. _default-pid-input:
+
+:el-prefix:`default/` |-| **pid** |?|
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+All :ref:`pid <actuator-pid>` attributes are available here except: name, class, joint, jointinparent,
+site, refsite, tendon, slidersite, cranksite.
+
+
+.. _default-orientation:
+
+.. _default-orientation-forcelimited:
+
+.. _default-orientation-ctrlrange:
+
+.. _default-orientation-forcerange:
+
+.. _default-orientation-user:
+
+.. _default-orientation-group:
+
+.. _default-orientation-nsample:
+
+.. _default-orientation-interp:
+
+.. _default-orientation-delay:
+
+.. _default-orientation-kp:
+
+.. _default-orientation-kv:
+
+.. _default-orientation-dampratio:
+
+.. _default-orientation-input:
+
+:el-prefix:`default/` |-| **orientation** |?|
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+All :ref:`orientation <actuator-orientation>` attributes are available here except: name, class, joint, site, refsite.
+
+
 .. _default-damper:
 
 .. _default-damper-forcelimited:

doc/XMLschema.rst

@@ -2378,6 +2378,12 @@
             .. grid-item::
                :ref:`input<actuator-general-input>`
 
+            .. grid-item::
+               :ref:`velrange<actuator-general-velrange>`
+
+            .. grid-item::
+               :ref:`ffrange<actuator-general-ffrange>`
+
             .. grid-item::
                :ref:`dyntype<actuator-general-dyntype>`
 
@@ -2793,6 +2799,114 @@
                :ref:`input<actuator-orientation-input>`
 
 
+      .. dropdown:: :ref:`pid<actuator-pid>` |*|
+
+         .. grid:: 2 3 4 4
+            :gutter: 0
+
+            .. grid-item::
+               :ref:`name<actuator-pid-name>`
+
+            .. grid-item::
+               :ref:`class<actuator-pid-class>`
+
+            .. grid-item::
+               :ref:`group<actuator-pid-group>`
+
+            .. grid-item::
+               :ref:`nsample<actuator-pid-nsample>`
+
+            .. grid-item::
+               :ref:`interp<actuator-pid-interp>`
+
+            .. grid-item::
+               :ref:`delay<actuator-pid-delay>`
+
+            .. grid-item::
+               :ref:`ctrllimited<actuator-pid-ctrllimited>`
+
+            .. grid-item::
+               :ref:`forcelimited<actuator-pid-forcelimited>`
+
+            .. grid-item::
+               :ref:`ctrlrange<actuator-pid-ctrlrange>`
+
+            .. grid-item::
+               :ref:`posrange<actuator-pid-posrange>`
+
+            .. grid-item::
+               :ref:`velrange<actuator-pid-velrange>`
+
+            .. grid-item::
+               :ref:`ffrange<actuator-pid-ffrange>`
+
+            .. grid-item::
+               :ref:`forcerange<actuator-pid-forcerange>`
+
+            .. grid-item::
+               :ref:`inheritrange<actuator-pid-inheritrange>`
+
+            .. grid-item::
+               :ref:`lengthrange<actuator-pid-lengthrange>`
+
+            .. grid-item::
+               :ref:`gear<actuator-pid-gear>`
+
+            .. grid-item::
+               :ref:`damping<actuator-pid-damping>`
+
+            .. grid-item::
+               :ref:`armature<actuator-pid-armature>`
+
+            .. grid-item::
+               :ref:`cranklength<actuator-pid-cranklength>`
+
+            .. grid-item::
+               :ref:`user<actuator-pid-user>`
+
+            .. grid-item::
+               :ref:`joint<actuator-pid-joint>`
+
+            .. grid-item::
+               :ref:`jointinparent<actuator-pid-jointinparent>`
+
+            .. grid-item::
+               :ref:`tendon<actuator-pid-tendon>`
+
+            .. grid-item::
+               :ref:`slidersite<actuator-pid-slidersite>`
+
+            .. grid-item::
+               :ref:`cranksite<actuator-pid-cranksite>`
+
+            .. grid-item::
+               :ref:`site<actuator-pid-site>`
+
+            .. grid-item::
+               :ref:`refsite<actuator-pid-refsite>`
+
+            .. grid-item::
+               :ref:`kp<actuator-pid-kp>`
+
+            .. grid-item::
+               :ref:`kv<actuator-pid-kv>`
+
+            .. grid-item::
+               :ref:`dampratio<actuator-pid-dampratio>`
+
+            .. grid-item::
+               :ref:`ki<actuator-pid-ki>`
+
+            .. grid-item::
+               :ref:`imax<actuator-pid-imax>`
+
+            .. grid-item::
+               :ref:`slewmax<actuator-pid-slewmax>`
+
+            .. grid-item::
+               :ref:`input<actuator-pid-input>`
+
+
       .. dropdown:: :ref:`damper<actuator-damper>` |*|
 
          .. grid:: 2 3 4 4
@@ -5927,6 +6041,12 @@
             .. grid-item::
                :ref:`input<default-general-input>`
 
+            .. grid-item::
+               :ref:`velrange<default-general-velrange>`
+
+            .. grid-item::
+               :ref:`ffrange<default-general-ffrange>`
+
             .. grid-item::
                :ref:`dyntype<default-general-dyntype>`
 
@@ -6165,6 +6285,126 @@
                :ref:`dampratio<default-intvelocity-dampratio>`
 
 
+      .. dropdown:: :ref:`orientation<default-orientation>` :octicon:`dot`
+
+         .. grid:: 2 3 4 4
+            :gutter: 0
+
+            .. grid-item::
+               :ref:`forcelimited<default-orientation-forcelimited>`
+
+            .. grid-item::
+               :ref:`ctrlrange<default-orientation-ctrlrange>`
+
+            .. grid-item::
+               :ref:`forcerange<default-orientation-forcerange>`
+
+            .. grid-item::
+               :ref:`user<default-orientation-user>`
+
+            .. grid-item::
+               :ref:`group<default-orientation-group>`
+
+            .. grid-item::
+               :ref:`nsample<default-orientation-nsample>`
+
+            .. grid-item::
+               :ref:`interp<default-orientation-interp>`
+
+            .. grid-item::
+               :ref:`delay<default-orientation-delay>`
+
+            .. grid-item::
+               :ref:`kp<default-orientation-kp>`
+
+            .. grid-item::
+               :ref:`kv<default-orientation-kv>`
+
+            .. grid-item::
+               :ref:`dampratio<default-orientation-dampratio>`
+
+            .. grid-item::
+               :ref:`input<default-orientation-input>`
+
+
+      .. dropdown:: :ref:`pid<default-pid>` :octicon:`dot`
+
+         .. grid:: 2 3 4 4
+            :gutter: 0
+
+            .. grid-item::
+               :ref:`ctrllimited<default-pid-ctrllimited>`
+
+            .. grid-item::
+               :ref:`forcelimited<default-pid-forcelimited>`
+
+            .. grid-item::
+               :ref:`ctrlrange<default-pid-ctrlrange>`
+
+            .. grid-item::
+               :ref:`posrange<default-pid-posrange>`
+
+            .. grid-item::
+               :ref:`velrange<default-pid-velrange>`
+
+            .. grid-item::
+               :ref:`ffrange<default-pid-ffrange>`
+
+            .. grid-item::
+               :ref:`forcerange<default-pid-forcerange>`
+
+            .. grid-item::
+               :ref:`inheritrange<default-pid-inheritrange>`
+
+            .. grid-item::
+               :ref:`gear<default-pid-gear>`
+
+            .. grid-item::
+               :ref:`damping<default-pid-damping>`
+
+            .. grid-item::
+               :ref:`armature<default-pid-armature>`
+
+            .. grid-item::
+               :ref:`cranklength<default-pid-cranklength>`
+
+            .. grid-item::
+               :ref:`user<default-pid-user>`
+
+            .. grid-item::
+               :ref:`group<default-pid-group>`
+
+            .. grid-item::
+               :ref:`nsample<default-pid-nsample>`
+
+            .. grid-item::
+               :ref:`interp<default-pid-interp>`
+
+            .. grid-item::
+               :ref:`delay<default-pid-delay>`
+
+            .. grid-item::
+               :ref:`kp<default-pid-kp>`
+
+            .. grid-item::
+               :ref:`kv<default-pid-kv>`
+
+            .. grid-item::
+               :ref:`dampratio<default-pid-dampratio>`
+
+            .. grid-item::
+               :ref:`ki<default-pid-ki>`
+
+            .. grid-item::
+               :ref:`imax<default-pid-imax>`
+
+            .. grid-item::
+               :ref:`slewmax<default-pid-slewmax>`
+
+            .. grid-item::
+               :ref:`input<default-pid-input>`
+
+
       .. dropdown:: :ref:`damper<default-damper>` :octicon:`dot`
 
          .. grid:: 2 3 4 4

doc/changelog.rst

@@ -5,6 +5,23 @@ Changelog
 Upcoming version (not yet released)
 -----------------------------------
 
+Actuation
+^^^^^^^^^
+- Added the :ref:`pid<actuator-pid>` actuator: a PID controller with real position and velocity setpoint inputs,
+  optional integral action (:ref:`ki<actuator-pid-ki>`, integrating the position error with
+  :ref:`imax<actuator-pid-imax>` anti-windup), setpoint rate limiting (:ref:`slewmax<actuator-pid-slewmax>`), and an
+  optional feedforward input. This subsumes the functionality of the ``mujoco.pid`` plugin with proper activation
+  state: correct under all integrators and visible to keyframes and sensors. With a zero velocity setpoint it is
+  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.
+
+.. admonition:: Breaking ABI changes
+   :class: caution
+
+   - :ref:`mjsActuator` gained ``velrange`` and ``ffrange`` fields, changing its size and layout. The :ref:`mjtGain`
+     and :ref:`mjtDyn` enums gained ``pid`` members, shifting the values of ``mjGAIN_USER`` and ``mjDYN_USER``.
+
 Engine
 ^^^^^^
 

doc/includes/references.h

@@ -2244,6 +2244,8 @@ typedef struct mjsActuator_ {      // actuator specification
   double dynprm[mjNDYN];           // dynamics parameters
   int actdim;                      // number of activation variables
   int ctrlspec;                    // input signature, scoped by gaintype; 0: type default
+  double velrange[2];              // range of the velocity-setpoint input (pid)
+  double ffrange[2];               // range of the feedforward input (pid)
   mjtBool actearly;                // apply next activations to qfrc
 
