calibration.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# UR10 Calibration\n",
    "- Step-by-step introduction to `pybotics`\n",
    "- Simplified calibration of UR10 industrial collaborative robot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "# pybotics\n",
    "from pybotics import Robot, KinematicChain, LinkConvention, RobotOptimizationMask, Tool, Frame\n",
    "from pybotics.calibration import compute_absolute_errors\n",
    "from pybotics.constants import TRANSFORM_MATRIX_SHAPE, POSITION_VECTOR_LENGTH, TRANSFORM_VECTOR_LENGTH\n",
    "\n",
    "# essentials\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from copy import deepcopy\n",
    "\n",
    "# optimization\n",
    "import scipy.optimize\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# plotting\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline  \n",
    "\n",
    "# printing options\n",
    "np.set_printoptions(suppress=True)\n",
    "pd.set_option('precision', 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Optimization Function\n",
    "- Computes the errors between a robot model and the measured positions (i.e., real life)\n",
    "    - Requires a series of measured joint-position pairs\n",
    "        - Joints = random robot configurations\n",
    "        - Positions = measured real-world Cartesian positions with a laser tracker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def fitness_function(optimization_vector, robot, joints, positions):\n",
    "    \"\"\"Return absolute distance errors of a given robot model from corresponding joints and positions.\"\"\"\n",
    "    \n",
    "    # apply latest optimization vector     \n",
    "    robot.apply_optimization_vector(optimization_vector)\n",
    "    \n",
    "    # compute absolute errors\n",
    "    # errors = abs(calculated fk - actual position)     \n",
    "    errors = compute_absolute_errors(robot, joints, positions)\n",
    "    \n",
    "    return errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# World Frame\n",
    "- Describes the geometric transformation between our global reference frame and the base of the robot\n",
    "    - Here:\n",
    "        - Global reference frame = laser tracker's origin\n",
    "        - Assumed to be well defined"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   -0.910397,     0.413555,    -0.012223,  2289.101393],\n",
       "       [   -0.413474,    -0.910475,    -0.008638,    36.666412],\n",
       "       [   -0.014701,    -0.00281 ,     0.999888,  -899.473355],\n",
       "       [    0.      ,     0.      ,     0.      ,     1.      ]])"
      ]
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     "metadata": {},
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   ],
   "source": [
    "world_frame = np.array(\n",
    "    [-0.910397, 0.413555, -0.012223, 2289.101393,\n",
    "     -0.413474, -0.910475, -0.008638, 36.666412,\n",
    "     -0.014701, -0.002810, 0.999888, -899.473355,\n",
    "     0, 0, 0, 1]\n",
    ").reshape(TRANSFORM_MATRIX_SHAPE)\n",
    "\n",
    "display(world_frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Tool Frame\n",
    "- Describes the geometric transformation between our robot flange and the tool centre point (TCP)\n",
    "    - TCP = centre of spherically mounted retroreflector (SMR)\n",
    "- Derived from mechanical CAD measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.      ,    0.      ,    0.      ,  -31.418407],\n",
       "       [   0.      ,    1.      ,    0.      , -119.737717],\n",
       "       [   0.      ,    0.      ,    1.      ,   27.368691],\n",
       "       [   0.      ,    0.      ,    0.      ,    1.      ]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tool_frame = np.array(\n",
    "    [1, 0, 0, -31.418407,\n",
    "     0, 1, 0, -119.737717,\n",
    "     0, 0, 1, 27.368691,\n",
    "     0, 0, 0, 1]\n",
    ").reshape(TRANSFORM_MATRIX_SHAPE)\n",
    "\n",
    "display(tool_frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Measured Tool Frame Poses\n",
    "- Calibrate the tool frame\n",
    "- Simple poses that just rotate the last three joints (i.e., robot wrist)\n",
    "    - Minimize sources of error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>joint_0</th>\n",
       "      <th>joint_1</th>\n",
       "      <th>joint_2</th>\n",
       "      <th>joint_3</th>\n",
       "      <th>joint_4</th>\n",
       "      <th>joint_5</th>\n",
       "      <th>laser_x</th>\n",
       "      <th>laser_y</th>\n",
       "      <th>laser_z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>-30</td>\n",
       "      <td>0</td>\n",
       "      <td>1800.732</td>\n",
       "      <td>406.872</td>\n",
