3_invkine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inverse kinematics\n",
    "This notebook considers the problem of inverse kinematics, ie solving at each control cycle of the robot a quadratic program from the derivatives (jacobian) of the current state. It introduces the basic function to compute the Jacobians of the robot, and how to use them to compute an inverse-kinematics control law. One of the key difficulties is to understand in which frames each quantities is computed (might be in the world frame, in the local frame attached to the end effector, in some arbitrary goal frame, etc), as we should never mixed quantities expressed in different frames without transporting them in the right frame. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NB: as for all the tutorials, a magic command %do_not_load is introduced to hide the solutions to some questions. Change it for %load if you want to see (and execute) the solution.\n"
     ]
    }
   ],
   "source": [
    "import magic_donotload  # noqa: F401"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up\n",
    "We will use a Gepetto-viewer, and the linear algebra of NumPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pinocchio as pin\n",
    "import numpy as np\n",
    "import time\n",
    "from numpy.linalg import pinv,inv,norm,svd,eig\n",
    "from tp3.tiago_loader import loadTiago\n",
    "import matplotlib.pylab as plt; plt.ion()\n",
    "from utils.meshcat_viewer_wrapper import MeshcatVisualizer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the Tiago robot (https://youtu.be/6BwRqwD066g). This mobile manipulator from PAL Robotics as a mobile basis which can move in the plane (3 dof), a manipulator arm (7 dof) and a head (2 dof) both mounted on a prismatic axis moving vertically (1 dof). This makes 3 dof for the basis, and 9 dof for the body. It also has 2 extra joints tot figure the wheels, which are not very useful for this notebook. The wheels and the basis rotations are represented by the cos and sin of the angle. The size of the configuration vector is then 18, while the velocity vector has dimension 15.\n",
    "\n",
    "A load function is available to make it easy to load the robot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You can open the visualizer by visiting the following URL:\n",
      "http://127.0.0.1:7006/static/\n"
     ]
    }
   ],
   "source": [
    "robot = loadTiago()\n",
    "viz = MeshcatVisualizer(robot)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "            <iframe src=\"http://127.0.0.1:7006/static/\" style=\"width: 100%; height: 100%; border: none\"></iframe>\n",
       "            </div>\n",
       "            "
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     "execution_count": 4,
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   ],
   "source": [
    "viz.viewer.jupyter_cell()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The configuration is represented by a vector of larger dimension, subject to constraints (cos^2+sin^2=1). It is not possible to randomly sample a configuration vector q, as these constraints should be respected. Similarly, we should take care when integrating a velocity as summing a configuration q with a velocity v will not work (dimensions do not match). Two functions in Pinocchio implements these functionnalities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = pin.randomConfiguration(robot.model)\n",
    "vq = np.random.rand(robot.model.nv)*2 - 1\n",
    "DT = 1e-3\n",
    "qnext = pin.integrate(robot.model,q,vq*DT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple example moving the robot in the viewer following a constant (random) velocity is as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t in range(1000):\n",
    "    q = pin.integrate(robot.model,q,vq*DT)\n",
    "    viz.display(q)\n",
    "    time.sleep(DT/10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The robot is mobile, hence the camera view in the viewer is not always centered. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward kinematics and Jacobian\n",
    "We recall first the basic method to compute the robot forward kinematics.\n",
    "We will consider two frames of interest on the robot: the first one, named <tool> is at the tip of the end-effector ; the second one, named <basis>, is on the front of the robot basis, 10 cm above the ground. Both are represented in Gepetto-Viewer by a frame composed of three RGB arrows. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "IDX_TOOL = robot.model.getFrameId('frametool')\n",
    "IDX_BASIS = robot.model.getFrameId('framebasis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Frame name: frametool paired to (parent joint/ previous frame)(9/52)\n",
       "with relative placement wrt parent joint:\n",
       "  R =\n",
       "1 0 0\n",
       "0 1 0\n",
       "0 0 1\n",
       "  p =    0    0 0.08\n",
       "containing inertia:\n",
       "  m = 0\n",
       "  c = 0 0 0\n",
       "  I = \n",
       "0 0 0\n",
       "0 0 0\n",
       "0 0 0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot.model.frames[IDX_TOOL]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`model.frame` contains a relative placement ($SE(3)$) to a parent frame which will be a joint frame (aka a principal frame). It also contains dynamic constant if it is a representing a link (aka associated to a mesh)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing frame placement\n",
    "The global placement of the frames are computed by the Pinocchio function framesForwardKinematics, whose results are stored in robot.data.oMf.     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tool placement:   R =\n",
      " -0.363023  -0.136222  -0.921769\n",
      "  -0.91304  -0.145399   0.381073\n",
      " -0.185934    0.97995 -0.0715931\n",
      "  p = -0.710293  0.537753   2.03849\n",
      "\n",
      "Basis placement:   R =\n",
      "-0.986933  0.161131         0\n",
      "-0.161131 -0.986933         0\n",
      "        0         0         1\n",
      "  p = -0.305086  0.654484      0.15\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "\n",
    "oMtool = robot.data.oMf[IDX_TOOL]\n",
    "oMbasis = robot.data.oMf[IDX_BASIS]\n",
    "\n",
    "print(\"Tool placement:\",oMtool)\n",
    "print(\"Basis placement:\",oMbasis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is very important to notice the instruction pattern (which is standard in all Pinocchion functions): first call a whole-body algorithm (here *pin.framesForwardKinematics*), then access the results into *robot.data*.\n",