   // transmission
@@ -2513,6 +2515,7 @@ typedef enum mjtDyn {             // type of actuator dynamics
   mjDYN_FILTEREXACT,              // linear filter: da/dt = (u-a) / tau, with exact integration
   mjDYN_MUSCLE,                   // piecewise linear filter with two time constants
   mjDYN_DCMOTOR,                  // DC motor electrical dynamics
+  mjDYN_PID,                      // PID controller states: slew, integral
   mjDYN_USER                      // user-defined dynamics type
 } mjtDyn;
 typedef enum mjtGain {            // type of actuator gain
@@ -2521,6 +2524,7 @@ typedef enum mjtGain {            // type of actuator gain
   mjGAIN_MUSCLE,                  // muscle FLV curve computed by mju_muscleGain()
   mjGAIN_DCMOTOR,                 // DC motor gain: K or K/R
   mjGAIN_SO3,                     // geodesic servo on an SO3 transmission: force = kp * log(error)
+  mjGAIN_PID,                     // PID controller: position and velocity setpoint inputs
   mjGAIN_USER                     // user-defined gain type
 } mjtGain;
 typedef enum mjtBias {            // type of actuator bias
@@ -2535,6 +2539,11 @@ typedef enum mjtCtrlChart {       // so3 input signature (actuator_ctrlspec): or
   mjCHART_EXPMAP      = 1,        // exponential-map orientation target: 3 controls
   mjCHART_QUAT        = 2         // quaternion orientation target: 4 controls
 } mjtCtrlChart;
+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
+} mjtCtrlInput;
 typedef enum mjtObj {             // type of MujoCo object
   mjOBJ_UNKNOWN       = 0,        // unknown object type
   mjOBJ_BODY,                     // body
@@ -3989,6 +3998,9 @@ const char* mjs_setToIntVelocity(mjsActuator* actuator, double kp, double kv[1],
 const char* mjs_setToVelocity(mjsActuator* actuator, double kv);
 const char* mjs_setToOrientation(mjsActuator* actuator, double kp, double kv[1],
                                  double dampratio[1], int ctrlspec);
+const char* mjs_setToPID(mjsActuator* actuator, double kp, double kv[1], double dampratio[1],
+                         double ki[1], double imax[1], double slewmax[1], double inheritrange,
+                         int ctrlspec);
 const char* mjs_setToDamper(mjsActuator* actuator, double kv);
 const char* mjs_setToCylinder(mjsActuator* actuator, double timeconst,
                               double bias, double area, double diameter);

include/mujoco/mjspec.h

@@ -725,6 +725,8 @@ typedef struct mjsActuator_ {      // actuator specification
   double dynprm[mjNDYN];           // dynamics parameters
   int actdim;                      // number of activation variables
   int ctrlspec;                    // input signature, scoped by gaintype; 0: type default
+  double velrange[2];              // range of the velocity-setpoint input (pid)
+  double ffrange[2];               // range of the feedforward input (pid)
   mjtBool actearly;                // apply next activations to qfrc
 
   // transmission

include/mujoco/mjspecmacro.h

@@ -497,6 +497,8 @@
     XVEC( double,        dynprm,        mjNDYN    ) \
     X   ( int,           actdim,        1         ) \
     X   ( int,           ctrlspec,      1         ) \
+    XVEC( double,        velrange,      2         ) \
+    XVEC( double,        ffrange,       2         ) \
     X   ( mjtBool,       actearly,      1         ) \
     X   ( mjtTrn,        trntype,       1         ) \
     XVEC( double,        gear,          6         ) \

include/mujoco/mjtype.h

@@ -247,6 +247,7 @@ typedef enum mjtDyn {             // type of actuator dynamics
   mjDYN_FILTEREXACT,              // linear filter: da/dt = (u-a) / tau, with exact integration
   mjDYN_MUSCLE,                   // piecewise linear filter with two time constants
   mjDYN_DCMOTOR,                  // DC motor electrical dynamics
+  mjDYN_PID,                      // PID controller states: slew, integral
   mjDYN_USER                      // user-defined dynamics type
 } mjtDyn;
 
@@ -257,6 +258,7 @@ typedef enum mjtGain {            // type of actuator gain
   mjGAIN_MUSCLE,                  // muscle FLV curve computed by mju_muscleGain()
   mjGAIN_DCMOTOR,                 // DC motor gain: K or K/R
   mjGAIN_SO3,                     // geodesic servo on an SO3 transmission: force = kp * log(error)
+  mjGAIN_PID,                     // PID controller: position and velocity setpoint inputs
   mjGAIN_USER                     // user-defined gain type
 } mjtGain;
 
@@ -277,6 +279,13 @@ typedef enum mjtCtrlChart {       // so3 input signature (actuator_ctrlspec): or
 } mjtCtrlChart;
 
 
+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
+} mjtCtrlInput;
+
+
 typedef enum mjtObj {             // type of MujoCo object
   mjOBJ_UNKNOWN       = 0,        // unknown object type
   mjOBJ_BODY,                     // body

include/mujoco/mujoco.h

@@ -1760,6 +1760,11 @@ MJAPI const char* mjs_setToVelocity(mjsActuator* actuator, double kv);
 MJAPI const char* mjs_setToOrientation(mjsActuator* actuator, double kp, double kv[1],
                                        double dampratio[1], int ctrlspec);
 
+// Set actuator to PID controller.
+MJAPI const char* mjs_setToPID(mjsActuator* actuator, double kp, double kv[1], double dampratio[1],
+                               double ki[1], double imax[1], double slewmax[1], double inheritrange,
+                               int ctrlspec);
+
 // Set actuator to activate damper; return error if any.
 MJAPI const char* mjs_setToDamper(mjsActuator* actuator, double kv);
 

python/mujoco/introspect/enums.py

@@ -266,7 +266,8 @@ ENUMS: Mapping[str, EnumDecl] = dict([
              ('mjDYN_FILTEREXACT', 3),
              ('mjDYN_MUSCLE', 4),
              ('mjDYN_DCMOTOR', 5),
-             ('mjDYN_USER', 6),
+             ('mjDYN_PID', 6),
+             ('mjDYN_USER', 7),
          ]),
      )),
     ('mjtGain',
@@ -279,7 +280,8 @@ ENUMS: Mapping[str, EnumDecl] = dict([
              ('mjGAIN_MUSCLE', 2),
              ('mjGAIN_DCMOTOR', 3),
              ('mjGAIN_SO3', 4),
-             ('mjGAIN_USER', 5),
+             ('mjGAIN_PID', 5),
+             ('mjGAIN_USER', 6),
          ]),
      )),
     ('mjtBias',
@@ -304,6 +306,16 @@ ENUMS: Mapping[str, EnumDecl] = dict([
              ('mjCHART_QUAT', 2),
          ]),
      )),
+    ('mjtCtrlInput',
+     EnumDecl(
+         name='mjtCtrlInput',
+         declname='enum mjtCtrlInput',
+         values=dict([
+             ('mjINPUT_POS', 1),
+             ('mjINPUT_VEL', 2),
+             ('mjINPUT_FF', 4),
+         ]),
+     )),
     ('mjtObj',
      EnumDecl(
          name='mjtObj',

python/mujoco/introspect/functions.py

@@ -11035,6 +11035,69 @@ FUNCTIONS: Mapping[str, FunctionDecl] = dict([
          ),
          doc='Set actuator to orientation servo.',
      )),
+    ('mjs_setToPID',
+     FunctionDecl(
+         name='mjs_setToPID',
+         return_type=PointerType(
+             inner_type=ValueType(name='char', is_const=True),
+         ),
+         parameters=(
+             FunctionParameterDecl(
+                 name='actuator',
+                 type=PointerType(
+                     inner_type=ValueType(name='mjsActuator'),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='kp',
+                 type=ValueType(name='double'),
+             ),
+             FunctionParameterDecl(
+                 name='kv',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(1,),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='dampratio',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(1,),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='ki',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(1,),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='imax',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(1,),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='slewmax',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(1,),
+                 ),
+             ),
+             FunctionParameterDecl(
+                 name='inheritrange',
+                 type=ValueType(name='double'),
+             ),
+             FunctionParameterDecl(
+                 name='ctrlspec',
+                 type=ValueType(name='int'),
+             ),
+         ),
+         doc='Set actuator to PID controller.',
+     )),
     ('mjs_setToDamper',
      FunctionDecl(
          name='mjs_setToDamper',

python/mujoco/introspect/structs.py

@@ -9647,6 +9647,22 @@ STRUCTS: Mapping[str, StructDecl] = dict([
                  type=ValueType(name='int'),
                  doc='input signature, scoped by gaintype; 0: type default',
              ),
+             StructFieldDecl(
+                 name='velrange',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(2,),
+                 ),
+                 doc='range of the velocity-setpoint input (pid)',
+             ),
+             StructFieldDecl(
+                 name='ffrange',
+                 type=ArrayType(
+                     inner_type=ValueType(name='double'),
+                     extents=(2,),
+                 ),
+                 doc='range of the feedforward input (pid)',
+             ),
              StructFieldDecl(
                  name='actearly',
                  type=ValueType(name='mjtBool'),