       "      <td>-406.413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1774.976</td>\n",
       "      <td>465.445</td>\n",
       "      <td>-406.164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>1781.964</td>\n",
       "      <td>529.086</td>\n",
       "      <td>-405.476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-30</td>\n",
       "      <td>1752.478</td>\n",
       "      <td>516.228</td>\n",
       "      <td>-374.215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1774.973</td>\n",
       "      <td>465.446</td>\n",
       "      <td>-406.169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>1800.434</td>\n",
       "      <td>406.647</td>\n",
       "      <td>-406.076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>90</td>\n",
       "      <td>-90</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1774.963</td>\n",
       "      <td>465.474</td>\n",
       "      <td>-406.162</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   joint_0  joint_1  joint_2  joint_3  joint_4  joint_5   laser_x  laser_y  \\\n",
       "0       90      -90       90        0      -30        0  1800.732  406.872   \n",
       "1       90      -90       90        0        0        0  1774.976  465.445   \n",
       "2       90      -90       90        0       30        0  1781.964  529.086   \n",
       "3       90      -90       90        0        0      -30  1752.478  516.228   \n",
       "4       90      -90       90        0        0        0  1774.973  465.446   \n",
       "5       90      -90       90        0        0       30  1800.434  406.647   \n",
       "6       90      -90       90        0        0        0  1774.963  465.474   \n",
       "\n",
       "   laser_z  \n",
       "0 -406.413  \n",
       "1 -406.164  \n",
       "2 -405.476  \n",
       "3 -374.215  \n",
       "4 -406.169  \n",
       "5 -406.076  \n",
       "6 -406.162  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tool_df = pd.read_csv('tool.csv')\n",
    "\n",
    "display(tool_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# split df into inputs/outputs\n",
    "tool_joints = tool_df[['joint_{}'.format(i) for i in range(6)]]\n",
    "tool_positions = tool_df[['laser_{}'.format(i) for i in 'xyz']]\n",
    "\n",
    "# pybotics uses radians\n",
    "tool_joints = np.deg2rad(tool_joints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Measured Robot Poses\n",
    "- Calibrate the robot kinematic chain (i.e., MDH parameters)\n",
    "- Many random robot configurations (i.e., joints) are measured"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>joint_0</th>\n",
       "      <th>joint_1</th>\n",
       "      <th>joint_2</th>\n",
       "      <th>joint_3</th>\n",
       "      <th>joint_4</th>\n",
       "      <th>joint_5</th>\n",
       "      <th>laser_x</th>\n",
       "      <th>laser_y</th>\n",
       "      <th>laser_z</th>\n",
       "      <th>tool_x</th>\n",
       "      <th>tool_y</th>\n",
       "      <th>tool_z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>141.158</td>\n",
       "      <td>-56.026</td>\n",
       "      <td>16.648</td>\n",
       "      <td>26.515</td>\n",
       "      <td>71.239</td>\n",
       "      <td>74.703</td>\n",
       "      <td>1329.845</td>\n",
       "      <td>-40.650</td>\n",
       "      <td>-76.294</td>\n",
       "      <td>-31.418</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>113.155</td>\n",
       "      <td>-38.278</td>\n",
       "      <td>29.866</td>\n",
       "      <td>156.538</td>\n",
       "      <td>-28.555</td>\n",
       "      <td>3.794</td>\n",
       "      <td>1388.183</td>\n",
       "      <td>462.718</td>\n",
       "      <td>-104.241</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>80.101</td>\n",
       "      <td>-45.366</td>\n",
       "      <td>27.095</td>\n",
       "      <td>60.263</td>\n",
       "      <td>-14.974</td>\n",
       "      <td>-68.352</td>\n",
       "      <td>1742.167</td>\n",
       "      <td>875.745</td>\n",
       "      <td>-321.800</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>159.618</td>\n",
       "      <td>-10.312</td>\n",
       "      <td>27.396</td>\n",
       "      <td>139.321</td>\n",
       "      <td>-96.898</td>\n",
       "      <td>16.232</td>\n",
       "      <td>1136.559</td>\n",
       "      <td>-196.619</td>\n",
       "      <td>-587.373</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>74.023</td>\n",
       "      <td>-24.307</td>\n",
       "      <td>34.791</td>\n",
       "      <td>39.111</td>\n",
       "      <td>-18.101</td>\n",
       "      <td>3.256</td>\n",
       "      <td>1867.326</td>\n",
       "      <td>915.997</td>\n",
