rdeits/opensim-knee-reflex.ipynb

## opensim-knee-reflex.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import opensim as osim\n",
    "import math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1A: Create a Model object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = osim.Model()\n",
    "model.setName(\"leg\")\n",
    "model.setUseVisualizer(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: Create the thigh body."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "hipHeight = 1.0\n",
    "linkLength = 0.5\n",
    "linkMass = 5\n",
    "thigh = osim.Body(\"thigh\", linkMass, osim.Vec3(0), osim.Inertia(1))\n",
    "thigh.attachGeometry(osim.Ellipsoid(linkLength/10, linkLength/2, linkLength/10))\n",
    "model.addBody(thigh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: Create the hip joint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "hip = osim.PinJoint(\"hip\",\n",
    "    model.getGround(),  # parent body\n",
    "    osim.Vec3(0, hipHeight, 0),  # location in parent\n",
    "    osim.Vec3(0),  # orientation in child\n",
    "    thigh,  # child body\n",
    "    osim.Vec3(0, linkLength/2, 0),  # location in child\n",
    "    osim.Vec3(0)  # orientation in child\n",
    ")\n",
    "model.addJoint(hip)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4: Set the default value of the hip coordinate to +90 degrees."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "hip.getCoordinate().setDefaultValue(0.5 * math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 8A: Lock the hip coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "hip.getCoordinate().setDefaultLocked(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 5: Create the shank body and knee joint.\n",
    "* Create a body named 'shank', with the same mass properties as the thigh.\n",
    "* Attach the same ellipsoid geometry as for the thigh.\n",
    "* Add the shank body to the model.\n",
    "\n",
    "\n",
    "* Create a PinJoint named 'knee' Parent: thigh; child: shank.\n",
    "* The location of the joint in the parent body is (0, -linkLength/2, 0).\n",
    "* The location of the joint in the child body is (0, +linkLength/2, 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "shank = osim.Body(\"shank\", linkMass, osim.Vec3(0), osim.Inertia(1))\n",
    "shank.attachGeometry(osim.Ellipsoid(linkLength/10, linkLength/2, linkLength/10))\n",
    "model.addBody(shank)\n",
    "\n",
    "knee = osim.PinJoint(\"knee\",\n",
    "    thigh,  # parent body\n",
    "    osim.Vec3(0, -linkLength/2, 0),  # location in parent\n",
    "    osim.Vec3(0),  # orientation in child\n",
    "    shank,  # child body\n",
    "    osim.Vec3(0, linkLength/2, 0),  # location in child\n",
    "    osim.Vec3(0)  # orientation in child\n",
    ")\n",
    "model.addJoint(knee)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 8B: Set the default value of the knee coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "knee.getCoordinate().setDefaultValue(-0.5 * math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 6A: Add a vastus muscle (actuator)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "vastus = osim.Millard2012EquilibriumMuscle()\n",
    "vastus.setName(\"vastus\")\n",
    "vastus.setMaxIsometricForce(500)\n",
    "vastus.setOptimalFiberLength(0.19)\n",
    "vastus.setTendonSlackLength(0.19)\n",
    "\n",
    "vastus.addNewPathPoint(\"origin\", thigh, osim.Vec3(linkLength/10, 0, 0))\n",
    "insertion = osim.Vec3(0.75 * linkLength/10, 0.7 * linkLength/2, 0)\n",
    "vastus.addNewPathPoint(\"insertion\", shank, insertion)\n",
    "\n",
    "model.addForce(vastus)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 7: The vastus muscle wraps over the knee cap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "patella = osim.WrapCylinder()\n",
    "patella.setName(\"patella\")\n",
    "patella.set_translation(osim.Vec3(0, -linkLength/2, 0))\n",
    "patella.set_radius(0.04)\n",
    "patella.set_length(0.1)\n",
    "patella.set_quadrant(\"x\")\n",
    "thigh.addWrapObject(patella)\n",
    "vastus.updGeometryPath().addPathWrap(patella)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 9: Add an open-loop controller for the muscle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "brain = osim.PrescribedController()\n",
    "brain.addActuator(vastus)\n",
    "\n",
    "# Between 0.3 and 0.35 seconds, excitation transitions from 0.05 to 0.5\n",
    "brain.prescribeControlForActuator(\"vastus\", \n",
    "    osim.StepFunction(0.3, 0.35, 0.05, 0.5))\n",
    "model.addController(brain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 10A: Add reflex control (and disable the open-loop control)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Disable the open-loop control\n",
    "brain.setEnabled(False)\n",
    "\n",
    "reflex = osim.ToyReflexController()\n",
    "reflex.addActuator(vastus)\n",
    "reflex.set_gain(40.0)\n",
    "model.addController(reflex)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 11A: Add a reporter to obtain muscle behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "o1 = vastus.getOutput(\"normalized_fiber_length\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "reporter = osim.TableReporter()\n",
    "reporter.set_report_time_interval(0.01)\n",
    "reporter.addToReport(vastus.getOutput(\"normalized_fiber_length\"), \"1m\")\n",
    "reporter.addToReport(vastus.getOutput(\"active_force_length_multiplier\"), \"fl\")\n",
    "model.addComponent(reporter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 1B: Build the model and obtain its default state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = model.initSystem()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 10B: Set the initial speed of the knee coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "knee.getCoordinate().setSpeedValue(state, -3.0)  # units: radians per second"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 6B: Initialize the muscle fiber length state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.equilibrateMuscles(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 1C: Simulate the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<opensim.simbody.State; proxy of <Swig Object of type 'SimTK::State *' at 0x7f0ddebaac90> >"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "osim.simulate(model, state, 3.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Part 11B: Plot muscle behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "table = reporter.getTable()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = {\n",
    "    \"1m\": table.getDependentColumn(\"1m\"),\n",
    "    \"fl\": table.getDependentColumn(\"fl\"),\n",
    "}\n",
    "signals = {\n",
    "    name: [col.getElt(i, 0) for i in range(col.nrow())] for (name, col) in columns.items()\n",
    "}\n",
    "t = list(table.getIndependentColumn())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e0123c250>,\n",
       " <matplotlib.lines.Line2D at 0x7f0de7d7b9d0>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0de245d490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, signals[\"1m\"], t, signals[\"fl\"])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}