python/mujoco/specs.cc

@@ -1567,6 +1567,23 @@ PYBIND11_MODULE(_specs, m, pybind11::mod_gil_not_used()) {
       },
       py::arg("kp"), py::arg("kv") = -1, py::arg("dampratio") = -1,
       py::arg("ctrlspec") = 0);
+  mjsActuator.def(
+      "set_to_pid",
+      [](raw::MjsActuator* self, double kp, double kv, double dampratio,
+         double ki, double imax, double slewmax, double inheritrange,
+         int ctrlspec) {
+        std::string err = mjs_setToPID(
+            self, kp, kv == -1 ? nullptr : &kv,
+            dampratio == -1 ? nullptr : &dampratio, ki == -1 ? nullptr : &ki,
+            imax == -1 ? nullptr : &imax, slewmax == -1 ? nullptr : &slewmax,
+            inheritrange, ctrlspec);
+        if (!err.empty()) {
+          throw pybind11::value_error(err);
+        }
+      },
+      py::arg("kp"), py::arg("kv") = -1, py::arg("dampratio") = -1,
+      py::arg("ki") = -1, py::arg("imax") = -1, py::arg("slewmax") = -1,
+      py::arg("inheritrange") = 0, py::arg("ctrlspec") = 0);
   mjsActuator.def(
       "set_to_damper",
       [](raw::MjsActuator* self, double kv) {

python/mujoco/specs_test.py

@@ -1596,6 +1596,15 @@ class SpecsTest(absltest.TestCase):
     self.assertEqual(actuator.biastype, mujoco.mjtBias.mjBIAS_SO3)
     self.assertEqual(actuator.dyntype, mujoco.mjtDyn.mjDYN_NONE)
 
+    actuator.set_to_pid(kp=2.0, kv=3.0, ki=0.5, imax=1.5, slewmax=4.0)
+    self.assertEqual(actuator.biasprm[1], -2)
+    self.assertEqual(actuator.biasprm[2], -3)
+    self.assertEqual(actuator.gainprm[0], 0.5)
+    self.assertEqual(actuator.dynprm[0], 1.5)
+    self.assertEqual(actuator.dynprm[1], 4.0)
+    self.assertEqual(actuator.gaintype, mujoco.mjtGain.mjGAIN_PID)
+    self.assertEqual(actuator.dyntype, mujoco.mjtDyn.mjDYN_PID)
+
     actuator.set_to_velocity(kv=5.0)
     self.assertEqual(actuator.gainprm[0], 5)
     self.assertEqual(actuator.biasprm[2], -5)

src/engine/engine_forward.c

@@ -225,6 +225,16 @@ void mj_fwdVelocity(const mjModel* m, mjData* d) {
 }
 
 
+// unpack servo-family inputs from control block in canonical order [pos, vel, ff]
+// absent input: setpoint 0
+static void unpackServoInputs(const mjtNum* u, int spec, mjtNum out[3]) {
+  int adr = 0;
+  out[0] = (spec & mjINPUT_POS) ? u[adr++] : 0;
+  out[1] = (spec & mjINPUT_VEL) ? u[adr++] : 0;
+  out[2] = (spec & mjINPUT_FF)  ? u[adr]   : 0;
+}
+
+
 // helper for DC motor: computes control voltage from PID state
 static mjtNum dcmotorVoltage(mjtNum ctrl, mjtNum length, mjtNum velocity,
                              mjtNum x_I, const mjtNum* gainprm) {
@@ -285,10 +295,15 @@ static void expmap2Quat(mjtNum quat[4], const mjtNum v[3]) {
 static mjtNum wrapPeriod(const mjModel* m, int i) {
   // servo shape: fixed gain, affine bias, matching kp, setpoint input
   mjtDyn dyntype = m->actuator_dyntype[i];
-  if (m->actuator_gaintype[i] != mjGAIN_FIXED  ||
+  int servo = m->actuator_gaintype[i] == mjGAIN_FIXED  &&
-      m->actuator_biastype[i] != mjBIAS_AFFINE ||
+              m->actuator_biastype[i] == mjBIAS_AFFINE &&
-      m->actuator_gainprm[mjNGAIN*i] != -m->actuator_biasprm[mjNBIAS*i+1] ||
+              m->actuator_gainprm[mjNGAIN*i] == -m->actuator_biasprm[mjNBIAS*i+1] &&
-      (dyntype != mjDYN_NONE && dyntype != mjDYN_INTEGRATOR)) {
+              (dyntype == mjDYN_NONE || dyntype == mjDYN_INTEGRATOR);
+
+  // PID shape: kp and kv are single-sourced in the affine bias
+  int pid = m->actuator_gaintype[i] == mjGAIN_PID;
+
+  if (!servo && !pid) {
     return 0;
   }
 
@@ -318,6 +333,20 @@ static mjtNum wrapSetpoint(mjtNum u, mjtNum length, mjtNum period) {
 }
 
 
+// slew-rate-limit setpoint u given previous effective setpoint u_prev, write act_dot
+// period > 0: wrap u to the representative nearest u_prev before limiting
+static mjtNum slewLimit(mjtNum u, mjtNum u_prev, mjtNum slew_s, mjtNum dt,
+                        mjtNum period, mjtNum* act_dot) {
+  if (period > 0) {
+    u = wrapSetpoint(u, u_prev, period);
+  }
+  mjtNum slew = slew_s * dt;
+  mjtNum u_eff = mju_clip(u, u_prev - slew, u_prev + slew);
+  *act_dot = (u_eff - u_prev) / dt;
+  return u_eff;
+}
+
+
 // (qpos, qvel, ctrl, act) => (qfrc_actuator, actuator_force, act_dot)
 void mj_fwdActuation(const mjModel* m, mjData* d) {
   TM_START;
@@ -419,6 +448,42 @@ void mj_fwdActuation(const mjModel* m, mjData* d) {
       d->act_dot[act_last] = mju_muscleDynamics(ctrl[uadr], d->act[act_last], dynprm);
       break;
 
+    case mjDYN_PID: {               // PID controller states, slot order: slew, integral
+      int adr = act_first;
+      mjtNum period = wrapPeriod(m, i);
+
+      // slew rate limiting of the position setpoint
+      mjtNum slew_s = dynprm[1];
+      if (slew_s > 0) {
+        ctrl[uadr] = slewLimit(ctrl[uadr], d->act[adr], slew_s, m->opt.timestep,
+                               period, d->act_dot + adr);
+        adr++;
+      }
+
+      // integral of the position error
+      if (m->actuator_gainprm[mjNGAIN*i] > 0) {
+        mjtNum err = ctrl[uadr] - d->actuator_length[oadr];
+
+        // rotational transmission: error on the circle
+        if (period > 0) {
+          err -= period*mju_round(err/period);
+        }
+
+        // anti-windup: stop accumulating beyond imax
+        mjtNum imax = dynprm[0];
+        if (imax > 0) {
+          mjtNum z = d->act[adr];
+          if (z >= imax) {
+            err = mju_min(err, 0);
+          } else if (z <= -imax) {
+            err = mju_max(err, 0);
+          }
+        }
+        d->act_dot[adr] = err;
+      }
+      break;
+    }
+
     case mjDYN_DCMOTOR: {           // DC motor: up to 5 optional states
       const mjtNum* gainprm = m->actuator_gainprm + mjNGAIN*i;
 
@@ -630,6 +695,10 @@ void mj_fwdActuation(const mjModel* m, mjData* d) {
       gain = gainprm[0];
       break;
 
+    case mjGAIN_PID:                // PID servo: input side handled below, state side in bias
+      gain = 0;
+      break;
+
     case mjGAIN_AFFINE:             // affine: prm = [const, kp, kv]
       gain = gainprm[0] + gainprm[1]*d->actuator_length[oadr] +
              gainprm[2]*d->actuator_velocity[oadr];
@@ -693,7 +762,36 @@ void mj_fwdActuation(const mjModel* m, mjData* d) {
 
     // DC motor without current state: use ctrl even if other activations exist
     int dcmotor_no_current = (gaintype == mjGAIN_DCMOTOR && dynprm[0] <= 0);
-    if (actnum == 0 || dcmotor_no_current) {
+
+    // PID servo: force = kp*(qref - l) + kv*(vref - l_dot) [+ ff] [+ ki*z]
+    // input-side terms computed here; state-side terms added by the affine bias below
+    if (gaintype == mjGAIN_PID) {
+      const mjtNum* prm = m->actuator_biasprm + mjNBIAS*i;
+
+      // unpack present inputs in canonical order [pos, vel, ff]; absent input: setpoint 0
+      mjtNum u3[3];
+      unpackServoInputs(ctrl + uadr, m->actuator_ctrlspec[i], u3);
+      mjtNum qref = u3[0], vref = u3[1], ff = u3[2];
+
+      // position setpoint: representative nearest the length on rotational transmissions
+      mjtNum period = wrapPeriod(m, i);
+      if (period > 0) {
+        qref = wrapSetpoint(qref, d->actuator_length[oadr], period);
+      }
+
+      // kp and kv are single-sourced in the affine bias parameters
+      force[oadr] = -prm[1]*qref - prm[2]*vref + ff;
+
+      // integral state (last slot): force += ki * z
+      if (actnum && gainprm[0] > 0) {
+        int act_adr = m->actuator_actadr[i] + actnum - 1;
+        mjtNum z = m->actuator_actearly[i]
+                       ? mj_nextActivation(m, d, i, act_adr, d->act_dot[act_adr])
+                       : d->act[act_adr];
+        force[oadr] += gainprm[0]*z;
+      }
+    }
+    else if (actnum == 0 || dcmotor_no_current) {
       mjtNum input = ctrl[uadr];
 