       "      <td>-774.333</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   joint_0  joint_1  joint_2  joint_3  joint_4  joint_5   laser_x  laser_y  \\\n",
       "0  141.158  -56.026   16.648   26.515   71.239   74.703  1329.845  -40.650   \n",
       "1  113.155  -38.278   29.866  156.538  -28.555    3.794  1388.183  462.718   \n",
       "2   80.101  -45.366   27.095   60.263  -14.974  -68.352  1742.167  875.745   \n",
       "3  159.618  -10.312   27.396  139.321  -96.898   16.232  1136.559 -196.619   \n",
       "4   74.023  -24.307   34.791   39.111  -18.101    3.256  1867.326  915.997   \n",
       "\n",
       "   laser_z  tool_x   tool_y  tool_z  \n",
       "0  -76.294 -31.418 -119.738  27.369  \n",
       "1 -104.241 -31.418 -119.738  27.369  \n",
       "2 -321.800 -31.418 -119.738  27.369  \n",
       "3 -587.373 -31.418 -119.738  27.369  \n",
       "4 -774.333 -31.418 -119.738  27.369  "
      ]
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       "      <th></th>\n",
       "      <th>joint_0</th>\n",
       "      <th>joint_1</th>\n",
       "      <th>joint_2</th>\n",
       "      <th>joint_3</th>\n",
       "      <th>joint_4</th>\n",
       "      <th>joint_5</th>\n",
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       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>128.119</td>\n",
       "      <td>-33.365</td>\n",
       "      <td>73.789</td>\n",
       "      <td>115.324</td>\n",
       "      <td>-41.703</td>\n",
       "      <td>63.009</td>\n",
       "      <td>1307.882</td>\n",
       "      <td>322.416</td>\n",
       "      <td>-581.836</td>\n",
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       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>168.337</td>\n",
       "      <td>-45.826</td>\n",
       "      <td>43.306</td>\n",
       "      <td>-13.215</td>\n",
       "      <td>105.359</td>\n",
       "      <td>-53.426</td>\n",
       "      <td>1195.157</td>\n",
       "      <td>-235.826</td>\n",
       "      <td>-464.456</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
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       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>80.145</td>\n",
       "      <td>-56.789</td>\n",
       "      <td>49.528</td>\n",
       "      <td>53.370</td>\n",
       "      <td>-9.567</td>\n",
       "      <td>-101.961</td>\n",
       "      <td>1759.802</td>\n",
       "      <td>848.527</td>\n",
       "      <td>-302.431</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>132.957</td>\n",
       "      <td>-69.031</td>\n",
       "      <td>66.650</td>\n",
       "      <td>-13.151</td>\n",
       "      <td>68.842</td>\n",
       "      <td>41.114</td>\n",
       "      <td>1315.753</td>\n",
       "      <td>155.694</td>\n",
       "      <td>-388.257</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>70.734</td>\n",
       "      <td>-67.434</td>\n",
       "      <td>33.176</td>\n",
       "      <td>39.382</td>\n",
       "      <td>-17.825</td>\n",
       "      <td>27.201</td>\n",
       "      <td>1952.649</td>\n",
       "      <td>628.436</td>\n",
       "      <td>-121.983</td>\n",
       "      <td>-31.418</td>\n",
       "      <td>-119.738</td>\n",
       "      <td>27.369</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     joint_0  joint_1  joint_2  joint_3  joint_4  joint_5   laser_x  laser_y  \\\n",
       "146  128.119  -33.365   73.789  115.324  -41.703   63.009  1307.882  322.416   \n",
       "147  168.337  -45.826   43.306  -13.215  105.359  -53.426  1195.157 -235.826   \n",
       "148   80.145  -56.789   49.528   53.370   -9.567 -101.961  1759.802  848.527   \n",
       "149  132.957  -69.031   66.650  -13.151   68.842   41.114  1315.753  155.694   \n",
       "150   70.734  -67.434   33.176   39.382  -17.825   27.201  1952.649  628.436   \n",
       "\n",
       "     laser_z  tool_x   tool_y  tool_z  \n",
       "146 -581.836 -31.418 -119.738  27.369  \n",
       "147 -464.456 -31.418 -119.738  27.369  \n",
       "148 -302.431 -31.418 -119.738  27.369  \n",
       "149 -388.257 -31.418 -119.738  27.369  \n",
       "150 -121.983 -31.418 -119.738  27.369  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "robot_df = pd.read_csv('ur10.csv')\n",
    "\n",
    "display(robot_df.head())\n",
    "display(robot_df.tail())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/fz75+flDpMoS9aUmeuypBr1eT1FRUULbyrJMIBBQ3QMulwu/349Op8Pv9zNz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\nTYOBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10808f240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# plot \n",
    "ax.scatter(robot_df['laser_x'],robot_df['laser_y'],robot_df['laser_z'],label='Measured Positions');\n",
    "ax.scatter(world_frame[0, -1],world_frame[1, -1],world_frame[2, -1],label='Robot Base');\n",