    "`robot.model` refers to the structure and `robot.data` as container for data that are populated using a whole body algorithm for a given configuration on other elements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tool-placement matrix $^0M_{tool}$ represents the displacement from the world frame $F_0$ to the tool frame $F_{tool}$ express in $F_0$. It is this matrix that must be applied to vector express in $F_{tool}$ to transform it as vector express in $F_0$. It is composed on a rotation matrix $^0R_{tool}$ and a 3D vector $^0T_{tool}$: $^0M_{tool}= [^0R_{tool}, ^0T_{tool}]$, when $^0T_{tool}$ is the vector $o_{tool} - o_{0}$ from the origin of frame $F_0$ to the origin of from $F_{tool}$ expressed in the world frame $F_o$. We can rather express $o_{tool} - o_{0}$ in the tool frame $F_{tool}$ by multiplying $^0T_{tool}$ by $^0R_{tool}^T$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take care to the multiplication operator in numpy. The operator* is (unintuitively) mapped to the coefficient-wise multiplication ... i.e. not at all the matrix multiplication. You should use the operator @ to get the real matrix-matrix product. \n",
    "Never mind, you will likely be tricked at least once by this design pattern. If you don't like it ... well there is nothing to do, this is the basic matrix library in Python, the world most used language. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing Jacobians\n",
    "The jacobian of a frame of the robot is computed using `pin.computeFrameJacobian`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 15)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Jtool = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL)\n",
    "Jtool.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This matrix has 6 rows and NV=15 columns. It corresponds to the \"spatial\" 6D velocity of the end effector. Let's first focus on the 3 first rows, corresponding to the linear velocity. Instant velocity of the original frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Jtool3 = Jtool[:3,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jacobian as a velocity operator\n",
    "A first way to understand what is this matrix is to see that as an operator that converts the velocity in the configuration space into the linear velocity of the end effector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "vtool = Jtool3 @ vq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But in which frame is vtool expressed? The choice in Pinocchio (following algorithmic principles described in [Featherstone 2009]) is to expressed quantities in the local frame by default. So vtool is expressed in the tool frame $F_{tool}$. We should better denote it with its frame. We can compute the velocity in the world frame $F_0$, knowing that $F_{tool}$ is place with a relative rotation $^{o}R_{tool}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "toolvtool = vtool\n",
    "ovtool = oMtool.rotation @ vtool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "tool_Jtool = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL, pin.LOCAL)\n",
    "tool_Jtool3 = tool_Jtool[:3,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are using here long variable names. In the code, these explicit notations are maybe to much. It is your choice to use them or not. For sure, you should use similar notations on the paper board when formulating your algorithm, but maybe you prefer lighter variable naming for implementing it.\n",
    "The tool velocity is easier to interpret in the world frame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generalize this notation to the jacobian part dedidcated to linear velocity expressed in the world frame $F_0$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "o_Jtool3 = oMtool.rotation @ tool_Jtool3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be more precise, relation between jacobian, motion and frame can be as follow:\n",
    "$$^{tool}J_{tool} \\dot{q} = ^{tool}w_{tool} = [^{tool}v_{tool}, ^{tool}\\omega_{tool}]$$ is the instantoneous solid motion of frame $F_{tool}$ express in itself. $^{tool}w_{tool}$ is a twist, an element of the algebra $\\mathfrak{se}(3)$. We can interpret $^{tool}v_{tool}$ as the point velocity of the frame $F_{tool}$ origin express in itself and $^{tool}\\omega_{tool}$ as the instaneous rotation axis/amplitude.\n",
    "\n",
    "Then we can express those two vectors in the world origin $F_{0}$ using $^0R_{tool}$. we have: $$[^{0}v_{tool}, ^{0}\\omega_{tool}] = [^0R_{tool}\\vphantom{.}^{tool}v_{tool}, ^0R_{tool}\\vphantom{.}^{tool}\\omega_{tool}]$$\n",
    "the quantities $^{0}v_{tool}$ and $^{0}\\omega_{tool}$ are easilly interpretable as the same vector quantities in a different frame.\n",
    "\n",
    "However, we can also expres the whole instantaneous motion in the original frame:\n",
    "$$^{0}w_{tool} = ^{0}J_{tool}\\dot{q} = ^{0}X_{tool}\\vphantom{.}^{tool}J_{tool} \\dot{q}$$\n",
    "where $^{0}X_{tool}$ is the adjoint operator related to $^{0}R_{tool}, ^{0}T_{tool}$ that allows to change frame for element of $\\mathfrak{se}(3)$. We can note that:\n",
    "$$^{0}w_{tool} = ^{0}X_{tool}[^{tool}v_{tool}, ^{tool}\\omega_{tool}] = [^0R_{tool}\\vphantom{.}^{tool}v_{tool} + ^0T_{tool} \\wedge ^0R_{tool}\\vphantom{.}^{tool}\\omega_{tool}, ^0R_{tool}\\vphantom{.}^{tool}\\omega_{tool}]=[^0v_{tool} + ^0T_{tool} \\wedge ^{0}\\omega_{tool}, ^{0}\\omega_{tool}]$$\n",
    "note here that the angular component of $^{0}w_{tool}$ is $^{0}\\omega_{tool}$ but the linear part is not $^0v_{tool}$ but use the Varignon formula instead. It has not an easy interpretation on its own, it is the linear part of the instantaneous motion express in the world frame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jacobian as a derivative\n",
    "In the previous, jacobians are operator transforming coinfiguration velocity into Frame instantaneous motion (velocity in $SE(3)$) and frame manipulation allow to express velocity of the origin or instaneous motion in every other frame.\n",
    "\n",
    "A second interpretation of is to observe that it is the derivative of the placement following q. For the three first colums, it is the derivative of the vector $^0T_{tool} = (o_{tool} - o_0)$ the tool position in world frame. Indeed $^0T_{tool}$ is a function of q: $^0T(q)$, the function is actually the forward kinematic. We can take its derivative with respect to q, denoted $\\frac{\\partial ^0T_{tool}}{\\partial q}$. This derivatives is equal to the Jacobian expressed in the world frame $F_0$: $\\frac{\\partial ^0T}{\\partial q} = \\vphantom{.}^0J_{tool}$.\n",
    "\n",
    "The global jacobian is the same for the whole motion expression using the algebra of the Lie group $SE(3)$\n",
    "\n",
    "$$^{tool}J_{tool}(q) u = \\lim_{t \\to 0^+}\\frac{^{0}M_{tool}(q \\oplus_{\\mathcal{C}} tu) \\ominus_{SE(3)} \\vphantom{.}^{0}M_{tool}(q)}{t}$$\n",
    "\n",
    "\n",
    "\n",