       // rotational setpoint: use representative nearest the length (local, no state change)

src/engine/engine_name.c

@@ -297,5 +297,20 @@ const char* mj_actuatorInputName(const mjModel* m, int id, int input) {
     return m->actuator_ctrlspec[id] == mjCHART_QUAT ? quat[input] : expmap[input];
   }
 
+  // servo family: input names are the present members of [pos, vel, ff]
+  if (m->actuator_gaintype[id] == mjGAIN_PID) {
+    static const char* servo[3] = {"pos", "vel", "ff"};
+    static const int bits[3] = {mjINPUT_POS, mjINPUT_VEL, mjINPUT_FF};
+    int spec = m->actuator_ctrlspec[id];
+    for (int k=0; k < 3; k++) {
+      if (spec & bits[k]) {
+        if (input == 0) {
+          return servo[k];
+        }
+        input--;
+      }
+    }
+  }
+
   return NULL;
 }

src/engine/engine_setconst.c

@@ -1138,8 +1138,9 @@ static void set0(mjModel* m, mjData* d) {
     mjtNum* biasprm = m->actuator_biasprm + i*mjNBIAS;
     mjtNum* gainprm = m->actuator_gainprm + i*mjNGAIN;
 
-    // not a position-like actuator: skip
+    // not a position-like actuator: skip (PID single-sources kp in biasprm[1])
-    if (gainprm[0] != -biasprm[1]) {
+    int is_pid = m->actuator_gaintype[i] == mjGAIN_PID;
+    if (!is_pid && gainprm[0] != -biasprm[1]) {
       continue;
     }
 
@@ -1165,7 +1166,8 @@ static void set0(mjModel* m, mjData* d) {
     }
 
     // damping = dampratio * 2 * sqrt(kp * mass)
-    mjtNum damping = biasprm[2] * 2 * mju_sqrt(gainprm[0] * mass);
+    mjtNum kp = is_pid ? -biasprm[1] : gainprm[0];
+    mjtNum damping = biasprm[2] * 2 * mju_sqrt(kp * mass);
 
     // set biasprm[2] to negative damping
     biasprm[2] = -damping;

src/user/user_api.cc

@@ -1348,6 +1348,48 @@ const char* mjs_setToOrientation(mjsActuator* actuator, double kp, double kv[1],
 }
 
 
+// Set to PID actuator.
+const char* mjs_setToPID(mjsActuator* actuator, double kp, double kv[1], double dampratio[1],
+                         double ki[1], double imax[1], double slewmax[1], double inheritrange,
+                         int ctrlspec) {
+  if (kv && dampratio) {
+    return "kv and dampratio cannot both be defined";
+  }
+  actuator->biasprm[1] = -kp;
+  if (kv) {
+    if (*kv < 0) return "kv cannot be negative";
+    actuator->biasprm[2] = -(*kv);
+  }
+  if (dampratio) {
+    if (*dampratio < 0) return "dampratio cannot be negative";
+    actuator->biasprm[2] = *dampratio;
+  }
+
+  // controller states: ki in gainprm[0], imax in dynprm[0], slewmax in dynprm[1]
+  double ki_value = ki ? *ki : 0;
+  double slew_value = slewmax ? *slewmax : 0;
+  if (slew_value < 0) return "slewmax cannot be negative";
+  actuator->gainprm[0] = ki_value;
+  actuator->dynprm[1] = slew_value;
+  actuator->dyntype = (ki_value || slew_value) ? mjDYN_PID : mjDYN_NONE;
+  if (ki_value && imax) {
+    actuator->dynprm[0] = *imax;
+  }
+
+  actuator->inheritrange = inheritrange;
+  if (inheritrange > 0) {
+    if (actuator->ctrlrange[0] || actuator->ctrlrange[1]) {
+      return "posrange and inheritrange cannot both be defined";
+    }
+  }
+
+  actuator->ctrlspec = ctrlspec;
+  actuator->gaintype = mjGAIN_PID;
+  actuator->biastype = mjBIAS_AFFINE;
+  return "";
+}
+
+
 
 // Set to velocity actuator.
 const char* mjs_setToVelocity(mjsActuator* actuator, double kv) {

src/user/user_api.h

@@ -189,6 +189,11 @@ MJAPI const char* mjs_setToVelocity(mjsActuator* actuator, double kv);
 MJAPI const char* mjs_setToOrientation(mjsActuator* actuator, double kp, double kv[1],
                                        double dampratio[1], int ctrlspec);
 
+// Set to PID actuator.
+MJAPI const char* mjs_setToPID(mjsActuator* actuator, double kp, double kv[1], double dampratio[1],
+                               double ki[1], double imax[1], double slewmax[1], double inheritrange,
+                               int ctrlspec);
+
 // Set actuator to damper, return error on failure.
 MJAPI const char* mjs_setToDamper(mjsActuator* actuator, double kv);
 

src/user/user_init.c

@@ -342,6 +342,8 @@ void mjs_defaultActuator(mjsActuator* actuator) {
   actuator->dynprm[0] = 1;
   actuator->actdim = -1;
   actuator->ctrlspec = 0;
+  actuator->velrange[0] = actuator->velrange[1] = 0;
+  actuator->ffrange[0] = actuator->ffrange[1] = 0;
 
   // transmission
   actuator->trntype = mjTRN_UNDEFINED;

src/user/user_model.cc

@@ -4066,10 +4066,10 @@ void mjCModel::CopyObjects(mjModel* m) {
     mjuu_copyvec(m->actuator_user+nuser_actuator*i, pac->get_userdata().data(), nuser_actuator);
 
     // per-input arrays, at the actuator's ctrl block
-    for (int j = m->actuator_ctrladr[i];
+    for (int k = 0; k < m->actuator_ctrlnum[i]; k++) {
-         j < m->actuator_ctrladr[i] + m->actuator_ctrlnum[i]; j++) {
+      int j = m->actuator_ctrladr[i] + k;
-      m->actuator_ctrllimited[j] = (mjtBool)pac->is_ctrllimited();
+      m->actuator_ctrllimited[j] = (mjtBool)pac->ctrllimiteds_[k];
-      mjuu_copyvec(m->actuator_ctrlrange + 2 * j, pac->ctrlrange, 2);
+      mjuu_copyvec(m->actuator_ctrlrange + 2 * j, pac->ctrlranges_[k], 2);
     }
 
     // per-output arrays, at the actuator's output block

src/user/user_objects.cc

@@ -7214,12 +7214,69 @@ void mjCActuator::Compile(void) {
     so3_ = true;
   }
 
-  // input signature selection is so3-only
+  // PID servo: validate and resolve input block
-  if (ctrlspec && gaintype != mjGAIN_SO3) {
+  if (gaintype == mjGAIN_PID) {
-    throw mjCError(this, "input is only available for so3 actuators, actuator '%s' (id = %d)",
+    if (biastype != mjBIAS_AFFINE) {
+      throw mjCError(this, "pid requires biastype 'affine' in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    if (dyntype != mjDYN_NONE && dyntype != mjDYN_PID) {
+      throw mjCError(this, "pid requires dyntype 'none' or 'pid' in actuator '%s' "
+                     "(id = %d)", name.c_str(), id);
+    }
+    if (dyntype == mjDYN_NONE && gainprm[0]) {
+      throw mjCError(this, "ki (gainprm[0]) requires dyntype 'pid' in actuator '%s' "
+                     "(id = %d)", name.c_str(), id);
+    }
+    if (trntype == mjTRN_BODY) {
+      throw mjCError(this, "pid cannot use body transmission, actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+
+    // controller states, slot order [slew, integral]: gated on slewmax (dynprm[1]) and ki
+    if (dyntype == mjDYN_PID) {
+      if (dynprm[0] < 0) {
+        throw mjCError(this, "imax (dynprm[0]) must be non-negative in actuator '%s' (id = %d)",
+                       name.c_str(), id);
+      }
+      if (dynprm[1] < 0) {
+        throw mjCError(this, "slewmax (dynprm[1]) must be non-negative in actuator '%s' (id = %d)",
+                       name.c_str(), id);
+      }
+      int nslot = (dynprm[1] > 0) + (gainprm[0] > 0);
+      if (actdim > 0 && actdim != nslot) {
+        throw mjCError(this, "pid controller states require matching actdim in actuator '%s' "
+                       "(id = %d)", name.c_str(), id);
+      }
+      actdim = nslot;
+    }
+
+    // input block: any subset of [pos, vel, ff], default [pos, vel]
+    ctrlspec_ = ctrlspec ? ctrlspec : (mjINPUT_POS | mjINPUT_VEL);
+    if (ctrlspec_ & ~(mjINPUT_POS | mjINPUT_VEL | mjINPUT_FF)) {
+      throw mjCError(this, "pid inputs are a subset of [pos, vel, ff] in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    if (dyntype == mjDYN_PID && !(ctrlspec_ & mjINPUT_POS)) {
+      throw mjCError(this, "pid controller states require the pos input in actuator '%s' (id = %d)",
+                     name.c_str(), id);
+    }
+    ctrlnum_ = !!(ctrlspec_ & mjINPUT_POS) + !!(ctrlspec_ & mjINPUT_VEL) +
+               !!(ctrlspec_ & mjINPUT_FF);
+  }
+
+  // pid dynamics are pid-only
+  if (dyntype == mjDYN_PID && gaintype != mjGAIN_PID) {
+    throw mjCError(this, "dyntype 'pid' requires gaintype 'pid', actuator '%s' (id = %d)",
                    name.c_str(), id);
   }
 
+  // input signature selection is so3- or pid-only
+  if (ctrlspec && gaintype != mjGAIN_SO3 && gaintype != mjGAIN_PID) {
+    throw mjCError(this, "input is only available for so3 and pid actuators, actuator '%s' "
+                   "(id = %d)", name.c_str(), id);
+  }
+
   // check damping/armature only valid for joint and tendon transmission
   bool has_damping = false;
   for (int i = 0; i < mjNPOLY+1; i++) {
@@ -7242,12 +7299,13 @@ void mjCActuator::Compile(void) {
   }
 