    "ax.scatter(0,0,0,label='Laser Tracker');\n",
    "\n",
    "ax.legend();\n",
    "ax.set_aspect('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Bias towards region between laser tracker and robot base\n",
    "- Good enough for a demo! 😛"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# split df into inputs/outputs\n",
    "robot_joints = robot_df[['joint_{}'.format(i) for i in range(6)]]\n",
    "robot_positions = robot_df[['laser_{}'.format(i) for i in 'xyz']]\n",
    "\n",
    "# pybotics uses radians\n",
    "robot_joints = np.deg2rad(robot_joints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Split Testing and Training Data\n",
    "- Put aside a set of measures for validation after calibration\n",
    "- Prevent overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "train_robot_joints, \\\n",
    "test_robot_joints, \\\n",
    "train_robot_positions, \\\n",
    "test_robot_positions = train_test_split(robot_joints,\n",
    "                                        robot_positions,\n",
    "                                        test_size=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Nominal Model\n",
    "- Represents the manufacturer's intended mathematical model for the robot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>a</th>\n",
       "      <th>theta</th>\n",
       "      <th>d</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "      <td>118.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.571</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.142</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000</td>\n",
       "      <td>612.7</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000</td>\n",
       "      <td>571.6</td>\n",
       "      <td>0.000</td>\n",
       "      <td>163.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.571</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "      <td>115.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.571</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.142</td>\n",
       "      <td>92.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   alpha      a  theta      d\n",
       "0  0.000    0.0  0.000  118.0\n",
       "1  1.571    0.0  3.142    0.0\n",
       "2  0.000  612.7  0.000    0.0\n",
       "3  0.000  571.6  0.000  163.9\n",
       "4 -1.571    0.0  0.000  115.7\n",
       "5  1.571    0.0  3.142   92.2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load UR10 kinematic chain (i.e., MDH parameters)\n",
    "mdh = np.loadtxt('ur10-mdh.csv', delimiter=',')\n",
    "kc = KinematicChain.from_array(mdh)\n",
    "\n",
    "# construct nominal robot\n",
    "nominal_robot = Robot(kc)\n",
    "nominal_robot.world_frame = Frame(world_frame)\n",
    "nominal_robot.tool = Tool(tool_frame)\n",
    "\n",
    "display(pd.DataFrame(\n",
    "        nominal_robot.kinematic_chain.vector.reshape(nominal_robot.num_dof,-1),\n",
    "        columns=('alpha', 'a', 'theta', 'd')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Initial Errors\n",
    "- What would the offline programming errors look like if we did not calibrate the robot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    46.000\n",
       "mean      2.666\n",
       "std       0.634\n",
       "min       1.081\n",
       "25%       2.251\n",
       "50%       2.667\n",
       "75%       3.001\n",
       "max       4.350\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nominal_errors = compute_absolute_errors(nominal_robot, test_robot_joints, test_robot_positions)\n",
    "\n",
    "display(pd.Series(nominal_errors).describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ltodCROwUET+IiEciYmVEfLrdNUiShjephjbXAWdm5gMRsTVwf0TclpmP1FCLJGmQtp8p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\nqWQoSJJK/x+3nQ4ehepijwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1080815f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.hist(x=nominal_errors,\n",
    "         label='Nominal',\n",
    "         bins='auto');\n",
    "\n",
    "plt.xlabel('Absolute Error [mm]');\n",
    "plt.ylabel('Frequency');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "- Ouch! Pretty large errors!\n",
    "- Don't forget, these are real measurements of a real industrial (expensive) robot!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Tool Calibration\n",
    "- Poorly designed and measured tooling often has a large error contribution\n",
    "- Simply screwing a tool to a robot isn't that accurate..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# create a robot copy for tool calibration\n",
    "tool_calibration_robot = deepcopy(nominal_robot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# we are only going to calibrate \n",