    "To be convinced of that, let's check the finite differences. We take a small movement dq, and see that the change in position `o_OT(q+dq)` corresponds to the linear prediction `o_Jtool3*dq`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full jacobian in the tool frame\n",
      "[ 0.01687904 -1.35284442 -0.41396667  0.74925829  0.56925209 -0.63622862]\n",
      "[ 0.01689381 -1.35287161 -0.4139453   0.74917048  0.56926814 -0.63626554]\n",
      "\n",
      "Origin velocity in the world frame\n",
      "[ 0.55974128  0.02353882 -1.29922167]\n",
      "[ 0.55971992  0.02353743 -1.2992526 ]\n",
      "[ 0.55978494  0.02356582 -1.29922407]\n"
     ]
    }
   ],
   "source": [
    "# Sample between -0.001 and 0.001\n",
    "EPS = 1e-4\n",
    "u = (np.random.rand(robot.model.nv)*2-1)\n",
    "dq = u*EPS\n",
    "\n",
    "# q2 = q+dq\n",
    "q2 = pin.integrate(robot.model,q,dq)                     \n",
    "\n",
    "# tool position for q\n",
    "pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "o_M_tool = robot.data.oMf[IDX_TOOL].copy()\n",
    "o_T_tool = o_M_tool.translation\n",
    "\n",
    "# tool position for q+dq\n",
    "pin.framesForwardKinematics(robot.model,robot.data,q2)\n",
    "o_M_tool2 = robot.data.oMf[IDX_TOOL].copy()\n",
    "o_T_tool2 = o_M_tool2.translation\n",
    "\n",
    "print('Full jacobian in the tool frame')\n",
    "print((tool_Jtool @ u))\n",
    "print(pin.log(o_M_tool.inverse() * o_M_tool2).vector / EPS)\n",
    "\n",
    "print('\\nOrigin velocity in the world frame')\n",
    "print((o_Jtool3 @ u))\n",
    "print(o_M_tool.rotation @ pin.log(o_M_tool.inverse() * o_M_tool2).linear / EPS)\n",
    "print((o_T_tool2 - o_T_tool)/EPS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Frame options in Pinocchio\n",
    "Most algorithms accept an option to specify in wich frame the spatial quantity should be expressed. The two basic options are `pin.LOCAL` and `pin.WORLD`. When related to velocity, *LOCAL* is the linear velocity of the center of the local frame (the TOOL_IDX frame, here) and the angular velocity, both expressed in the local frame. With *WORLD* frame, this is the instantaneous motion expressed in the world frame. It is also compose of a linear and an angular velocity but remember that the linear velocity is then difficult to interpret.\n",
    "\n",
    "A last option is given by convenience, which does not respect the mathematics of spatial velocity, but matches the French \"torseur cinématique\": `pin.LOCAL_WORLD_ALIGNED` gives the linear velocity of the center of the local frame and the angular velocity, both expressed in the world frame. It is convenient especially when we are interested to consider the linear velocity as the derivative of the position. This is what we did above.\n",
    "\n",
    "To recap:\n",
    "- `pin.LOCAL` gives $^{tool}w_{tool} = [^{tool}v_{tool}, ^{tool}\\omega_{tool}]$\n",
    "- `pin.WORLD` gives $^{0}w_{tool} =\\vphantom{.}^{0}X_{tool}\\vphantom{.}^{tool}w_{tool}=\\left(\\begin{array}{c|c} \n",
    "  ^0R_{tool} & [^0T_{tool}]_{\\times}\\vphantom{.}^0R_{tool} \\\\ \n",
    "  \\hline \n",
    "  0 & ^0R_{tool}\n",
    "\\end{array} \n",
    "\\right)\\vphantom{.}^{0}w_{tool}$\n",
    "- `pin.LOCAL_WORLD_ALIGNED` gives $[^{0}v_{tool}, ^{0}\\omega_{tool}]=\\left(\n",
    "\\begin{array}{c|c} \n",
    "  ^0R_{tool} & 0 \\\\ \n",
    "  \\hline \n",
    "  0 & ^0R_{tool}\n",
    "\\end{array} \n",
    "\\right)\\vphantom{.}^{0}w_{tool}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.86678885  0.83611224 -0.70970803  0.23691264 -1.00932114  0.46407544]\n",
      "[ 2.86678884  0.83611226 -0.70970803  0.23691265 -1.00932114  0.46407543]\n",
      "[ 0.55987131  0.02359559 -1.29916461]\n",
      "[ 0.55974128  0.02353882 -1.29922167]\n"
     ]
    }
   ],
   "source": [
    "# 0wtool and toolwtool\n",
    "tool_Jtool = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL, pin.LOCAL)\n",
    "o_Jtool = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL, pin.WORLD)\n",
    "print(o_Jtool @ u)\n",
    "print(oMtool.action @ (tool_Jtool @ u))\n",
    "\n",
    "# 0vtool and toolwtool\n",
    "o_Jtool3 = oMtool.rotation @ tool_Jtool[:3, :]\n",
    "print((o_Jtool3 @ u))\n",
    "new_o_Jtool3 = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL, pin.LOCAL_WORLD_ALIGNED)[:3,:]\n",
    "print((new_o_Jtool3 @ u))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may see this video which explain with more illustriations the 3 frame options:  https://youtu.be/MLFtHLTprE4 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inverse kinematics for the moving the robot effector\n",
    "We will first move only the robot end effector, to reach a target defined by a frame F_goal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Goal placement, and integration in the viewer of the goal.\n",
    "oMgoal = pin.SE3(pin.Quaternion(-0.5, 0.58, -0.39, 0.52).normalized().matrix(),\n",
    "                np.array([1.2, .4, .7]))\n",
    "viz.addBox('goal', [.1,.1,.1], [ .1,.1,.5, .6] )\n",
    "viz.applyConfiguration('goal',oMgoal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Position the effector (3d)\n",
    "It is time to write your first control law. Write a for-loop to iterate along the control cycles of the robot. At each control cycle, you should:\n",
    "* compute the Jacobian 3D in the world frame `o_Jtool3`\n",
    "* compute the vector from the tool to the goal, expressed in world frame: o_TG = o_goal - o_tool \n",
    "* compute the control law as vq=pinv(o_Jtool3) * o_TG\n",
    "* integrated the velocity vq during DT to get a new configuration q.\n",
    "You might want to start from the following initial configuration, or from any random one.\n",
    "\n",
    "`pinv(J)` computes  $J^+$ the moore penrose pseudo inverse of $J$. Precisely, for any $e$, $J^+ e$ is the solution of the linear least square problem:\n",
    "$$\\min_x \\|Jx - e\\|_2^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Robot initial configuration.\n",
    "q0 = np.array([ 0.  ,  0.  ,  1.  ,  0.  ,  0.18,  1.37, -0.24, -0.98,  0.98,\n",
    "                0.  ,  0.  ,  0.  ,  0.  , -0.13,  0.  ,  0.  ,  0.  ,  0.  ])\n",
    "DT = 1e-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a good idea to store the values of the error between tool and goal o_TG, to plot them later. For that, simply append each o_TG computed at every control cycle in a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = q0.copy()\n",
    "herr = [] # Log the value of the error between tool and goal.\n",
    "\n",
    "for i in range(500):  # Integrate over 2 second of robot life\n",
    "\n",
    "    # REPLACE\n",
    "    o_TG = np.zeros(3)    \n",
    "    q = q0    \n",
    "\n",
    "    viz.display(q)\n",
    "    time.sleep(1e-3)\n",
    "\n",