   // handle inheritrange
-  if (gaintype == mjGAIN_FIXED && biastype == mjBIAS_AFFINE &&
+  if (((gaintype == mjGAIN_FIXED && gainprm[0] == -biasprm[1]) || gaintype == mjGAIN_PID) &&
-      gainprm[0] == -biasprm[1] && inheritrange > 0) {
+      biastype == mjBIAS_AFFINE && inheritrange > 0) {
     // semantic of actuator is the same as transmission, inheritrange is applicable
     double* range;
-    if (dyntype == mjDYN_NONE || dyntype == mjDYN_FILTEREXACT) {
+    if (dyntype == mjDYN_NONE || dyntype == mjDYN_FILTEREXACT ||
-      // position actuator
+        dyntype == mjDYN_PID) {
+      // position or pd actuator: range applies to the position input
       range = ctrlrange;
     } else if (dyntype == mjDYN_INTEGRATOR) {
       // intvelocity actuator
@@ -7397,6 +7455,28 @@ void mjCActuator::Compile(void) {
   if (nsample > 16777216) {
     throw mjCError(this, "at most 2^24 samples in history buffer, got %d", nullptr, nsample);
   }
+
+  // resolve per-input control ranges: broadcast ctrlrange, pd overrides vel and ff
+  for (int j=0; j < ctrlnum_ && j < 4; j++) {
+    ctrllimiteds_[j] = (mjtByte)is_ctrllimited();
+    ctrlranges_[j][0] = ctrlrange[0];
+    ctrlranges_[j][1] = ctrlrange[1];
+  }
+  if (gaintype == mjGAIN_PID) {
+    // present inputs pack in canonical order [pos, vel, ff]; pos keeps the ctrlrange broadcast
+    int j = ctrlspec_ & mjINPUT_POS ? 1 : 0;
+    if (ctrlspec_ & mjINPUT_VEL) {
+      ctrllimiteds_[j] = velrange[0] < velrange[1];
+      ctrlranges_[j][0] = velrange[0];
+      ctrlranges_[j][1] = velrange[1];
+      j++;
+    }
+    if (ctrlspec_ & mjINPUT_FF) {
+      ctrllimiteds_[j] = ffrange[0] < ffrange[1];
+      ctrlranges_[j][0] = ffrange[0];
+      ctrlranges_[j][1] = ffrange[1];
+    }
+  }
 }
 
 

src/user/user_objects.h

@@ -1816,6 +1816,8 @@ class mjCActuator_ : public mjCBase {
   int outadr_;                                      // address of first force output
   int outnum_;                                      // number of force outputs, from trntype
   bool so3_;                                        // compiles to an SO3 transmission
+  double ctrlranges_[4][2];                         // resolved per-input control ranges
+  mjtByte ctrllimiteds_[4];                         // resolved per-input limited flags
   std::map<std::string, std::vector<mjtNum>> act_;  // act at the previous step
   std::map<std::string, mjtNum> ctrl_;              // ctrl at the previous step
 

src/xml/xml_base.h

@@ -41,7 +41,8 @@ extern const int colorspace_sz;
 extern const int builtin_sz;
 extern const int mark_sz;
 extern const int dyn_sz;
-extern const int input_sz;
+extern const int inputchart_sz;
+extern const int inputbit_sz;
 extern const int gain_sz;
 extern const int bias_sz;
 extern const int interp_sz;
@@ -76,7 +77,8 @@ extern const mjMap texrole_map[];
 extern const mjMap builtin_map[];
 extern const mjMap mark_map[];
 extern const mjMap dyn_map[];
-extern const mjMap input_map[];
+extern const mjMap inputchart_map[];
+extern const mjMap inputbit_map[];
 extern const mjMap gain_map[];
 extern const mjMap bias_map[];
 extern const mjMap interp_map[];

src/xml/xml_native_reader.cc

@@ -258,7 +258,7 @@ std::vector<const char*> MJCF[nMJCF] = {
             "margin", "stiffness", "damping", "rgba", "user"},
         {"general", "?", "ctrllimited", "forcelimited", "actlimited", "ctrlrange", "forcerange",
             "actrange", "gear", "damping", "armature", "cranklength", "user", "group", "nsample",
-            "interp", "delay", "actdim", "input", "dyntype", "gaintype", "biastype", "dynprm", "gainprm",
+            "interp", "delay", "actdim", "input", "velrange", "ffrange", "dyntype", "gaintype", "biastype", "dynprm", "gainprm",
             "biasprm", "actearly"},
         {"motor", "?", "ctrllimited", "forcelimited", "ctrlrange", "forcerange",
             "gear", "damping", "armature", "cranklength", "user", "group", "nsample", "interp", "delay"},
@@ -270,6 +270,12 @@ std::vector<const char*> MJCF[nMJCF] = {
         {"intvelocity", "?", "ctrllimited", "forcelimited", "actlimited", "ctrlrange", "forcerange",
              "actrange", "inheritrange", "gear", "damping", "armature", "cranklength", "user", "group",
             "nsample", "interp", "delay", "kp", "kv", "dampratio"},
+        {"orientation", "?", "forcelimited", "ctrlrange", "forcerange", "user", "group",
+            "nsample", "interp", "delay", "kp", "kv", "dampratio", "input"},
+        {"pid", "?", "ctrllimited", "forcelimited", "ctrlrange", "posrange", "velrange", "ffrange",
+            "forcerange", "inheritrange", "gear", "damping", "armature", "cranklength", "user",
+            "group", "nsample", "interp", "delay", "kp", "kv", "dampratio", "ki", "imax", "slewmax",
+            "input"},
         {"damper", "?", "forcelimited", "ctrlrange", "forcerange",
             "gear", "damping", "armature", "cranklength", "user", "group", "nsample", "interp", "delay", "kv"},
         {"cylinder", "?", "ctrllimited", "forcelimited", "ctrlrange", "forcerange",
@@ -476,7 +482,7 @@ std::vector<const char*> MJCF[nMJCF] = {
             "ctrllimited", "forcelimited", "actlimited", "ctrlrange", "forcerange", "actrange",
             "lengthrange", "gear", "damping", "armature", "cranklength", "user",
             "joint", "jointinparent", "tendon", "slidersite", "cranksite", "site", "refsite",
-            "body", "actdim", "input", "dyntype", "gaintype", "biastype", "dynprm", "gainprm", "biasprm",
+            "body", "actdim", "input", "velrange", "ffrange", "dyntype", "gaintype", "biastype", "dynprm", "gainprm", "biasprm",
             "actearly"},
         {"motor", "*", "name", "class", "group", "nsample", "interp", "delay",
             "ctrllimited", "forcelimited", "ctrlrange", "forcerange",
@@ -502,6 +508,12 @@ std::vector<const char*> MJCF[nMJCF] = {
             "forcelimited", "ctrlrange", "forcerange", "user",
             "joint", "site", "refsite",
             "kp", "kv", "dampratio", "input"},
+        {"pid", "*", "name", "class", "group", "nsample", "interp", "delay",
+            "ctrllimited", "forcelimited", "ctrlrange", "posrange", "velrange", "ffrange",
+            "forcerange", "inheritrange", "lengthrange", "gear", "damping", "armature",
+            "cranklength", "user",
+            "joint", "jointinparent", "tendon", "slidersite", "cranksite", "site", "refsite",
+            "kp", "kv", "dampratio", "ki", "imax", "slewmax", "input"},
         {"damper", "*", "name", "class", "group", "nsample", "interp", "delay",
             "forcelimited", "ctrlrange", "forcerange",
             "lengthrange", "gear", "damping", "armature", "cranklength", "user",
@@ -822,7 +834,7 @@ const mjMap mark_map[mark_sz] = {
 
 
 // dyn type
-const int dyn_sz = 7;
+const int dyn_sz = 8;
 const mjMap dyn_map[dyn_sz] = {
   {"none",          mjDYN_NONE},
   {"integrator",    mjDYN_INTEGRATOR},
@@ -830,6 +842,7 @@ const mjMap dyn_map[dyn_sz] = {
   {"filterexact",   mjDYN_FILTEREXACT},
   {"muscle",        mjDYN_MUSCLE},
   {"dcmotor",       mjDYN_DCMOTOR},
+  {"pid",           mjDYN_PID},
   {"user",          mjDYN_USER}
 };
 
@@ -844,25 +857,61 @@ const mjMap dcmotorinput_map[dcmotorinput_sz] = {
 
 
 // gain type
-const int gain_sz = 6;
+const int gain_sz = 7;
 const mjMap gain_map[gain_sz] = {
   {"fixed",         mjGAIN_FIXED},
   {"affine",        mjGAIN_AFFINE},
   {"muscle",        mjGAIN_MUSCLE},
   {"dcmotor",       mjGAIN_DCMOTOR},
   {"so3",           mjGAIN_SO3},
+  {"pid",           mjGAIN_PID},
   {"user",          mjGAIN_USER}
 };
 
 
 // so3 input chart
-const int input_sz = 2;
+const int inputchart_sz = 2;
-const mjMap input_map[input_sz] = {
+const mjMap inputchart_map[inputchart_sz] = {
   {"expmap",        mjCHART_EXPMAP},
   {"quat",          mjCHART_QUAT}
 };
 