    "# the tool centre point position (TCP) not orientation\n",
    "tool_mask = [False] * TRANSFORM_VECTOR_LENGTH\n",
    "\n",
    "for i in range(POSITION_VECTOR_LENGTH):\n",
    "    tool_mask[i] = True\n",
    "\n",
    "tool_calibration_robot.optimization_mask \\\n",
    "    = RobotOptimizationMask(world_frame=False,\n",
    "                            kinematic_chain=False,\n",
    "                            tool=tool_mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.        ,    0.        ,    0.        ,  -32.78366082],\n",
       "       [  -0.        ,    1.        ,    0.        , -119.1872499 ],\n",
       "       [   0.        ,   -0.        ,    1.        ,   27.41458655],\n",
       "       [   0.        ,    0.        ,    0.        ,    1.        ]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scipy to the rescue!\n",
    "# minimize the error of the tool_calibration_robot model\n",
    "result = scipy.optimize.leastsq(func=fitness_function,\n",
    "                                x0=tool_calibration_robot.optimization_vector,\n",
    "                                args=(tool_calibration_robot,\n",
    "                                      tool_joints,\n",
    "                                      tool_positions))\n",
    "\n",
    "# apply the solution vector to the model\n",
    "tool_calibration_robot.apply_optimization_vector(result[0])\n",
    "\n",
    "# optimized tool frame\n",
    "display(tool_calibration_robot.tool.matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.        ,  0.        , -1.36525382],\n",
       "       [-0.        ,  0.        ,  0.        ,  0.5504671 ],\n",
       "       [ 0.        , -0.        ,  0.        ,  0.04589555],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# diff vs old frame\n",
    "display(tool_calibration_robot.tool.matrix - tool_frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "- Even with our well design tool and CAD measurements, the actual tool was off by a few mm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Robot Calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# make a new robot copy\n",
    "calibration_robot = deepcopy(tool_calibration_robot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True],\n",
       "       [ True,  True,  True, False],\n",
       "       [ True,  True,  True, False],\n",
       "       [ True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True]], dtype=bool)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# init the optimization mask\n",
    "mask = np.array(calibration_robot.kinematic_chain.optimization_mask) \\\n",
    "        .reshape((calibration_robot.num_dof, -1))\n",
    "mask[:] = True\n",
    "\n",
    "# filter out a couple of redundant parameters\n",
    "# outside the scope of the presentation\n",
    "mask[1:3, -1] = False\n",
    "display(mask)\n",
    "\n",
    "# apply mask to robot\n",
    "# filter out world/tool calibrations\n",
    "calibration_robot.optimization_mask \\\n",
    "    = RobotOptimizationMask(world_frame=False,\n",
    "                            kinematic_chain=mask.ravel(),\n",
    "                            tool=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/scipy/optimize/minpack.py:427: RuntimeWarning: Number of calls to function has reached maxfev = 50.\n",
      "  warnings.warn(errors[info][0], RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "# maxfev is set way lower than it should for a quick demo\n",
    "result = scipy.optimize.leastsq(func=fitness_function,\n",
    "                                x0=calibration_robot.optimization_vector,\n",
    "                                maxfev=50,\n",
    "                                args=(calibration_robot,\n",
    "                                      train_robot_joints,\n",
    "                                      train_robot_positions))\n",
    "\n",
    "# apply the solution vector to the model\n",
    "calibration_robot.apply_optimization_vector(result[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>a</th>\n",
       "      <th>theta</th>\n",
       "      <th>d</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.532e-06</td>\n",
       "      <td>0.334</td>\n",
       "      <td>4.992e-04</td>\n",
       "      <td>118.258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.572e+00</td>\n",
       "      <td>-0.204</td>\n",
       "      <td>3.139e+00</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-7.380e-04</td>\n",
       "      <td>613.103</td>\n",
       "      <td>2.124e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.952e-03</td>\n",
       "      <td>571.667</td>\n",
       "      <td>-2.174e-03</td>\n",
       "      <td>164.354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.572e+00</td>\n",
       "      <td>-0.225</td>\n",
       "      <td>1.637e-02</td>\n",
       "      <td>115.762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.571e+00</td>\n",
       "      <td>0.079</td>\n",
       "      <td>3.154e+00</td>\n",
       "      <td>91.696</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       alpha        a      theta        d\n",
       "0  3.532e-06    0.334  4.992e-04  118.258\n",
       "1  1.572e+00   -0.204  3.139e+00    0.000\n",
       "2 -7.380e-04  613.103  2.124e-03    0.000\n",
       "3  1.952e-03  571.667 -2.174e-03  164.354\n",
       "4 -1.572e+00   -0.225  1.637e-02  115.762\n",
       "5  1.571e+00    0.079  3.154e+00   91.696"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_model = calibration_robot \\\n",
    "            .kinematic_chain \\\n",
    "            .vector \\\n",
    "            .reshape(calibration_robot.num_dof,-1)\n",
    "\n",
    "display(pd.DataFrame(new_model,\n",
    "        columns=('alpha', 'a', 'theta', 'd')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>delta alpha</th>\n",
       "      <th>delta a</th>\n",
       "      <th>delta theta</th>\n",
       "      <th>delta d</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.532e-06</td>\n",
       "      <td>0.334</td>\n",
       "      <td>4.992e-04</td>\n",
       "      <td>0.258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.086e-03</td>\n",
       "      <td>-0.204</td>\n",
       "      <td>-2.157e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-7.380e-04</td>\n",
       "      <td>0.403</td>\n",
       "      <td>2.124e-03</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.952e-03</td>\n",
       "      <td>0.067</td>\n",
       "      <td>-2.174e-03</td>\n",
       "      <td>0.454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-8.295e-04</td>\n",
       "      <td>-0.225</td>\n",
       "      <td>1.637e-02</td>\n",
       "      <td>0.062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.975e-05</td>\n",
       "      <td>0.079</td>\n",
       "      <td>1.265e-02</td>\n",
       "      <td>-0.504</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   delta alpha  delta a  delta theta  delta d\n",
       "0    3.532e-06    0.334    4.992e-04    0.258\n",
       "1    1.086e-03   -0.204   -2.157e-03    0.000\n",
       "2   -7.380e-04    0.403    2.124e-03    0.000\n",
       "3    1.952e-03    0.067   -2.174e-03    0.454\n",
       "4   -8.295e-04   -0.225    1.637e-02    0.062\n",
       "5    5.975e-05    0.079    1.265e-02   -0.504"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "old_model = nominal_robot \\\n",
    "            .kinematic_chain \\\n",
    "            .vector \\\n",
    "            .reshape(nominal_robot.num_dof,-1)\n",
    "\n",
    "display(pd.DataFrame(new_model - old_model,\n",
    "        columns=('delta alpha', 'delta a',\n",
    "                 'delta theta', 'delta d')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "- Little errors here and there through the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Error Improvement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    46.000\n",
       "mean      0.232\n",
       "std       0.130\n",
       "min       0.044\n",
       "25%       0.142\n",
       "50%       0.213\n",
       "75%       0.310\n",
       "max       0.612\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "calibrated_errors = compute_absolute_errors(calibration_robot,\n",
    "                                            test_robot_joints,\n",
    "                                            test_robot_positions)\n",
    "\n",
    "display(pd.Series(calibrated_errors).describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bqr00BLAz8HJmfh1oj4gh1awUEbsCc4Apmflyx88yM9nCew0yc0ZmtmZma3NzczfKlCR1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\nEEhSyf1/iZ0E/AKyFEMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1080816d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.hist(x=[nominal_errors,calibrated_errors],\n",
    "         label=['Nominal', 'Calibrated'],\n",
    "         bins=10);\n",
    "\n",
    "plt.xlabel('Absolute Error [mm]');\n",
    "plt.ylabel('Frequency');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](doge-accuracy.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083fbd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# more zoom!\n",
    "plt.figure()\n",
    "\n",
    "plt.hist(x=calibrated_errors,\n",
    "         label='Calibrated',\n",
    "         bins='auto');\n",
    "\n",
    "plt.xlabel('Absolute Error [mm]');\n",
    "plt.ylabel('Frequency');\n",
    "plt.legend();"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}