    "    herr.append(o_TG) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load tp3/generated/inverse_kinematics_3d_loop\n",
    "q = q0.copy()\n",
    "herr = [] # Log the value of the error between tool and goal.\n",
    "# Loop on an inverse kinematics for 200 iterations.\n",
    "for i in range(500):  # Integrate over 2 second of robot life\n",
    "\n",
    "    # Run the algorithms that outputs values in robot.data\n",
    "    pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "    pin.computeJointJacobians(robot.model,robot.data,q)\n",
    "\n",
    "    # Placement from world frame o to frame f oMtool\n",
    "    oMtool = robot.data.oMf[IDX_TOOL]\n",
    "\n",
    "    # 3D jacobian in world frame\n",
    "    o_Jtool3 = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL,pin.LOCAL_WORLD_ALIGNED)[:3,:]\n",
    "\n",
    "    # vector from tool to goal, in world frame\n",
    "    o_TG = oMtool.translation-oMgoal.translation\n",
    "    \n",
    "    # Control law by least square\n",
    "    vq = -pinv(o_Jtool3)@o_TG\n",
    "\n",
    "    q = pin.integrate(robot.model,q, vq * DT)\n",
    "    viz.display(q)\n",
    "    time.sleep(1e-3)\n",
    "\n",
    "    herr.append(o_TG) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is interesting to plot the behavior of the robot. If the error at each iteration has been stored as a list of 3x1 matrices, the following code plots it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1gaezszMJzgTahbVrunY7R+Nxe29nZa6H/Rsgc4M3BOWnH/01Ee0gpgfE9oLYHhDTE2J7eruh+5jySg9bswpIyShg0758UjLy2ZSRf9RBBC0W6BgVQve4MLq3Dqd7XBhdY8NIiAnFGaxpiURAYUikRXF73OzO383GnI2k5KaQkpPC5tzNFFYU1nl8uD2c7q26071Vd7pFdqN7q+50dXYlMiiyaQs/mvIib+jJWAf713uDT1YKHK1BdmQniOvtDTqxvbyhJ6Y7BPnmgKl5ReU1YWdTRj6b9uWzPbuQCveRt/cCrBY6RVeFnrhwurcOo1tV8AmyN/9beiJmUhgS8VGVnkq2H9xeE3o25WwiNS+1zp5bdqudrpFdawJP90hvAGod0rr5NHStLPOGnX1rYF+y9zF7c93j8dhDIK4PtOkHrauXPt7bXj6qsKySDXtdrE07yLp0F2vTD5KeV3foiwiy0bttBL3bRtAnPoI+bSPoFqfQI1JfCkMiPiK7OJt12etYe2At67LXsSlnU53BJ9gWTK+oXvSO6k2f6D70ju5NZ2fnk58KojF53N4rPHtXV4WfX2D/JvDUcasnPB7aJlYFn77Quj9EdfaJBsxHU1bpZnNGAevSD7I23RuAtmUX1jk+T8eoEPocFnx6tw2nXWRw8wmxIi2AwpBIM1TuLiclN4V12etqln1FR3b3DrWH1go9faL60CmiEwHNLSiUFUD6Kkhb7l3SV9U91URwFLQbBPGDIH6gd4lo2/T1NrCcwjJW7c5j9e48Vu3KZcPe/Drn0op3BjGgfSSJHSJJbO+kX3snEUHNKMSKtFAKQyLNQGF5IcnZyazKXMXq/avZmLORil9dJbFgoVurbgyIGUBibCKJsYkkOBMad7Tl+jqYBnuWHgo/+zceebvLHuoNPoeHn8iOzWq05fowDIMdB4pYvSuPlbtyWb07jx0HjpxENTLETmJ7b+gZ0D6SAR2cxIU38VhLIgIoDImY4mDpQdZkrWH1/tWs2r+Kzbmbjxi0sJWjFYmxiQyIHcCA2AH0i+lHqD3UpIqPw5UOuxbDzkWwa5F3eopfi+wIHYYdWuL6QIDv/wkyDINtWYUs3ZHDkm05rNiVW+eghd3jwhiSEMWQTq0Y3KkVnaIbYMJXEWkQvv+XSMQHFFUUsSpzFUszlrIicwVb87YecUy7sHYMaT2Ewa0HM7j1YDqEd2i+P5b5+6rCz0/ex7ydtfdbAiD+NOgwHDoM9YafFnC7C7zhZ09uMUu257B0ew5LtudwoLD2AIYOm5XE9pEMSWjFkIRWDOrYisiQQJMqFpHjURgSaQSVnko2HNjAsoxlLN23lHXZ644Y06ezszODWw+uCUBtQtuYVO0JKC/yhp5t38P27yFnW+391eEnYaR36TgMHOGmlNoYcgrLWLT1AIu2HmDp9gPsc9UeidthszIkoRUjusYwvEsU/dtFEmhrhrcvRaROCkMiDSStII0le5d4r/5krKCgoqDW/nZh7UiKT2J42+EMbj2YmOBmPOCfYUDWJtg23xuA9iwF92G3fixWaHsaJJwJnUd5r/z46Fg+dal0e0hOO8jCLdks3JLN+r2uWj297AEWBnZoRVLXaJK6RjOwYyQOWzNrtC4iJ0xhSKSeKj2VJGcl81P6TyxMX8gO145a+8MDwxnWZhhJ8UkktU2iQ0QHkyo9QaX5VeFnPmz/AQoyau+P7Ahdx0C3Md4A5MNj+tQlK7+UH1O94WfR1mzyS2tfyevTNoJRPWI5o1s0gzu1IiRQfz5FWgr9r1nkJLjKXCzeu5iF6Qv5ee/P5Jcf6h4eYAkgMTaREfEjSIpPom903+bXxf3XDqbBljmw+VvvbbDDe7DZgqHzyEMBKLqbz/f0OpxhGGzNKmTepv3M3bSftWkHa+2PDLEzsnssZ/WIZVT3GOIi1NNLpKVSGBI5jv1F+5m/Zz7zd8/nl6xfcBvumn1Oh5OR7UYyqv0oRsSPwOlo5ldLDAMy18Hm2ZA627t+uOju0GM8dBsLHZPA3rICQKXbw6rdeczbtJ/5KfvZnVNca39ih0hG9/QGoAHtIwnQzOwifkFhSKQO6QXpzN89n3l75rEuu3Zg6BbZjbPan8VZHc5iQMyA5n/1xzC8gxxu+hI2fQWutEP7LFZvj6+e53uXmO6mldlYKtweFm87wLfrMvg+ZT95h83iHmizcma3GM7t05oxveM0zo+In1IYEqmy07WTebvnMX/3fFJyU2q2W7BwWtxpjO04ljGdxtAurJ2JVZ4gw4C9a2Dj50cGIHsIdD0Hek2A7uN8cub246l0e1iyPYdv12UwZ2NmrRndI0PsnNMrjnF9WjOyeyyhDv0ZFPF3+isgfi2rOIv/7fwf3+74tlYAslqsnN76dMZ2GsuYjmOIDYk1scoTZBjeOb42fgEbvwTXnkP7AsO8V376XuwNQvZg08psLJVuDyt25vL1ugy+25hZa+DDmDAHF/Rvw/n92nJ6QitsAer2LiKHKAyJ3ykoL2D+7vl8u/NbVmaurBn5OcASwPD44Zzb8VxGdxxNVFCUyZWeoIN7YN2nsPaT2uP/2EMPBaBuY1pkAALYtC+fz9ek82XyvlqDH0aFBnJ+vzZMGNCWYZ2j1f5HRI5KYUj8QoWngkXpi/hmxzcsTFtIuefQVYPTYk9jQpcJjEsY5zsBqNTlvf219lPYvfjQdlsw9DwP+l4C3c9tsQEoK7+Ur5L3MXNNOpszD43nFBli9wag/vEM7xKlK0AickIUhqRF2+HawRdbv2DW9lnklubWbO/i7MKELhO4oPMFtA9vb2KFJ8HjgR0L4JcPvD3BKqtHQbZ4u8AnXgm9f9OiRn4+XGmFm7mb9jNzdTqLtmbjqRoEMTDAytg+cVwysD1n9YzFrgAkIidJYUhanOKKYr7b9R2fb/2c5Ozkmu3RQdFM7DKRCV0m0CuqV/Od9+vX8jMg+QNY8573lli1mJ6QOBkG/BacPhLo6mFbVgEfr0hj5pp0Dh7WE2xwp1ZcMqgdE/vH4wyxm1ihiPg6hSFpMTYe2MhnWz5jzs45FFd6x48JsAQwst1ILu5+MSPbj8Ru9ZEfTY/bOxL06ne9gyJWj23kcHrDz8CrvdNh+EqgO0mlFW7+tyGDj5ensWLXoSt6bZ1BXDa4PZcMak/nmFATKxSRlkRhSHxambuMubvm8vHmj1l/YH3N9k4RnZjUbRIXdb3IN3qCVSvMgtXveENQfvqh7R2TYNB10OciCAwxrbzGtj27kA+W7ebzNXtrusMHWC2c0yuOq4Z2ZFSPWDWEFpEGpzAkPmlf4T4+S/2Mz7d+Tl5ZHgA2q43xCeO5rPtlDG492Hdug4F3TKAV/4YNMw9NiBrcChKvgkHXQlwvc+trRB6PwU9bs5nx8y4Wbsmu2d4uMpjJp3fg8iEdaOPUYIgi0ngUhsRnGIbBysyVfJDyAQvTF9Z0iW8d0prf9vwtl3S/pHnPBP9r7gpvj7Dlr0P6ikPb258OQ2+B3he2uOkwDldUVsnMNem8s2QXO7KLAO9dvzG94rhmeCdGdtdVIBFpGgpD0uxVeiqZt3seMzbMqDUw4rA2w7iy15Wc1eEsbFYf+k+5OBdWvQUr3zo0M7zVDv0ugaG/h/aDza2vkaXlFvPOkl18tjKNgjLvzPDhDhu/Pb0D1yZ1olO02gKJSNPyoV8Q8TdFFUV8vvVzPtj0AfuK9gEQFBDERd0u4speV9I1sqvJFZ4kVzosfcXbJqjCeyWE0Dg4/SYYfAOEtza1vMaWkpHPawu38826DNxV/eK7xIRy/RkJXDKoPWGaFkNETKK/PtLsZBdn82HKh3y25TMKyr0D6kUFRTG512Qm95xMq6BWJld4krJS4Od/wvr/gMd7JYTW/WDEHd7RoW2B5tbXiAzDYOWuPF79cRsLUg+1BxrZPYabzuzMqO6xWHUrTERMpjAkzUZmUSZvrX+Lz7d+XjNCdEJEAtf2vZbfdPkNQTYfaz+zZxks/ru3a3y1hJFwxl3e6TF8qYH3SfJ4DL7fnMWrP25jzZ6DAFgtcEH/ttx6Vlf6tXOaW6CIyGEUhsR0ewv38ub6N/ly25dUVl05OS32NG7odwNndzgbq8XHRhTevRR+/Avs/KlqgwV6T4Qz7m7x7YE8HoP/bcjkX99vJXW/96peoM3K5YPbc8uoLmoPJCLNksKQmGZP/h7eWP8G32z/hkrDG4JOb3M6tw64ldPbnO5bXePBeyVowV9g50Lvc6vdO0L0GXdCTHdza2tkHo/Bdxsz+ef3W2vmCgt32JiS1Inrz0ggLtzHruqJiF9RGJIml1mUyatrX+WrbV/hrhpZeUT8CH4/4PcMaj3I5OrqYc8y+HE67PjR+9xqh4HXwMh7ILKjqaU1NsMw+G7jfv75/VZSMvIBCA+ycdOZnbnhjM44g31kxG8R8WsKQ9JkcktzeWPdG3ya+ikVHu/owiPbjeTWxFsZEDvA5OrqIXM9zH8Sts3zPrfaqkLQvX4Rgn7aeoC/ztnMxn3eEBTmsHHjGQncdGYXzRUmIj5FYUgaXUF5Ae9ufJf3N71fM2fY6W1O546Bd3Ba3GnmFlcfebthwTOw7jPA8Iag0672hqBWncyurtGtSz/Is//bzJLtOQCEBgZw/RkJ3DyyC5EhLbdnnIi0XApD0mgq3BV8kvoJr697HVeZC4C+0X25Y9AdJLVN8r02QUUH4KfnvQMmVk+Z0e9SGP0IRPvYmEf1sOtAEc/PTeWbdd6BIgMDrFyb1Ik/ju5GVKhCkIj4LoUhaXCGYfBD2g+8sOoF9hTsAaCLswu3D7ydMR3H+F4IqiiBpS/D4n9A1bhHdDkbxk6D+IEmFtY0cgrL+Nf3W/lw+R4qPQYWC1x8WjvuGdeD9q1a7qSxIuI/FIakQaXkpPC3VX9jZeZKAKKDorl94O1M6jaJAGuAydWdJMPwzh029zFweUMdbRO9IajrOaaW1hQq3B7eXbKLf36/lYJSb2+/s3rE8sB5vegTH2FydSIiDUdhSBpEVnEW/1rzL2Ztn4WBQaA1kOv6XsdN/W8i1O6DY8tkrof/PQi7F3ufR7TzhqB+l4HVx8Y9qocfU7P48zeb2F41gWrf+AgeuaA3I7r50ES4IiInSGFITkmFp4KPUj7ileRXahpHX9D5Au4cdCfxYfEmV1cPRQfgh6dhzbtgeMAW5B0x+ow7INAHQ91J2nmgiKe/2cT3m7MAiA4N5E/je3L5kA6aQV5EWiyFIam3VZmreGb5M2w7uA2AATEDuH/o/STGJppcWT14PLD6bZj/FFQ19qbvJXDuky2+mzxAcXkl//p+G28t3kGF28BmtXD9iATuGNudiCB1kxeRlk1hSE7agZIDvLDqBb7e8TUAkY5I7h58N5O6TfK9qTMAMtbBN3fD3lXe520GwPnPQacR5tbVRH7YvJ/HvtzI3oMlAJzdM5bHJvaha2yYyZWJiDQNhSE5YW6Pm8+2fMaLa16koKIACxYu63EZdwy8g8igSLPLO3llhd7pM5a/6r0lFhgOYx6H028CX2vsXQ/780t58uuNzF6fCUC7yGCevLAvY/u0NrkyEZGmpTAkJ2T7we08seQJ1mavBaBPdB8eHfYo/WP7m1xZPRgGbP4W/nc/5O/1but7MYyfDhFtza2tCbg9Bu8v3cXzc7dQWFZJgNXCTWd25q6x3QkJ1J8EEfE/+ssnx1ThqeDt9W/z+rrXqfBUEGoP5a5Bd3F5j8t9r6s8QGEWfHsPpHhv8RHZCSa8AN3HmltXE9mcmc8D/13H2nRvu6jTOkTyl4v7q6u8iPg1hSE5qo05G3n858fZkrcFgFHtR/HY8MdoE9rG5MrqwTBgw0yYfR+U5Hmn0DjjThh5HwS2/IEDK90eXlu4nX9+v5UKt0F4kI37z+vFVUM7qpeYiPg9hSE5QmllKa+sfYV3N76Lx/DQytGKB4c+yPmdz/e90aMBCvZ7rwZt/sb7vE1/mPSq99EPpGYWcN9/1rJ+r/dq0NjerfnLxf2IiwgyuTIRkeZBYUhq2ZSziQcXPchO104Azu98Pg8OfZCooCiTK6sHw4D1/4HZf4LSg2C1w1n3w5l3Q0DL7y5e6fbw+k87+Of8rZS7PTiD7Uy7sA+TTmvnm6FWRKSRKAwJ4O0p9vaGt3kl+RUqjUpigmN4IukJzu5wttml1U9RDnx9x6GrQW0T4aJXoE0/c+tqItuyCrjns7WsS6++GhTHXy7ur6tBIiJ1UBgS0grSeHjRwyRnJwNwbqdzeXz4477ZXR5g2/fw5R+gcL/3atDZD3hHkfaDq0GGYfDB8j08/c0myio9RATZeOI3fblkkK4GiYgcjcKQHzMMgy+2fcFzK56juLKYMHsYDw97mIldJvrmD2dlGcx/Epa97H0e0xMufRPaDjC3riaSW1TO/f9dx/yU/QCM7B7D3y5LpI1TV4NERI5FYchPucpcPP7z4/yQ9gMAg1sP5i9n/sU35xMDyEqBmb+D/Ru8z4fcBOOe9oueYgCLtx7gns+SySooIzDAyv3n9eTGMzpjVU8xEZHjUhjyQ8lZydz/0/1kFGVgt9q5Y+AdTOkzxTfHDTIMWPkmzH0UKkshJBouehl6nm92ZU2ivNLD/81N5fWfdgDQNTaUf105kL7xTpMrExHxHQpDfsRjeHhn4zv8a82/cBtuOoZ35G9n/Y0+0X3MLq1+Sl3w1VRImeV93nWMt8t8uH9MJ5GWW8xtH62paSR91bCOPDahD8GBPhhqRURMpDDkJ3JLc3lk8SMs3rsYgPMTzufxpMcJC/TRyTgz18Nn10LuDu8Aiuc+BcP+AFYfnCi2HuZv2s89nyWTX1pJZIid5y4dwPi+PjgYpohIM6Aw5AeSs5K598d7ySrJwhHg4KGhD3FJ90t8s5G0YcAv73vHDqoshYj2cPk70OF0sytrEpVuD8/P3cJrC7cDMLBjJC9fNYj4yGCTKxMR8V0KQy2YYRh8mvopz618jkpPJZ2dnXn+rOfp0aqH2aXVT3mxdyTptR97n3cfBxe/DiE+OCBkPWTllzL1419YsTMXgBvOSOCh83sTaPOPq2EiIo1FYaiFKq0s5ellT/PV9q8AGJ8wnqdGPEWI3Ud7V+Xthk+uhv3rwWKFcx6FM+72m9tiK3fl8ocP1nCgsIzQwAD+elkiEwa0NbssEZEWQWGoBdpXuI+7FtxFSm4KVouVuwfdzXV9r/PN22IAO3+Cz66DklwIjYXLZkDnkWZX1WQ+Wr6HJ2ZtoMJt0LN1OK9cM4iusT7a1ktEpBnymf9bnZeXx5QpU3A6nTidTqZMmcLBgweP+ZrPP/+c8ePHExMTg8ViITk5uUlqNdOyjGVc8c0VpOSm0MrRin+f+2+u73e9bwYhw4Blr8F7k7xBqO1pcMuPfhOEyis9PPrleh7+Yj0VboMJ/dvyxW0jFIRERBqYz4Shq666iuTkZObMmcOcOXNITk5mypQpx3xNUVERZ5xxBs8++2wTVWmuTzd/yq3zbuVg2UH6Rvfl04mfMqztMLPLqp+KUvjqNpjzABhuGHAF3DgHnO3NrqxJHCgs45q3lvPBsj1YLPCn8T156aqBhATqYq6ISEPzib+sKSkpzJkzh2XLljFsmPfH/Y033iApKYnU1FR69uxZ5+uqw9KuXbtO+LPKysooKyureZ6fn1//wptIpaeSv638Gx9t/giAiV0mMm3ENBwBDpMrq6fCLPj4Sti7yts+6Nw/Q9Jt4ItXt+ph4z4Xt7y3mr0HSwhz2Pjn5NMY09s/xk4SETGDT4ShpUuX4nQ6a4IQwPDhw3E6nSxZsuSoYag+pk+fzpNPPtlg79fYCsoL+NPCP/Hzvp8BuHPQndzU7ybfvC0G3mk1PvwtuPZAUCRcPgO6nmN2VU3m+5T93P7xLxSXu+kcE8ob1w6mW1y42WWJiLRoPnGbLDMzk7i4uCO2x8XFkZmZ2aCf9dBDD+FyuWqWtLS0Bn3/hpRWkMY1s6/h530/E2wL5u9n/53f9f+d7wah7QvgrXHeIBTVBW7+wa+C0LtLdnHze6soLndzZrcYvvzjGQpCIiJNwNQwNG3aNCwWyzGXVatWAdT5A28YRoP/8DscDiIiImotzdHa7LVc/e3V7HDtIC4kjnfOe4exncaaXVb9rX4XPrwMyvKh4wj43fcQ3dXsqpqE22Pw1NebeGLWRjwGXDGkAzNuOB1niN3s0kRE/IKpt8mmTp3K5MmTj3lMQkIC69atY//+/Ufsy87OpnVr/2tL8WPaj/xp4Z8odZfSJ7oPL57zInEhR1458wkeD/zwFCz+u/d5/9/CRS+BzUfbO52kknI3d37yC3M3ef/7/tP4nvzx7K6+e3VPRMQHmRqGYmJiiImJOe5xSUlJuFwuVqxYwdChQwFYvnw5LpeLESNGNHaZzcp/tvyHp5c9jcfwcGa7M/m/s/7PdwdSrCyHr/4I6//jfX7Wg3D2g37TUPpAYRk3vbOStekuAm1Wnr88kQsT480uS0TE7/hEA+revXtz3nnncfPNN/P6668DcMsttzBx4sRajad79erF9OnTufjiiwHIzc1lz5497Nu3D4DU1FQA2rRpQ5s2vjWppWEYvLL2FV5b+xoAF3e7mMeSHsNu9dFbKWWF3olWt3/vnWj1opch8dhXCVuStNxirnt7BTsOFNEqxM4b1w5hSIJ/TCsiItLc+EQDaoAPP/yQ/v37M27cOMaNG8eAAQN4//33ax2TmpqKy+WqeT5r1iwGDhzIhAkTAJg8eTIDBw7ktddea9LaT1WFp4InljxRE4RuTbyVJ0c86btBqCgH3rvQG4TsIXDVp34VhFIzC7jstSXsOFBEu8hgZv5hhIKQiIiJLIZhGGYX0Zzl5+fjdDpxuVymNKYuc5dx38L7+DHtR6wWK48Of5TLe1ze5HU0mINp8P7FkLMVgqPg6v9A+yFmV9VkVu/O5cZ3VuEqqaBH6zDeu3EYbZxBZpclItLinMzvt0/cJvNXxRXF3LHgDpZnLMcR4OBvo/7G6I6jzS6r/rI2e4NQwT6IaA9TvoDYHmZX1WQWpGbxhw9WU1rhYVDHSN6+/nQiQwLNLktExO8pDDVT+eX5/HH+H1mbvZYQWwgvjXmJ09ucbnZZ9bcvGd6fBCV5ENsLrvkcnO3MrqrJzFq7j3s+TabSY3B2z1heuXqQptYQEWkm9Ne4GcopyeHW+beyOXcz4YHhvDb2NQbEDjC7rPpLWwkfXAplLmg3GK7+L4T4TxuZ/65O50//XYthwEWnxfP85YnYA3ymuZ6ISIunMNTMZBZlcsu8W9jp2klUUBT/Pvff9IxquOlGmtzuJfDh5VBeCB2T4KrPIKh5DmTZGD5esYeHv1iPYcCVQzvyzKR+WK3+MXSAiIivUBhqRjIKM7jhuxvYW7iXNqFteOPcN0hwJphdVv3t+NE74WpFMXQeBVd+AoGhZlfVZN5buovHv9oIwHVJnZh2YV8Npigi0gwpDDUThwehDuEdeHPcm8SH+fAAfFvmwqfXgLsMuo2FKz4Ae7DZVTWZNxft4OlvUwC4eWRnHr6gt4KQiEgzpTDUDGQWZXLjdzfWBKG3x79Nm1DfGhSyli3fwSdXg6cCel4Al7/jN9NrALz643aem7MZgNtGd+W+cT0VhEREmjGFIZNVB6H0wnTah7X3/SC07XvvFSFPBfS5CC59CwJ8dHDIevj3T4eC0N1je3DHmG4KQiIizZzCkIn2F+3npu9uIq0gjXZh7Xw/CO38CT65Ctzl0Gui3wWhd5fs4i+zvUHo3nN7cPuY7iZXJCIiJ0L9e02yv2g/N829iT0Fe2gX1o4Z42fQNqyt2WXV3+6l8NEVUFkK3cfDZTP8Kgh9smIPT8zyNpaeOrqbgpCIiA9RGDLJ/63+P3bn7665IuTTQSh9lbf7fEUxdD0Hfvse2PxnZOXP16Tz0BfrAW9j6XvH+c+o2iIiLYFuk5nk0eGPUump5N4h9/p2r7F9yfD+JVBeAAkj4YoPwe4/c219s24f9/3HO6DitUmd1GtMRMQHKQyZJCIwghfOfsHsMk7NgW3wwSXekaU7DK8aRyjE7KqazPcp+7nrk2Q8BlwxpAPTfqNxhEREfJFuk0n95O/zTrpanANtT/POPu8IM7uqJrNyVy5//HANlR6DSafF85dL+mtkaRERH6UwJCevONd7a8y1B6K7eeca86MpNjZn5nPTOyspq/Qwplccz1+eSICCkIiIz1IYkpNTXuztNZadAuFtvbPPh8WaXVWTSc8r5rq3V5BfWsngTq146apB2DTpqoiIT9NfcTlx7gr4z3WQvgKCnN4g1KqT2VU1mdyicq59awX788vo0TqMt64bQnBggNlliYjIKVIYkhPj8cBXU2HrXLAFw1X/gdZ9zK6qyRSVVXLDjBXsOFBEvDOId28cSmSI/wwfICLSkikMyYlZ8DSs+wQsAd5xhDoOM7uiJlPh9vCHD9ewNt1FZIid924aRlun/0w6KyLS0ikMyfGteR8W/Z93/cIXocc4c+tpQoZh8PhXG/lpSzbB9gBmXH863eL8p9eciIg/UBiSY9u+AL65y7s+6k8w8GpTy2lqbyzawccr9mCxwD8nn8bAjq3MLklERBqYwpAcXVYKfHYteCqh/+Uw+hGzK2pSczZkMP1/3olXH53Qh3F9fXgSXREROSqFIalbwX748LdQlg8dk+Cil8GPRldem3aQuz5NxjBgyvBO3HhGgtkliYhII1EYkiOVF8PHk72DKkZ1hckfgc1hdlVNJj2vmJveXUVphYeze8byxG/6aJoNEZEWTGFIajMM+PIPsG8NBEd5p9kIiTK7qiZTUFrBTe+s4kBhGb3ahGtQRRERP6C/8lLboudh05dgtcPkDyG6q9kVNRmPx+DuT5NJ3V9AXLiDt68/nTCH5jIWEWnpFIbkkNT/wQ/PeNcnPA+dRphbTxP7x/wtzE/JItBm5Y1rhxAfqbGERET8gcKQeGWnwsybAQNO/x0Mvt7siprUnA0Z/OuHbQBMv7g/iR0izS1IRESajMKQQEkefHwllBdApzPgvGfNrqhJpWYWcM9nawG48YzOXDq4vckViYhIU1IY8nceN8z8HeRuB2cH71QbAXazq2oyB4vLufm9VRSXuxnRNZqHL+hldkkiItLEFIb83fdPwrb53slXJ38EoTFmV9RkKt0ebv/4F/bkFtO+VbB6jomI+Cn95fdnm2bBz//0rk96GdoOMLeeJva3uaks2nqAYHsA/54yhKhQzUIvIuKPFIb8Vc52+Oo273rSVOh3qbn1NLF5m/bz+sIdAPz1sgH0iY8wuSIRETGLwpA/qiiBz647NNXG2GlmV9Sk0nKLufezZMDbYPo3ifHmFiQiIqZSGPJH/7sf9q+HkBi47G2/ajBdVunmto/WkF9aycCOkTx4vhpMi4j4O4Uhf5P8Eax5D7DApW9ChH9dFXnm2xTWpbuIDLHz0lWDCLTpfwIiIv5OvwT+ZP9G+OYe7/roh6HraHPraWJfr93He0t3A/D3K06jnUaYFhERFIb8R1mBt51QZQl0HQMj7zO7oia1PbuQB2euA+C20V0Z3TPO5IpERKS5UBjyF9/eBzlbIaIdXPIGWP3nn760ws1tH66hqNzNsM5R3D22h9kliYhIM+I/v4j+bN1nsO4TsFi9DaZDo82uqEk9820KmzMLiAlz8OKVAzWwooiI1KJfhZYud+ehdkJnPQgdh5tbTxObv2k/7y/zthN64beJxEUEmVyRiIg0NwpDLZm7wjvvWHkBdBgOI+81u6ImlZVfyv1V7YRuOrMzo3rEmlyRiIg0RwpDLdnC52DvKnA44dI3IMBmdkVNxuMxuPc/a8ktKqd32wjuP6+n2SWJiEgzpTDUUu1aDD89712f+AJEdjS3nib29s87WbT1AA6blX9NPg2HLcDskkREpJlSGGqJSvLg81sAA067GvpfZnZFTWrjPhd/nZMKwKMT+9C9dbjJFYmISHOmMNTSGAZ8fRfk74WoLnD+c2ZX1KRKyt3c+Uky5W4PY3u35pph/nVFTERETp7CUEuzYSZs+hKsNu90Gw7/uiry7P9S2JZVSGy4g+cu7Y/FYjG7JBERaeYUhlqS/Az4tqrH2Kg/QbvB5tbTxH7edoB3q6bb+L/LE4kOc5hckYiI+AKFoZbCMGDW7VB6ENqe5nfd6AtKK7j/v95u9FcP66hu9CIicsIUhlqKNe/BtnkQ4ICLX4MAu9kVNamnv0lh78ESOkQF8/AFvc0uR0REfIjCUEuQtxu+e9i7fs6jEOdfYWDB5iw+XZWGxQLPX5ZIqMN/xlMSEZFTpzDk6zwe+Oo2KC/0jjKddJvZFTUpV3EFD37uvT12w4jODOviX/OuiYjIqVMY8nWr3oJdi8AeApNeAat/DS447euN7M8vo0tMqEaZFhGRelEY8mUH98D8ad71sU9CdFdTy2lq36fs54tf9mK1wPO/TSTI7l9BUEREGobCkK8yDPjm7kO3x07/ndkVNamC0goe/XIDAL8b2YVBHVuZXJGIiPgqhSFfte4z2DYfAgLhwhfB6l//lH+dk0qGq5RO0SHcPbaH2eWIiIgP869f0JaiMBvmPOBdP+sBiPWvMLByVy7vL/MOrjj94v4EB+r2mIiI1F+9+yCnpaWxa9cuiouLiY2NpW/fvjgcGvG3Scx5wDsZa+v+cMadZlfTpEor3Dww09t77IohHRjRLcbkikRExNedVBjavXs3r732Gh9//DFpaWkYhlGzLzAwkJEjR3LLLbdw6aWXYvWz2zZNJvV/3vnHLFa46EW/G1zx5QXb2JFdRGy4Q4MriohIgzjhxHLnnXfSv39/tm7dylNPPcXGjRtxuVyUl5eTmZnJ7NmzOfPMM3nssccYMGAAK1eubMy6/VNZwaG5x0bcDvEDza2niaVk5PPqj9sBeOrCvjhD/CsIiohI4zjhK0OBgYFs376d2Ngj53yKi4vjnHPO4ZxzzuGJJ55g9uzZ7N69m9NPP71Bi/V7Pz4L+XuhVQKc/ZDZ1TQpj8fg4S/WU+kxGN+3Nef3b2t2SSIi0kKccBj629/+dsJvesEFF9SrGDmGzPWw7FXv+gX/B/Zgc+tpYp+sTOOXPQcJc9h48sJ+ZpcjIiItiBr2+AKPxzumkOGGPpOg+1izK2pSOYVlPDdnMwD3nNuDNs4gkysSEZGWpF69yXJycnj88cdZsGABWVlZeDyeWvtzc3MbpDipsuZdSF8JgWFw3nSzq2ly0/+3GVdJBX3aRnBtUiezyxERkRamXmHommuuYfv27dx00020bt0ai8XS0HUdIS8vjzvuuINZs2YBcOGFF/Liiy8SGRlZ5/EVFRU8+uijzJ49mx07duB0Ohk7dizPPvss8fHxjV5vgynMhvlPeNdHPwIRPlR7A1ixM5f/rk7HYoGnL+6HLUAXM0VEpGHVKwwtXryYxYsXk5iY2ND1HNVVV11Feno6c+bMAeCWW25hypQpfP3113UeX1xczJo1a3jsscdITEwkLy+Pu+66iwsvvJBVq1Y1Wd2nbN5jUOqCNv1h6C1mV9OkKtweHv1yPQCTT++oKTdERKRR1CsM9erVi5KSkoau5ahSUlKYM2cOy5YtY9iwYQC88cYbJCUlkZqaSs+eR85W7nQ6mTdvXq1tL774IkOHDmXPnj107Nixzs8qKyujrKys5nl+fn4DfpOTtGsxrP0YsMDEf0BAvcfI9ElvL97Jlv2FRIUG8oBmpBcRkUZSr3sOr7zyCo888ggLFy4kJyeH/Pz8WktDW7p0KU6nsyYIAQwfPhyn08mSJUtO+H1cLhcWi+Wot9YApk+fjtPprFk6dOhwKqXXn7sSZt/vXR98PbQfYk4dJtl3sIR/zN8KwEPn9yIyJNDkikREpKWq16WGyMhIXC4X55xzTq3thmFgsVhwu90NUly1zMxM4uLijtgeFxdHZmbmCb1HaWkpDz74IFdddRURERFHPe6hhx7innvuqXmen59vTiBaPQOyNkJQJIx5vOk/32TT/7eZkgo3pye04rLB7c0uR0REWrB6haGrr76awMBAPvroo1NqQD1t2jSefPLJYx5TPZJ1XZ9RHb6Op6KigsmTJ+PxeHjllVeOeazD4TB/jrXiXPjhae/6OY9CSJS59TSxFTtz+XrtPiwWeOI3fZukgb6IiPiveoWhDRs28Msvv9TZVudkTJ06lcmTJx/zmISEBNatW8f+/fuP2JednU3r1q2P+fqKigp++9vfsnPnTn744YdjXhVqNn54GkoPQlxfGHyD2dU0KbfHYNqsjYC30XS/dk6TKxIRkZauXmFoyJAhpKWlnXIYiomJISbm+LOOJyUl4XK5WLFiBUOHDgVg+fLluFwuRowYcdTXVQehrVu3smDBAqKjo0+p3iaRud57iwzg/Of8rtH0pyvT2JSRT3iQjfvG9TC7HBER8QP1+qW9/fbbufPOO/nTn/5E//79sdtrT5g5YMCABimuWu/evTnvvPO4+eabef311wFv1/qJEyfWCmS9evVi+vTpXHzxxVRWVnLZZZexZs0avvnmG9xud037oqioKAIDm2GDXMOA/z0Ahgf6XgydR5pdUZNyFVfw/NxUAO4e24PoMJNvV4qIiF+oVxi64oorALjxxhtrtlkslkZrQA3w4YcfcscddzBu3DjAO+jiSy+9VOuY1NRUXC4XAOnp6TUDNJ522mm1jluwYAFnn312g9d4yjZ+Drt/BlswnPtns6tpcv/4fgu5ReV0jwtjikaaFhGRJlKvMLRz586GruO4oqKi+OCDD455jGEYNesJCQm1njd7FSUwt6rX2Jl3Q6RJXfpNsnV/Ae8t3Q3A47/pg10jTYuISBOpVxjq1En/r73BLXsF8tMhoj2ccYfZ1TS5P3+bgttjcG6f1ozsHmt2OSIi4kdO+P9+L1269ITftKioiI0bN9arIL9UmA2L/u5dH/sE2IPNraeJ/bQlm5+2ZGMPsPDIBb3NLkdERPzMCYeha6+9lnPPPZfPPvuMwsLCOo/ZtGkTDz/8MN26dWPNmjUNVmSL9+N0KC+A+IHQ7zKzq2lSbo/BX2anADBleAIJMaEmVyQiIv7mhG+Tbdq0iddff53HH3+cq6++mh49ehAfH09QUBB5eXls3ryZoqIiLrnkEubNm0e/fv0as+6WIzsVVr/jXR/3NFj9q63MzDXpbM4sICLIxu3ndDO7HBER8UMWox6tjNesWcOiRYvYtWsXJSUlxMTEMHDgQEaPHk1UVMsaLTk/Px+n04nL5WqcARs/ugK2zIGeE+DKjxr+/ZuxknI3Zz+/gP35ZTx8QS9uGdXV7JJERKSFOJnf73o1oB40aBCDBg2qV3FymB0LvUHIaoNznzK7mib35qId7M8vo32rYK5NSjC7HBER8VP+dU+mOfF4YO6j3vUhN0KMf90iyi4o47WF2wG4/7xeBNkDTK5IRET8lcKQWdZ9CpnrwBEBZz1gdjVN7h/zt1BU7iaxvZPfDGhrdjkiIuLHFIbMUpABVjuMvBdCjz8/W0uyLauQT1amAfDwBb01K72IiJjKv2YBbU5G3gN9J0F4vNmVNLkX5qXi9hiM7d2aYV18YPJcERFp0U76ylBFRQWjR49my5YtjVGPf4nqAvYgs6toUuvTXcxen4nFAn8a3/P4LxAREWlkJx2G7HY7GzZs0K0NqZe/frcZgEmntaNnm3CTqxEREalnm6Frr72Wt956q6FrkRZu6fYcFm09gM1q4e6xPcwuR0REBKhnm6Hy8nLefPNN5s2bx5AhQwgNrT2FwgsvvNAgxUnLYRgGf6u6KnTl0I50jA4xuSIRERGveoWhDRs21Ay6+Ou2Q7p9JnX5PiWLNXsOEmS3atoNERFpVuoVhhYsWNDQdUgL5vEYPD83FYDrR3QmLsK/Go2LiEjzdsrjDKWnp7N3796GqEVaqK/X7WNzZgHhQTb+cJbmHxMRkealXmHI4/Hw1FNP4XQ66dSpEx07diQyMpI///nPeDyehq5RfFil28M/5m8F4NazuuIMsZtckYiISG31uk32yCOP8NZbb/Hss89yxhlnYBgGP//8M9OmTaO0tJRnnnmmoesUHzVr7T52HigiKjSQ60ckmF2OiIjIEeoVht59913efPNNLrzwwpptiYmJtGvXjj/+8Y8KQwJ4rwq9+MM2AG4Z1YVQhwY8FxGR5qdet8lyc3Pp1avXEdt79epFbm7uKRclLcNXyYeuCk0Z3snsckREROpUrzCUmJjISy+9dMT2l156icTExFMuSnyf96qQt62QrgqJiEhzVq9fqL/+9a9MmDCB+fPnk5SUhMViYcmSJaSlpTF79uyGrlF80FfJ+9iVU6yrQiIi0uzV68rQWWedxZYtW7j44os5ePAgubm5XHLJJaSmpjJy5MiGrlF8jK4KiYiILznpX6mKigrGjRvH66+/robSUiddFRIREV+iWeulQemqkIiI+BrNWi8N6ut1uiokIiK+RbPWS4PxeAxeWbAdgJvO7KyrQiIi4hM0a700mHkp+9maVUi4w8aUJF0VEhER33DSYcjtdjNt2jT69+9PVFRUY9QkPsgwDF750XtV6NoRnYgI0hxkIiLiG066zVBAQADjx4/H5XI1Rj3io5Zsz2Ft2kEcNis3nNHZ7HJEREROWL0aUPfv358dO3Y0dC3iw15e4J2D7MqhHYkJc5hcjYiIyImrVxh65plnuO+++/jmm2/IyMggPz+/1iL+Zc2ePJZsz8FmtXDzqC5mlyMiInJS6tWA+rzzzgPgwgsvrNVg2jAMLBYLbre7YaoTn1Ddg+zige1oFxlscjUiIiInp15haMGCBQ1dh/io1MwC5qfsx2KBW8/uanY5IiIiJ61eYeiss85q6DrER736o7et0Pn92tA1NszkakRERE5evdoMASxatIhrrrmGESNGsHfvXgDef/99Fi9e3GDFSfO292AJX6/LAOAPZ3UzuRoREZH6qVcYmjlzJuPHjyc4OJg1a9ZQVlYGQEFBAX/5y18atEBpvmYs3onbYzCiazT92zvNLkdERKRe6hWGnn76aV577TXeeOMN7PZDg+uNGDGCNWvWNFhx0nzll1bwyco0APUgExERn1avMJSamsqoUaOO2B4REcHBgwdPtSbxAZ+s2ENhWSXd48I4u0es2eWIiIjUW73CUNu2bdm2bdsR2xcvXkyXLrpK0NKVV3p4e/EuwHtVSPPRiYiIL6tXGPr973/PnXfeyfLly7FYLOzbt48PP/yQ++67jz/+8Y8NXaM0M9+u30dmfimx4Q4uOi3e7HJEREROSb261t9///24XC5Gjx5NaWkpo0aNwuFwcN999zF16tSGrlGaEcMw+PdPOwG4fkQCDluAyRWJiIicGothGEZ9X1xcXMymTZvweDz06dOHsLCWN85Mfn4+TqcTl8tFRESE2eWYbvHWA1zz1nKC7QEsfegcIkMCzS5JRETkCCfz+12vK0PVQkJCGDJkyKm8hfiYfy/yTtB7xekdFIRERKRFqPegi+J/UjML+GlLNlYL3HhGZ7PLERERaRAKQ3LC3lnibSt0Xr82dIwOMbkaERGRhqEwJCckr6icz9d4p125QVeFRESkBVEYkhPyyco0yio99I2PYEinVmaXIyIi0mAUhuS4Kt0e3l+6C/B2p9cgiyIi0pIoDMlxzdu0n32uUqJDA/lNogZZFBGRlkVhSI5rxpJdAFw1rCNBdg2yKCIiLYvCkBzTxn0uVuzMxWa1cPWwTmaXIyIi0uAUhuSY3vl5FwDn929LG2eQucWIiIg0AoUhOaqcwjK+WrsPgBvOSDC3GBERkUaiMCRH9cnKNMorPSS2dzKwQ6TZ5YiIiDQKhSGpU6XbwwfLdgNwnbrTi4hIC6YwJHX6YXMWGa5SokIDmTCgrdnliIiINBqFIanTB8v3AHD5kPY4bOpOLyIiLZfCkBxhd04RP23JxmKBq4eqO72IiLRsCkNyhI+qrgqN6h6r2elFRKTFUxiSWkor3Hy2Kg2Aa4brqpCIiLR8CkNSy5wNmeQVV9DWGcTonrFmlyMiItLofCYM5eXlMWXKFJxOJ06nkylTpnDw4MFjvmbatGn06tWL0NBQWrVqxdixY1m+fHnTFOyjqrvTXzm0I7YAn/nPQ0REpN585tfuqquuIjk5mTlz5jBnzhySk5OZMmXKMV/To0cPXnrpJdavX8/ixYtJSEhg3LhxZGdnN1HVvmVzZj6rdudhs1qYfHoHs8sRERFpEhbDMAyzizielJQU+vTpw7Jlyxg2bBgAy5YtIykpic2bN9OzZ88Tep/8/HycTifz589nzJgxJ/Ual8tFREREvb+DL3j0y/V8sGwPF/RvwytXDza7HBERkXo7md9vn7gytHTpUpxOZ00QAhg+fDhOp5MlS5ac0HuUl5fz73//G6fTSWJi4lGPKysrIz8/v9biDwrLKvlizV4AzU4vIiJ+xSfCUGZmJnFxcUdsj4uLIzMz85iv/eabbwgLCyMoKIi///3vzJs3j5iYmKMeP3369Jp2SU6nkw4d/ON20azkfRSVu+kSE8qIrtFmlyMiItJkTA1D06ZNw2KxHHNZtWoVQJ1zYxmGcdw5s0aPHk1ycjJLlizhvPPO47e//S1ZWVlHPf6hhx7C5XLVLGlpaaf2JX3Ep1Xd6ScP7aB5yERExK/YzPzwqVOnMnny5GMek5CQwLp169i/f/8R+7Kzs2nduvUxXx8aGkq3bt3o1q0bw4cPp3v37rz11ls89NBDdR7vcDhwOBwn/iVagJSMfNamHcRmtXDJoPZmlyMiItKkTA1DMTExx7xlVS0pKQmXy8WKFSsYOnQoAMuXL8flcjFixIiT+kzDMCgrK6tXvS3Vpyu9V4XG9m5NTJh/BUERERGfaDPUu3dvzjvvPG6++WaWLVvGsmXLuPnmm5k4cWKtnmS9evXiiy++AKCoqIiHH36YZcuWsXv3btasWcPvfvc70tPTufzyy836Ks1OaYWbL