 
+// servo-family input tokens
+const int inputbit_sz = 3;
+const mjMap inputbit_map[inputbit_sz] = {
+  {"pos",           mjINPUT_POS},
+  {"vel",           mjINPUT_VEL},
+  {"ff",            mjINPUT_FF}
+};
+
+
+// read the "input" attribute: so3 chart keyword, or servo input token list
+static bool ReadInputSpec(tinyxml2::XMLElement* elem, int* ctrlspec) {
+  std::string text;
+  if (!mjXUtil::ReadAttrTxt(elem, "input", text)) {
+    return false;
+  }
+
+  // so3 chart keyword
+  int chart = mjXUtil::FindKey(inputchart_map, inputchart_sz, text);
+  if (chart >= 0) {
+    *ctrlspec = chart;
+    return true;
+  }
+
+  // servo input tokens
+  int bits[inputbit_sz];
+  int nbit = mjXUtil::MapValues(elem, "input", bits, inputbit_map, inputbit_sz);
+  int spec = 0;
+  for (int k=0; k < nbit; k++) {
+    spec |= bits[k];
+  }
+  *ctrlspec = spec;
+  return true;
+}
+
+
 // bias type
 const int bias_sz = 6;
 const mjMap bias_map[bias_sz] = {
@@ -2528,9 +2577,9 @@ void mjXReader::OneActuator(XMLElement* elem, mjsActuator* actuator) {
     ReadAttr(elem, "gainprm", mjNGAIN, actuator->gainprm, text, false, false);
     ReadAttr(elem, "biasprm", mjNBIAS, actuator->biasprm, text, false, false);
     ReadAttrInt(elem, "actdim", &actuator->actdim);
-    if (MapValue(elem, "input", &n, input_map, input_sz)) {
+    ReadInputSpec(elem, &actuator->ctrlspec);
-      actuator->ctrlspec = n;
+    ReadAttr(elem, "velrange", 2, actuator->velrange, text);
-    }
+    ReadAttr(elem, "ffrange", 2, actuator->ffrange, text);
   }
 
   // direct drive motor
@@ -2593,14 +2642,53 @@ void mjXReader::OneActuator(XMLElement* elem, mjsActuator* actuator) {
     }
 
     // input chart: expmap (default) or quat
-    int n;
+    ReadInputSpec(elem, &actuator->ctrlspec);
-    if (MapValue(elem, "input", &n, input_map, input_sz)) {
-      actuator->ctrlspec = n;
-    }
 
     err = mjs_setToOrientation(actuator, kp, kv, dampratio, actuator->ctrlspec);
   }
 
+  // PID servo: inputs are position and velocity setpoints
+  else if (type == "pid") {
+    // kp: default inherited via -biasprm[1]
+    double kp = -actuator->biasprm[1];
+    ReadAttr(elem, "kp", 1, &kp, text);
+
+    double kv_data;
+    double *kv = &kv_data;
+    if (!ReadAttr(elem, "kv", 1, kv, text)) {
+      kv = nullptr;
+    }
+
+    double dampratio_data;
+    double *dampratio = &dampratio_data;
+    if (!ReadAttr(elem, "dampratio", 1, dampratio, text)) {
+      dampratio = nullptr;
+    }
+
+    // controller parameters: ki (gainprm[0]), imax (dynprm[0]), slewmax (dynprm[1]); inherited
+    double ki = actuator->gainprm[0] * (actuator->dyntype == mjDYN_PID);
+    ReadAttr(elem, "ki", 1, &ki, text);
+    double imax = actuator->dynprm[0] * (actuator->dyntype == mjDYN_PID);
+    ReadAttr(elem, "imax", 1, &imax, text);
+    double slewmax = actuator->dynprm[1] * (actuator->dyntype == mjDYN_PID);
+    ReadAttr(elem, "slewmax", 1, &slewmax, text);
+
+    // input subset selection
+    ReadInputSpec(elem, &actuator->ctrlspec);
+
+    // per-input ranges; posrange is an alias of ctrlrange (input 0)
+    ReadAttr(elem, "posrange", 2, actuator->ctrlrange, text);
+    ReadAttr(elem, "velrange", 2, actuator->velrange, text);
+    ReadAttr(elem, "ffrange", 2, actuator->ffrange, text);
+
+    // handle inheritrange
+    double inheritrange = actuator->inheritrange;
+    ReadAttr(elem, "inheritrange", 1, &inheritrange, text);
+
+    err = mjs_setToPID(actuator, kp, kv, dampratio, &ki, &imax, &slewmax, inheritrange,
+                      actuator->ctrlspec);
+  }
+
   // velocity servo
   else if (type == "velocity") {
     double kv = actuator->gainprm[0];
@@ -3168,6 +3256,7 @@ void mjXReader::Default(XMLElement* section, const mjsDefault* def, const mjVFS*
              name == "damper"      ||
              name == "intvelocity" ||
              name == "orientation" ||
+             name == "pid"         ||
              name == "cylinder"    ||
              name == "muscle"      ||
              name == "adhesion"    ||

src/xml/xml_native_reader.h

@@ -102,7 +102,7 @@ class mjXReader : public mjXBase {
 };
 
 // MJCF schema
-#define nMJCF 249
+#define nMJCF 252
 extern std::vector<const char*> MJCF[nMJCF];
 
 #endif  // MUJOCO_SRC_XML_XML_NATIVE_READER_H_

src/xml/xml_native_writer.cc

@@ -899,7 +899,20 @@ void mjXWriter::OneActuator(XMLElement* elem, const mjCActuator* actuator, mjCDe
   // non-plugins: write actuator parameters
   else {
     WriteAttrKey(elem, "gaintype", gain_map, gain_sz, actuator->gaintype, def->Actuator().gaintype);
-    WriteAttrKey(elem, "input", input_map, input_sz, actuator->ctrlspec, def->Actuator().ctrlspec);
+    if (actuator->gaintype == mjGAIN_SO3) {
+      WriteAttrKey(elem, "input", inputchart_map, inputchart_sz, actuator->ctrlspec,
+                   def->Actuator().ctrlspec);
+    } else if (actuator->ctrlspec != def->Actuator().ctrlspec) {
+      std::string tokens;
+      for (int k=0; k < inputbit_sz; k++) {
+        if (actuator->ctrlspec & inputbit_map[k].value) {
+          tokens += std::string(tokens.empty() ? "" : " ") + inputbit_map[k].key;
+        }
+      }
+      WriteAttrTxt(elem, "input", tokens);
+    }
+    WriteAttr(elem, "velrange", 2, actuator->velrange, def->Actuator().velrange);
+    WriteAttr(elem, "ffrange", 2, actuator->ffrange, def->Actuator().ffrange);
     WriteAttrKey(elem, "biastype", bias_map, bias_sz, actuator->biastype, def->Actuator().biastype);
     WriteAttr(elem, "gainprm", mjNGAIN, actuator->gainprm, def->Actuator().gainprm, true);
     WriteAttr(elem, "biasprm", mjNBIAS, actuator->biasprm, def->Actuator().biasprm, true);

test/engine/engine_core_smooth_test.cc

@@ -17,6 +17,7 @@
 #include "src/engine/engine_core_smooth.h"
 
 #include <algorithm>
+#include <cstdio>
 #include <string>
 #include <string_view>
 #include <vector>
@@ -597,7 +598,7 @@ TEST_F(CoreSmoothTest, RefsiteConservesMomentum) {
   ASSERT_THAT(model, NotNull());
   mjData* data = mj_makeData(model);
 
-  // this test asserts tight momentum conservation: solve exactly, no early termination
+  // assert tight momentum conservation: solve exactly, no early termination
   model->opt.tolerance = 0;
 
   data->ctrl[0] = 1;
@@ -1378,6 +1379,362 @@ TEST_F(CoreSmoothTest, SO3QuatSetpointRequiresStateless) {
   EXPECT_THAT(error, HasSubstr("dyntype"));
 }
 
+// PID servo with vref = 0 reproduces the position servo exactly.
+TEST_F(CoreSmoothTest, PidMatchesPositionServo) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option integrator="implicitfast">
+      <flag contact="disable"/>
+    </option>
+    <worldbody>
+      <!-- identical overlapping bodies (contacts disabled): world-frame
+           arithmetic is bit-identical, so the trajectories must be too -->
+      <body pos="0 0 .2">
+        <joint name="h_position" axis="0 1 0"/>
+        <geom type="capsule" size=".02" fromto="0 0 0 .2 0 0"/>
+      </body>
+      <body pos="0 0 .2">
+        <joint name="h_pd" axis="0 1 0"/>
+        <geom type="capsule" size=".02" fromto="0 0 0 .2 0 0"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <position name="servo" joint="h_position" kp="10" dampratio="1"/>
+      <pid name="pid" joint="h_pd" kp="10" dampratio="1"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+
+  // layout: 2 actuators, 1+2 controls, 1+1 outputs
+  EXPECT_EQ(model->nactuator, 2);
+  EXPECT_EQ(model->nu, 3);
+  EXPECT_EQ(model->nout, 2);
+  int pid = mj_name2id(model.get(), mjOBJ_ACTUATOR, "pid");
+  int uadr = model->actuator_ctrladr[pid];
+  EXPECT_EQ(model->actuator_ctrlnum[pid], 2);
+
+  mjData* data = mj_makeData(model.get());
+  int j_servo = mj_name2id(model.get(), mjOBJ_JOINT, "h_position");
+  int j_pd = mj_name2id(model.get(), mjOBJ_JOINT, "h_pd");
+
+  // ramp the position target on both, v* = 0 on the pid
+  while (data->time < 3) {
+    mjtNum target = 0.8 * data->time;
+    data->ctrl[0] = target;
+    data->ctrl[uadr] = target;
+    data->ctrl[uadr+1] = 0;
+    mj_step(model.get(), data);
+    ASSERT_EQ(data->warning[mjWARN_BADQACC].number, 0) << "diverged";
+    ASSERT_EQ(data->qpos[model->jnt_qposadr[j_servo]],
+              data->qpos[model->jnt_qposadr[j_pd]])
+        << "trajectories diverge at time " << data->time;
+  }
+
+  mj_deleteData(data);
+}
+
+// Constant velocity setpoint produces steady motion at the commanded rate.
+TEST_F(CoreSmoothTest, PidVelocitySetpoint) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option integrator="implicitfast">
+      <flag contact="disable" gravity="disable"/>
+    </option>
+    <worldbody>
+      <body>
+        <joint name="slide" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".05 .05 .05"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="pid" joint="slide" kp="0" kv="10"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  mjData* data = mj_makeData(model.get());
+
+  data->ctrl[1] = 0.7;  // v*
+  while (data->time < 3) {
+    mj_step(model.get(), data);
+    ASSERT_EQ(data->warning[mjWARN_BADQACC].number, 0) << "diverged";
+  }
+  EXPECT_NEAR(data->qvel[0], 0.7, MjTol(1e-6, 2e-6));
+
+  mj_deleteData(data);
+}
+
+// The feedforward input adds directly to the actuator force.
+TEST_F(CoreSmoothTest, PidFeedforward) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <worldbody>
+      <body>
+        <joint name="slide" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".05 .05 .05"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="pid" joint="slide" kp="1" kv="1" input="pos vel ff"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  EXPECT_EQ(model->nu, 3);
+  EXPECT_EQ(model->nout, 1);
+
+  mjData* data = mj_makeData(model.get());
+  data->ctrl[2] = 1.25;  // ff, with zero position/velocity error
+  mj_forward(model.get(), data);
+  EXPECT_EQ(data->actuator_force[0], 1.25);
+
+  mj_deleteData(data);
+}
+
+// Input subsets: present inputs pack in canonical order, absent setpoints are
+// zero, making single-input PIDs match the corresponding SISO servos.
+TEST_F(CoreSmoothTest, PidInputSubsets) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <worldbody>
+      <body>
+        <joint name="j1" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".05 .05 .05"/>
+      </body>
+      <body>
+        <joint name="j2" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".05 .05 .05"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid joint="j1" kp="7" input="pos"/>
+      <position joint="j1" kp="7"/>
+      <pid joint="j2" kv="3" input="vel"/>
+      <velocity joint="j2" kv="3"/>
+      <pid joint="j2" kp="5" kv="2" input="pos ff"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  mjModel* m = model.get();
+
+  // layout: subsets shrink the control blocks
+  EXPECT_EQ(m->nactuator, 5);
+  EXPECT_EQ(m->nout, 5);
+  EXPECT_EQ(m->nu, 6);
+  int expected_ctrlnum[5] = {1, 1, 1, 1, 2};
+  for (int i=0; i < 5; i++) {
+    EXPECT_EQ(m->actuator_ctrlnum[i], expected_ctrlnum[i]) << "actuator " << i;
+  }
+
+  mjData* data = mj_makeData(m);
+  data->qpos[0] = 0.2;
+  data->qpos[1] = -0.3;
+  data->qvel[0] = 0.5;
+  data->qvel[1] = -0.4;
+  data->ctrl[0] = data->ctrl[1] = 0.6;   // pos-only pid and position servo
+  data->ctrl[2] = data->ctrl[3] = -0.8;  // vel-only pid and velocity servo
+  data->ctrl[4] = 0.3;                   // pos of the [pos, ff] pid
+  data->ctrl[5] = 0.9;                   // ff  of the [pos, ff] pid
+  mj_forward(m, data);
+
+  // single-input PIDs match the SISO servos
+  EXPECT_DOUBLE_EQ(data->actuator_force[0], data->actuator_force[1]);
+  EXPECT_DOUBLE_EQ(data->actuator_force[2], data->actuator_force[3]);
+
+  // [pos, ff]: kp*(qref - l) - kv*ldot + ff (absent velocity setpoint is zero)
+  mjtNum expected = 5*(0.3 - data->qpos[1]) - 2*data->qvel[1] + 0.9;
+  EXPECT_MJTNUM_EQ(data->actuator_force[4], expected);
+
+  // input names skip absent inputs
+  EXPECT_STREQ(mj_actuatorInputName(m, 4, 0), "pos");
+  EXPECT_STREQ(mj_actuatorInputName(m, 4, 1), "ff");
+
+  mj_deleteData(data);
+}
+
+// Integral action eliminates the steady-state error of a weak P servo under
+// gravity; the integral state is clamped by imax.
+TEST_F(CoreSmoothTest, PidIntegralAction) {
+  static constexpr char xml_fmt[] = R"(
+  <mujoco>
+    <option integrator="implicitfast">
+      <flag contact="disable"/>
+    </option>
+    <worldbody>
+      <body pos="0 0 .5">
+        <joint name="hinge" axis="0 1 0"/>
+        <geom type="capsule" size=".02" fromto="0 0 0 .2 0 0"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="pid" joint="hinge" kp="1" dampratio="1" ki="%s" imax="2"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  char xml[2048];
+
+  // P-only: gravity induces a steady-state error at target q* = 0
+  snprintf(xml, sizeof(xml), xml_fmt, "0");
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  EXPECT_EQ(model->na, 0);
+  mjData* data = mj_makeData(model.get());
+  while (data->time < 10) {
+    mj_step(model.get(), data);
+    ASSERT_EQ(data->warning[mjWARN_BADQACC].number, 0) << "diverged";
+  }
+  mjtNum p_error = mju_abs(data->qpos[0]);
+  EXPECT_GT(p_error, 0.05);
+  mj_deleteData(data);
+
+  // with integral action: error is eliminated, integral state is bounded
+  snprintf(xml, sizeof(xml), xml_fmt, "2");
+  model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  EXPECT_EQ(model->na, 1);
+  data = mj_makeData(model.get());
+  while (data->time < 20) {
+    mj_step(model.get(), data);
+    ASSERT_LE(mju_abs(data->act[0]), 2 + 1e-10)
+        << "integral state exceeds imax";
+  }
+  EXPECT_LT(mju_abs(data->qpos[0]), 1e-3);
+  mj_deleteData(data);
+}
+
+// slewmax limits the effective setpoint rate through an activation state.
+TEST_F(CoreSmoothTest, PidSlewRateLimit) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option timestep="0.001"/>
+    <worldbody>
+      <body>
+        <joint name="slide" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".1 .1 .1" mass="1"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="servo" joint="slide" kp="200" kv="30" slewmax="0.5"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  EXPECT_EQ(model->actuator_actnum[0], 1);  // slew state
+  mjData* data = mj_makeData(model.get());
+
+  // step the setpoint to 1: the effective setpoint (act) ramps at slewmax
+  data->ctrl[0] = 1.0;
+  mjtNum t_ramp = 1.0 / 0.5;  // setpoint distance / slewmax
+  while (data->time < t_ramp - 0.1) {
+    mj_step(model.get(), data);
+    EXPECT_LE(data->act[0], 0.5 * data->time + 1e-9) << "slew exceeded";
+  }
+  while (data->time < 3 * t_ramp) {
+    mj_step(model.get(), data);
+  }
+
+  // the effective setpoint reached the command, and the joint tracked it
+  EXPECT_NEAR(data->act[0], 1.0, 1e-6);
+  EXPECT_NEAR(data->qpos[0], 1.0, 0.01);
+
+  mj_deleteData(data);
+}
+
+// PID on a rotational transmission: the position setpoint wraps, winding
+// targets are tracked smoothly through pi.
+TEST_F(CoreSmoothTest, PidTracksWindingTarget) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option integrator="implicitfast">
+      <flag contact="disable" gravity="disable"/>
+    </option>
+    <worldbody>
+      <body>
+        <joint name="ball" type="ball"/>
+        <geom type="box" size=".05 .07 .03"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="rz" joint="ball" gear="0 0 1" kp="1" dampratio="1"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+  mjData* data = mj_makeData(model.get());
+
+  const mjtNum rate = 0.5;
+  while (data->time < 2*mjPI / rate) {
+    data->ctrl[0] = rate * data->time;
+    data->ctrl[1] = rate;  // matched velocity setpoint
+    mj_step(model.get(), data);
+    mjtNum err = data->ctrl[0] - data->actuator_length[0];
+    err -= 2*mjPI * mju_round(err / (2*mjPI));
+    ASSERT_LT(mju_abs(err), 0.5) << "tracking lost at time " << data->time;
+  }
+
+  mj_deleteData(data);
+}
+
+// PID parameters compose through defaults classes; the model round-trips.
+TEST_F(CoreSmoothTest, PidDefaultsAndRoundtrip) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <default>
+      <default class="arm">
+        <pid kp="7" ki="3" imax="1.5" velrange="-2 2" input="pos vel ff"/>
+      </default>
+    </default>
+    <worldbody>
+      <body>
+        <joint name="slide" type="slide" axis="1 0 0"/>
+        <geom type="box" size=".05 .05 .05"/>
+      </body>
+    </worldbody>
+    <actuator>
+      <pid name="pid" joint="slide" class="arm"/>
+    </actuator>
+  </mujoco>
+  )";
+  char error[1024];
+  MjModelPtr model = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(model.get(), NotNull()) << error;
+
+  // inherited: kp, ki, imax, input, velrange
+  EXPECT_EQ(model->nu, 3);
+  EXPECT_EQ(model->na, 1);
+  EXPECT_EQ(model->actuator_gainprm[0], 3);   // ki
+  EXPECT_EQ(model->actuator_biasprm[1], -7);  // -kp
+  EXPECT_EQ(model->actuator_dynprm[0], 1.5);  // imax
+  EXPECT_EQ(model->actuator_dyntype[0], mjDYN_PID);
+  EXPECT_EQ(model->actuator_ctrlrange[2], -2);  // velrange lo, input 1
+  EXPECT_EQ(model->actuator_ctrlrange[3], 2);
+  EXPECT_TRUE(model->actuator_ctrllimited[1]);
+
+  // round-trip preserves everything
+  std::string saved = SaveAndReadXml(model.get());
+  MjModelPtr model2 = LoadModelFromString(saved.c_str(), error, sizeof(error));
+  ASSERT_THAT(model2.get(), NotNull()) << error;
+  EXPECT_EQ(model2->nu, 3);
+  EXPECT_EQ(model2->na, 1);
+  EXPECT_EQ(model2->actuator_gainprm[0], 3);
+  EXPECT_EQ(model2->actuator_ctrlrange[2], -2);
+}
+
 static const char* const kInertiaPath = "engine/testdata/inertia.xml";
 
 TEST_F(CoreSmoothTest, FactorI) {

test/user/user_api_test.cc

@@ -18,7 +18,7 @@
 #include <cstddef>
 #include <cstdint>
 #include <cstring>
-#include <filesystem>
+#include <filesystem>  // NOLINT
 #include <functional>
 #include <map>
 #include <memory>
@@ -513,6 +513,41 @@ TEST_F(MujocoTest, SetToOrientation) {
   mj_deleteSpec(spec);
 }
 
+TEST_F(MujocoTest, SetToPID) {
+  mjSpec* spec = mj_makeSpec();
+  mjsActuator* actuator = mjs_addActuator(spec, 0);
+
+  // stateless PID with kv, default input signature
+  double kv = 3.0;
+  const char* err = mjs_setToPID(actuator, 5.0, &kv, nullptr, nullptr, nullptr,
+                                 nullptr, 0, 0);
+  EXPECT_STREQ(err, "");
+  EXPECT_EQ(actuator->gaintype, mjGAIN_PID);
+  EXPECT_EQ(actuator->biastype, mjBIAS_AFFINE);
+  EXPECT_EQ(actuator->dyntype, mjDYN_NONE);
+  EXPECT_EQ(actuator->biasprm[1], -5.0);
+  EXPECT_EQ(actuator->biasprm[2], -3.0);
+  EXPECT_EQ(actuator->gainprm[0], 0.0);
+
+  // integral action with anti-windup, pos-only signature
+  double ki = 0.5, imax = 2.0, dampratio = 1.0;
+  err = mjs_setToPID(actuator, 5.0, nullptr, &dampratio, &ki, &imax, nullptr, 0,
+                     mjINPUT_POS);
+  EXPECT_STREQ(err, "");
+  EXPECT_EQ(actuator->dyntype, mjDYN_PID);
+  EXPECT_EQ(actuator->gainprm[0], 0.5);
+  EXPECT_EQ(actuator->dynprm[0], 2.0);
+  EXPECT_EQ(actuator->biasprm[2], 1.0);
+  EXPECT_EQ(actuator->ctrlspec, mjINPUT_POS);
+
+  // kv and dampratio are mutually exclusive
+  err = mjs_setToPID(actuator, 5.0, &kv, &dampratio, nullptr, nullptr, nullptr,
+                     0, 0);
+  EXPECT_STREQ(err, "kv and dampratio cannot both be defined");
+
+  mj_deleteSpec(spec);
+}
+
 static constexpr char xml_plugin_1[] = R"(
   <mujoco model="MuJoCo Model">
     <worldbody>

unity/Runtime/Bindings/MjBindings.cs

@@ -276,7 +276,8 @@ public enum mjtDyn : int{
   mjDYN_FILTEREXACT = 3,
   mjDYN_MUSCLE = 4,
   mjDYN_DCMOTOR = 5,
-  mjDYN_USER = 6,
+  mjDYN_PID = 6,
+  mjDYN_USER = 7,
 }
 public enum mjtGain : int{
   mjGAIN_FIXED = 0,
@@ -284,7 +285,8 @@ public enum mjtGain : int{
   mjGAIN_MUSCLE = 2,
   mjGAIN_DCMOTOR = 3,
   mjGAIN_SO3 = 4,
-  mjGAIN_USER = 5,
+  mjGAIN_PID = 5,
+  mjGAIN_USER = 6,
 }
 public enum mjtBias : int{
   mjBIAS_NONE = 0,
@@ -298,6 +300,11 @@ public enum mjtCtrlChart : int{
   mjCHART_EXPMAP = 1,
   mjCHART_QUAT = 2,
 }
+public enum mjtCtrlInput : int{
+  mjINPUT_POS = 1,
+  mjINPUT_VEL = 2,
+  mjINPUT_FF = 4,
+}
 public enum mjtObj : int{
   mjOBJ_UNKNOWN = 0,
   mjOBJ_BODY = 1,

wasm/codegen/generated/bindings.cc

@@ -2923,6 +2923,15 @@ std::string mjs_setToOrientation_wrapper(MjsActuator& actuator, double kp, const
   return std::string(mjs_setToOrientation(actuator.get(), kp, kv_.data(), dampratio_.data(), ctrlspec));
 }
 
+std::string mjs_setToPID_wrapper(MjsActuator& actuator, double kp, const val& kv, const val& dampratio, const val& ki, const val& imax, const val& slewmax, double inheritrange, int ctrlspec) {
+  UNPACK_VALUE(double, kv);
+  UNPACK_VALUE(double, dampratio);
+  UNPACK_VALUE(double, ki);
+  UNPACK_VALUE(double, imax);
+  UNPACK_VALUE(double, slewmax);
+  return std::string(mjs_setToPID(actuator.get(), kp, kv_.data(), dampratio_.data(), ki_.data(), imax_.data(), slewmax_.data(), inheritrange, ctrlspec));
+}
+
 std::string mjs_setToPosition_wrapper(MjsActuator& actuator, double kp, const val& kv, const val& dampratio, const val& timeconst, double inheritrange) {
   UNPACK_VALUE(double, kv);
   UNPACK_VALUE(double, dampratio);
@@ -3981,6 +3990,10 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
   enum_<mjtCtrlChart>("mjtCtrlChart")
     .value("mjCHART_EXPMAP", mjCHART_EXPMAP)
     .value("mjCHART_QUAT", mjCHART_QUAT);
+  enum_<mjtCtrlInput>("mjtCtrlInput")
+    .value("mjINPUT_POS", mjINPUT_POS)
+    .value("mjINPUT_VEL", mjINPUT_VEL)
+    .value("mjINPUT_FF", mjINPUT_FF);
   enum_<mjtDataType>("mjtDataType")
     .value("mjDATATYPE_REAL", mjDATATYPE_REAL)
     .value("mjDATATYPE_POSITIVE", mjDATATYPE_POSITIVE)
@@ -4018,6 +4031,7 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
     .value("mjDYN_FILTEREXACT", mjDYN_FILTEREXACT)
     .value("mjDYN_MUSCLE", mjDYN_MUSCLE)
     .value("mjDYN_DCMOTOR", mjDYN_DCMOTOR)
+    .value("mjDYN_PID", mjDYN_PID)
     .value("mjDYN_USER", mjDYN_USER);
   enum_<mjtEnableBit>("mjtEnableBit")
     .value("mjENBL_OVERRIDE", mjENBL_OVERRIDE)
@@ -4082,6 +4096,7 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
     .value("mjGAIN_MUSCLE", mjGAIN_MUSCLE)
     .value("mjGAIN_DCMOTOR", mjGAIN_DCMOTOR)
     .value("mjGAIN_SO3", mjGAIN_SO3)
+    .value("mjGAIN_PID", mjGAIN_PID)
     .value("mjGAIN_USER", mjGAIN_USER);
   enum_<mjtGeom>("mjtGeom")
     .value("mjGEOM_PLANE", mjGEOM_PLANE)
@@ -5612,6 +5627,7 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
     .property("dynprm", &MjsActuator::dynprm)
     .property("dyntype", &MjsActuator::dyntype, &MjsActuator::set_dyntype, reference())
     .property("element", &MjsActuator::element, reference())
+    .property("ffrange", &MjsActuator::ffrange)
     .property("forcelimited", &MjsActuator::forcelimited, &MjsActuator::set_forcelimited, reference())
     .property("forcerange", &MjsActuator::forcerange)
     .property("gainprm", &MjsActuator::gainprm)
@@ -5628,7 +5644,8 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
     .property("slidersite", &MjsActuator::slidersite, &MjsActuator::set_slidersite, reference())
     .property("target", &MjsActuator::target, &MjsActuator::set_target, reference())
     .property("trntype", &MjsActuator::trntype, &MjsActuator::set_trntype, reference())
-    .property("userdata", &MjsActuator::userdata, reference());
+    .property("userdata", &MjsActuator::userdata, reference())
+    .property("velrange", &MjsActuator::velrange);
   emscripten::class_<MjsAuthored>("MjsAuthored")
     .property("disableactuator", &MjsAuthored::disableactuator, &MjsAuthored::set_disableactuator, reference())
     .property("disableflags", &MjsAuthored::disableflags, &MjsAuthored::set_disableflags, reference())
@@ -6510,6 +6527,7 @@ EMSCRIPTEN_BINDINGS(mujoco_bindings) {
   function("mjs_setToMotor", &mjs_setToMotor_wrapper);
   function("mjs_setToMuscle", &mjs_setToMuscle_wrapper);
   function("mjs_setToOrientation", &mjs_setToOrientation_wrapper);
+  function("mjs_setToPID", &mjs_setToPID_wrapper);
   function("mjs_setToPosition", &mjs_setToPosition_wrapper);
   function("mjs_setToVelocity", &mjs_setToVelocity_wrapper);
   function("mjs_wrapGeom", &mjs_wrapGeom_wrapper);

wasm/codegen/generated/bindings.h

@@ -6025,6 +6025,12 @@ struct MjsActuator {
   void set_ctrlspec(int value) {
     ptr_->ctrlspec = value;
   }
+  emscripten::val velrange() const {
+    return emscripten::val(emscripten::typed_memory_view(2, ptr_->velrange));
+  }
+  emscripten::val ffrange() const {
+    return emscripten::val(emscripten::typed_memory_view(2, ptr_->ffrange));
+  }
   mjtBool actearly() const {
     return ptr_->actearly;
   }