5O9DaevGOof7aNEREQO5xNhCODDDz+kf//+jBs3jnHjxjFgwADef//9WsekpqbicrkACAgIYPPmzVx66aX06NGDiRMnkp2dzaJFi+jbt68ZX6FZmrtpPwerRpwe1V0jTouIiP8x9TbZyYiKiuKDDz445jGHD5kUFBTE559/3thl+bxPV3onZb18cHsCrGo4LSIi/sdnrgxJw0vLLebnbTlYLHD5EN0iExER/6Qw5MeqZ6c/s1sMHaJCTK5GRETEHApDfsrtMfjPqnQAfqurQiIi4scUhvzUT1uyycwvJTLEzri+xx6rSUREpCVTGPJTn1Q1nL5kYHsctgCTqxERETGPwpAfyi0q54fN3ilJfnu6RpwWERH/pjDkh2Yl76XCbdCvXQS92kSYXY6IiIipFIb80Mw13hGnL9U8ZCIiIgpD/mbL/gLW73Vhs1q4MDHe7HJERERMpzDkZ2au8XanH90rjmhNyioiIqIw5E/cHoMvf6m+RdbO5GpERESaB4UhP7J42wH255cRGWJndK84s8sRERFpFhSG/MjnVbfILkyM19hCIiIiVRSG/ERBaQXfbcwE1ItMRETkcApDfmL2+gxKKzx0iwtjQHun2eWIiIg0GwpDfmLm6kNjC1ksFpOrERERaT4UhvzAnpxiVuzKxWKBiweqF5mIiMjhFIb8wFfJ3qtCZ3aLoY0zyORqREREmheFoRbOMAy+rApDk07TVSEREZFfUxhq4Tbuy2d7dhEOm5VxfVubXY6IiEizozDUws1auw+Asb1bEx5kN7kaERGR5kdhqAXzeAxmJXvD0IWnaVJWERGRuigMtWArduWSmV9KeJCNs3vGml2OiIhIs6Qw1IJ9VXVV6IJ+bTX9hoiIyFEoDLVQ5ZUeZq/PAOCigbpFJiIicjQKQy3Uwi3ZuEoqaB3hYFjnaLPLERERabYUhlqo6oEWfzMgngCrpt8QERE5GoWhFqiwrJL5KfsBuEgDLYqIiByTwlALNG9TJqUVHrrEhNKvXYTZ5YiIiDRrCkMt0FeHjS2kGepFRESOTWGohckrKmfR1gMAXJioXmQiIiLHozDUwszdlInbY9CnbQRdYsPMLkdERKTZUxhqYb5Z5x1baMKAtiZXIiIi4hsUhlqQ3KJylmzPAWBCf4UhERGRE6Ew1ILM3ei9RdY3PoKEmFCzyxEREfEJCkMtyLfrdYtMRETkZCkMtRA5hWW6RSYiIlIPCkMtxHcb9+P2GPRrF0GnaN0iExEROVEKQy1E9Qz1E/prbCEREZGToTDUAnhvkXkHWtQtMhERkZOjMNQCzNmYiceA/u2cdIwOMbscERERn6Iw1AJ8q4EWRURE6k1hyMcdKCxj2Q71IhMREakvhSEf913VLbIB7Z10iNItMhERkZOlMOTj5mzIBOD8froqJCIiUh8KQz7MVVLB0qqBFsf3bW1yNSIiIr5JYciH/bB5P5Uegx6tw+gSG2Z2OSIiIj5JYciHVd8iO69vG5MrERER8V0KQz6qpNzNwi3ZAIxTGBIREak3hSEftXBLNqUVHtq3CqZvfITZ5YiIiPgshSEfNXej9xbZ+L5tsFgsJlcjIiLiuxSGfFCF28P8lP0AnNdPt8hEREROhcKQD1q2I4f80kpiwgIZ1LGV2eWIiIj4NIUhH1Tdi+zcPm0IsOoWmYiIyKlQGPIxHo/B3E26RSYiItJQFIZ8zC9peWQXlBEeZCOpS7TZ5YiIiPg8hSEfU32LbEyvOAJt+ucTERE5Vfo19SGGYfDdRu8tsvEaaFFERKRBKAz5kK1ZhezJLSbQZmVUj1izyxEREWkRFIZ8SPXYQmd0jSbUYTO5GhERkZZBYciHzK/qRTamd2uTKxEREWk5FIZ8xIHCMn5JOwjAmN5x5hYjIiLSgigM+YgfNmdhGNCvXQRtncFmlyMiItJiKAz5iOpbZGN1i0xERKRB+UwYysvLY8qUKTidTpxOJ1OmTOHgwYMn/Prf//73WCwW/vGPfzRajY2ltMLNoq0HAIUhERGRhuYzYeiqq64iOTmZOXPmMGfOHJKTk5kyZcoJvfbLL79k+fLlxMfHN3KVjWPp9hxKKty0iQiib3yE2eWIiIi0KD7RPzslJYU5c+awbNkyhg0bBsAbb7xBUlISqamp9OzZ86iv3bt3L1OnTuW7775jwoQJTVVyg6ruUj+mdxwWiyZmFRERaUg+cWVo6dKlOJ3OmiAEMHz4cJxOJ0uWLDnq6zweD1OmTOFPf/oTffv2PaHPKisrIz8/v9ZiJsMw+D4lC4CxfXSLTEREpKH5RBjKzMwkLu7I7uRxcXFkZmYe9XXPPfccNpuNO+6444Q/a/r06TXtkpxOJx06dKhXzQ1l4758MvNLCQkM0MSsIiIijcDUMDRt2jQsFssxl1WrVgHUeXvIMIyj3jZavXo1//znP3nnnXdO6tbSQw89hMvlqlnS0tLq9+UayLyqXmQju8cQZA8wtRYREZGWyNQ2Q1OnTmXy5MnHPCYhIYF169axf//+I/ZlZ2fTunXdt44WLVpEVlYWHTt2rNnmdru59957+cc//sGuXbvqfJ3D4cDhcJz4l2hkh9oL6RaZiIhIYzA1DMXExBATE3Pc45KSknC5XKxYsYKhQ4cCsHz5clwuFyNGjKjzNVOmTGHs2LG1to0fP54pU6Zwww03nHrxTSDDVcLGfflYLHBOL406LSIi0hh8ojdZ7969Oe+887j55pt5/fXXAbjllluYOHFirZ5kvXr1Yvr06Vx88cVER0cTHV27jY3dbqdNmzbH7H3WnFQ3nB7YIZKYsOZztUpERKQl8YkG1AAffvgh/fv3Z9y4cYwbN44BAwbw/vvv1zomNTUVl8tlUoUN78dUbxjSLTIREZHG4xNXhgCioqL44IMPjnmMYRjH3H+0dkLNUWmFm5+35QBwds9Yk6sRERFpuXzmypC/Wbkrl5IKN3HhDvq01ajTIiIijUVhqJlasDkbgNE9Neq0iIhIY1IYaqaq2wvpFpmIiEjjUhhqhnbnFLHjQBE2q4Uzuh9/6AERERGpP4WhZujHVO8tsiEJrYgIsptcjYiISMumMNQMLai6RTa6pwZaFBERaWwKQ81MaYWbpduru9QrDImIiDQ2haFmZumOHMoqPcQ7g+jROszsckRERFo8haFm5sfNVb3IeqlLvYiISFNQGGpGDMNgQeqh8YVERESk8SkMNSM7DxSxJ7eYwAArI7pGH/8FIiIicsoUhpqR6qtCQztHEerwmWnjREREfJrCUDOiUadFRESansJQM1FS7mb5jlxAXepFRESaksJQM7F8Zw7lbg/tIoPpGhtqdjkiIiJ+Q2GomfhpywEARvWIUZd6ERGRJqQw1Ews2uptPD2yu9oLiYiINCWFoWYgw1XC1qxCrBbUpV5ERKSJKQw1A4u2em+RDWgfSWRIoMnViIiI+BeFoWagOgyN6qFbZCIiIk1NYchkHo/B4qr2QqO6x5hcjYiIiP9RGDLZxn355BVXEO6wkdgh0uxyRERE/I7CkMl+qroqlNQ1GnuA/jlERESamn59TfbTlqou9WovJCIiYgqFIRMVllWyZk8eoPZCIiIiZlEYMtHyHTlUuA06RoXQKVpTcIiIiJhBYchEh7rU66qQiIiIWRSGTPSTpuAQERExncKQSdLzitmRXUSA1UKSpuAQERExjcKQSapvkQ3sEElEkN3kakRERPyXwpBJcovKCbYH6BaZiIiIySyGYRhmF9Gc5efn43Q6cblcRERENOh7l1W6Ka/0EK4rQyIiIg3qZH6/bU1Uk9TBYQvAYQswuwwRERG/pttkIiIi4tcUhkRERMSvKQyJiIiIX1MYEhEREb+mMCQiIiJ+TWFIRERE/JrCkIiIiPg1hSERERHxawpDIiIi4tcUhkRERMSvKQyJiIiIX1MYEhEREb+mMCQiIiJ+TbPWH4dhGADk5+ebXImIiIicqOrf7erf8WNRGDqOgoICADp06GByJSIiInKyCgoKcDqdxzzGYpxIZPJjHo+Hffv2ER4ejsViadD3zs/Pp0OHDqSlpREREdGg7y2H6Dw3DZ3npqNz3TR0nptGY51nwzAoKCggPj4eq/XYrYJ0Zeg4rFYr7du3b9TPiIiI0P/QmoDOc9PQeW46OtdNQ+e5aTTGeT7eFaFqakAtIiIifk1hSERERPyawpCJHA4HTzzxBA6Hw+xSWjSd56ah89x0dK6bhs5z02gO51kNqEVERMSv6cqQiIiI+DWFIREREfFrCkMiIiLi1xSGRERExK8pDJnklVdeoXPnzgQFBTF48GAWLVpkdkk+5aeffuI3v/kN8fHxWCwWvvzyy1r7DcNg2rRpxMfHExwczNlnn83GjRtrHVNWVsbtt99OTEwMoaGhXHjhhaSnpzfht2j+pk+fzumnn054eDhxcXFMmjSJ1NTUWsfoXJ+6V199lQEDBtQMOpeUlMT//ve/mv06x41j+vTpWCwW7rrrrpptOtcNY9q0aVgsllpLmzZtavY3u/NsSJP75JNPDLvdbrzxxhvGpk2bjDvvvNMIDQ01du/ebXZpPmP27NnGI488YsycOdMAjC+++KLW/meffdYIDw83Zs6caaxfv9644oorjLZt2xr5+fk1x9x6661Gu3btjHnz5hlr1qwxRo8ebSQmJhqVlZVN/G2ar/HjxxszZswwNmzYYCQnJxsTJkwwOnbsaBQWFtYco3N96mbNmmV8++23RmpqqpGammo8/PDDht1uNzZs2GAYhs5xY1ixYoWRkJBgDBgwwLjzzjtrtutcN4wnnnjC6Nu3r5GRkVGzZGVl1exvbudZYcgEQ4cONW699dZa23r16mU8+OCDJlXk234dhjwej9GmTRvj2WefrdlWWlpqOJ1O47XXXjMMwzAOHjxo2O1245NPPqk5Zu/evYbVajXmzJnTZLX7mqysLAMwFi5caBiGznVjatWqlfHmm2/qHDeCgoICo3v37sa8efOMs846qyYM6Vw3nCeeeMJITEysc19zPM+6TdbEysvLWb16NePGjau1fdy4cSxZssSkqlqWnTt3kpmZWescOxwOzjrrrJpzvHr1aioqKmodEx8fT79+/fTvcAwulwuAqKgoQOe6Mbjdbj755BOKiopISkrSOW4Et912GxMmTGDs2LG1tutcN6ytW7cSHx9P586dmTx5Mjt27ACa53nWRK1N7MCBA7jdblq3bl1re+vWrcnMzDSpqpal+jzWdY53795dc0xgYCCtWrU64hj9O9TNMAzuuecezjzzTPr16wfoXDek9evXk5SURGlpKWFhYXzxxRf06dOn5g+/znHD+OSTT1izZg0rV648Yp/+e244w4YN47333qNHjx7s37+fp59+mhEjRrBx48ZmeZ4VhkxisVhqPTcM44htcmrqc47173B0U6dOZd26dSxevPiIfTrXp65nz54kJydz8OBBZs6cyXXXXcfChQtr9uscn7q0tDTuvPNO5s6dS1BQ0FGP07k+deeff37Nev/+/UlKSqJr1668++67DB8+HGhe51m3yZpYTEwMAQEBRyTbrKysI1Ky1E91j4VjneM2bdpQXl5OXl7eUY+RQ26//XZmzZrFggULaN++fc12neuGExgYSLdu3RgyZAjTp08nMTGRf/7znzrHDWj16tVkZWUxePBgbDYbNpuNhQsX8q9//QubzVZzrnSuG15oaCj9+/dn69atzfK/aYWhJhYYGMjgwYOZN29ere3z5s1jxIgRJlXVsnTu3Jk2bdrUOsfl5eUsXLiw5hwPHjwYu91e65iMjAw2bNigf4fDGIbB1KlT+fzzz/nhhx/o3Llzrf06143HMAzKysp0jhvQmDFjWL9+PcnJyTXLkCFDuPrqq0lOTqZLly46142krKyMlJQU2rZt2zz/m27wJtlyXNVd69966y1j06ZNxl133WWEhoYau3btMrs0n1FQUGD88ssvxi+//GIAxgsvvGD88ssvNcMTPPvss4bT6TQ+//xzY/369caVV15ZZ7fN9u3bG/PnzzfWrFljnHPOOeoe+yt/+MMfDKfTafz444+1usgWFxfXHKNzfeoeeugh46effjJ27txprFu3znj44YcNq9VqzJ071zAMnePGdHhvMsPQuW4o9957r/Hjjz8aO3bsMJYtW2ZMnDjRCA8Pr/mda27nWWHIJC+//LLRqVMnIzAw0Bg0aFBNV2U5MQsWLDCAI5brrrvOMAxv180nnnjCaNOmjeFwOIxRo0YZ69evr/UeJSUlxtSpU42oqCgjODjYmDhxorFnzx4Tvk3zVdc5BowZM2bUHKNzfepuvPHGmr8HsbGxxpgxY2qCkGHoHDemX4chneuGUT1ukN1uN+Lj441LLrnE2LhxY83+5naeLYZhGA1/vUlERETEN6jNkIiIiPg1hSERERHxawpDIiIi4tcUhkRERMSvKQyJiIiIX1MYEhEREb+mMCQiIiJ+TWFIRERE/JrCkIj4nHfeeYfIyEjTPv/6669n0qRJp/w+qamptGnThoKCAqDxv9dll13GCy+80GjvL+KrFIZEpEkkJCTwj3/8w+wympVHHnmE2267jfDwcACuuOIKtmzZUrN/2rRpnHbaaQ32eY8//jjPPPMM+fn5DfaeIi2BwpCINBtutxuPx2N2GU0iPT2dWbNmccMNN9RsCw4OJi4ursE/q6KiAoABAwaQkJDAhx9+2OCfIeLLFIZEBI/Hw3PPPUe3bt1wOBx07NiRZ555pmb/+vXrOeeccwgODiY6OppbbrmFwsLCmv3Vt42ef/552rZtS3R0NLfddlvNj/DZZ5/N7t27ufvuu7FYLFgsFuDQbaFvvvmGPn364HA42L17N3l5eVx77bW0atWKkJAQzj//fLZu3XpS3yk9PZ3JkycTFRVFaGgoQ4YMYfny5ezatQur1cqqVatqHf/iiy/SqVMnqqdr3LhxIxMmTCAiIoLw8HBGjhzJ9u3b6/wswzD461//SpcuXQgODiYxMZH//ve/x6zvs88+IzExkfbt29dsO/w22TvvvMOTTz7J2rVra87ZO++8A4DL5eKWW24hLi6OiIgIzjnnHNauXVvzPtVXlN5++226dOmCw+Go+V4XXnghH3/88UmdS5GWTmFIRHjooYd47rnneOyxx9i0aRMfffQRrVu3BqC4uJjzzjuPVq1asXLlSv7zn/8wf/58pk6dWus9FixYwPbt21mwYAHvvvsu77zzTs2P9+eff0779u156qmnyMjIICMjo+Z1xcXFTJ8+nTfffJONGzcSFxfH9ddfz6pVq5g1axZLly7FMAwuuOCCmnB1PIWFhZx11lns27ePWbNmsXbtWu6//348Hg8JCQmMHTuWGTNm1HrNjBkzuP7667FYLOzdu5dRo0YRFBTEDz/8wOrVq7nxxhuprKys8/MeffRRZsyYwauvvsrGjRu5++67ueaaa1i4cOFRa/zpp58YMmTIUfdfccUV3HvvvfTt27fmnF1xxRUYhsGECRPIzMxk9uzZrF69mkGDBjFmzBhyc3NrXr9t2zY+++wzZs6cSXJycs32oUOHsmLFCsrKyk7oXIr4hVOf+F5EfFl+fr7hcDiMN954o879//73v41WrVoZhYWFNdu+/fZbw2q1GpmZmYZhGMZ1111ndOrUyaisrKw55vLLLzeuuOKKmuedOnUy/v73v9d67xkzZhiAkZycXLNty5YtBmD8/PPPNdsOHDhgBAcHG5999lnN65xO51G/0+uvv26Eh4cbOTk5de7/9NNPjVatWhmlpaWGYRhGcnKyYbFYjJ07dxqGYRgPPfSQ0blzZ6O8vLzO11933XXGRRddZBiGYRQWFhpBQUHGkiVLah1z0003GVdeeeVRa0xMTDSeeuqpWtt+/b2eeOIJIzExsdYx33//vREREVFTe7WuXbsar7/+es3r7Ha7kZWVdcTnrl271gCMXbt2HbU2EX+jK0Mifi4lJYWysjLGjBlz1P2JiYmEhobWbDvjjDPweDykpqbWbOvbty8BAQE1z9u2bUtWVtZxPz8wMJABAwbU+jybzcawYcNqtkVHR9OzZ09SUlJO6DslJyczcOBAoqKi6tw/adIkbDYbX3zxBQBvv/02o0ePJiEhoeb1I0eOxG63H/ezNm3aRGlpKeeeey5hYWE1y3vvvXfU22oAJSUlBAUFndD3Odzq1aspLCwkOjq61uft3Lmz1ud16tSJ2NjYI14fHBwMeK/IiYiXzewCRMRc1T+OR2MYRk0bn187fPuvg4PFYjmhxtDBwcG13seoattyMnXU9Z7HEhgYyJQpU5gxYwaXXHIJH330Ua2ebsd7/eGqv+O3335Lu3btau1zOBxHfV1MTAx5eXkn/DmHf17btm358ccfj9h3eLf8w8Pr4apvpdUVlET8la4Mifi57t27ExwczPfff1/n/j59+pCcnExRUVHNtp9//hmr1UqPHj1O+HMCAwNxu93HPa5Pnz5UVlayfPnymm05OTls2bKF3r17n9BnDRgwgOTk5FptaH7td7/7HfPnz+eVV16hoqKCSy65pNbrFy1adEJtlKobfu/Zs4du3brVWjp06HDU1w0cOJBNmzYd873rOmeDBg0iMzMTm812xOfFxMQct94NGzbQvn37EzpWxF8oDIn4uaCgIB544AHuv//+mls7y5Yt46233gLg6quvJigoiOuuu44NGzawYMECbr/9dqZMmVLTyPpEJCQk8NNPP7F3714OHDhw1OO6d+/ORRddxM0338zixYtZu3Yt11xzDe3ateOiiy46oc+68soradOmDZMmTeLnn39mx44dzJw5k6VLl9Yc07t3b4YPH84DDzzAlVdeWetq0NSpU8nPz2fy5MmsWrWKrVu38v7779e6LVgtPDyc++67j7vvvpt3332X7du388svv/Dyyy/z7rvvHrXG8ePHs3Tp0mMGxISEBHbu3ElycjIHDhygrKyMsWPHkpSUxKRJk/juu+/YtWsXS5Ys4dFHHz2ih1xdFi1axLhx4457nIg/URgSER577DHuvfdeHn/8cXr37s0VV1xR094nJCSE7777jtzcXE4//XQuu+wyxowZw0svvXRSn/HUU0+xa9cuunbtetxbNDNmzGDw4MFMnDiRpKQkDMNg9uzZJ9SGB7xXVObOnUtcXBwXXHAB/fv359lnn63Vpgngpptuory8nBtvvLHW9ujoaH744YeaXmmDBw/mjTfeOOrn//nPf+bxxx9n+vTp9O7dm/Hjx/P111/TuXPno9Z4wQUXYLfbmT9//lGPufTSSznvvPMYPXo0sbGxfPzxx1gsFmbPns2oUaO48cYb6dGjB5MnT2bXrl3HDaelpaV88cUX3Hzzzcc8TsTfWIyj3aAXEWnhnnnmGT755BPWr19vyue/8sorfPXVV3z33XdN8nkvv/wyX331FXPnzm2SzxPxFWpALSJ+p7CwkJSUFF588UX+/Oc/m1bHLbfcQl5eHgUFBTVTcjQmu93Oiy++2OifI+JrdGVIRPzO9ddfz8cff8ykSZP46KOPjrh9JiL+RWFIRERE/JoaUIuIiIhfUxgSERERv6YwJCIiIn5NYUhERET8msKQiIiI+DWFIREREfFrCkMiIiLi1xSGRERExK/9P7ZoCjzfFBAVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(herr)\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (m)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can observe that each component of the error converges toward 0 following an exponential trajetory. The convergence is assymptotic. To fasten the convergence, increase the gain of the control law ($v_q = - \\lambda J^+ e$), where the gain $\\lambda$ has yet been set to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Place the end effector (6D)\n",
    "The previous control law brings the center of the effector toward the center of the goal frame. However, it does not control the orientation of the end effector: the axes of the two frames F_tool and F_goal do not converge.\n",
    "We should now modify the control law to take into account the tool orientation. For that, we compute the error to be the SE(3) log of the displacement from the tool frame F_tool to the goal frame F_goal.\n",
    "\n",
    "We will use `J` instead of `J3`, and we need to compute  a vector of the generalized difference between the tool frame and the goal frame:\n",
    "$$^{tool}M_{goal} = \\vphantom{.}^{o}M_{tool} \\vphantom{.}^{-1} \\vphantom{.}^{o}M_{tool}$$\n",
    "$$^{tool}w_{goal} = \\vphantom{.}^{o}M_{tool} \\ominus_{SE(3)} \\vphantom{.}^{o}M_{tool} = log_{SE(3)}(^{tool}M_{goal})$$\n",
    "where $^{tool}w_{goal}$ is a spatial vector in the local frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "toolMgoal = oMtool.inverse() * oMgoal\n",
    "tool_w = pin.log(toolMgoal).vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This error tool_nu is a 6d vector, that can be interpreted as the spatial (6d) velocity that should be applied during 1 second to displace the tool frame F_tool (placed at oMtool) to the goal frame F_goal (placed at oMgoal). This spatial velocity is expressed in the tool frame F_tool. It then corresponds to the 6D jacobian, that is also computed in the same frame F_tool.\n",
    "\n",
    "Implement a second control law, following the same pattern than the previous control law. At each control cycle, you should:\n",
    "* compute the displacement between F_tool and F_goal, denoted toolMgoal\n",
    "* compute the 6D error using the SE(3) log tool_nu\n",
    "* compute the 6D jacobian tool_Jtool\n",
    "* compute the control law vq = pinv(J)*nu\n",
    "* integrate the robot velocity vq during DT to get a new configuration q\n",
    "* log the error by storing it in a list herr."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load tp3/generated/inverse_kinematics_6d_loop\n",
    "q = q0.copy()\n",
    "herr = []\n",
    "for i in range(500):  # Integrate over 2 second of robot life\n",
    "\n",
    "    # Run the algorithms that outputs values in robot.data\n",
    "    pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "    pin.computeJointJacobians(robot.model,robot.data,q)\n",
    "\n",
    "    # Placement from world frame o to frame f oMtool  \n",
    "    oMtool = robot.data.oMf[IDX_TOOL]\n",
    "\n",
    "    # 6D error between the two frame\n",
    "    tool_nu = pin.log(oMtool.inverse()*oMgoal).vector\n",
    "\n",
    "    # Get corresponding jacobian\n",
    "    tool_Jtool = pin.computeFrameJacobian(robot.model, robot.data, q, IDX_TOOL)\n",
    "\n",
    "    # Control law by least square\n",
    "    vq = pinv(tool_Jtool)@tool_nu\n",
    "\n",
    "    q = pin.integrate(robot.model,q, vq * DT)\n",
    "    viz.display(q)\n",
    "    time.sleep(1e-3)\n",
    "\n",
    "    herr.append(tool_nu)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tool frame F_tool converges toward the gooal frame F_goal: the center and the axes are finally aligned. The trajectory of the tool center is not a straight line, as the frame F_tool follows a \"straight\" line, not in R^3 but in SE(3).\n",
    "We can also plot the error (assuming that herr is a list of the 6D errors herr)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(211)\n",
    "plt.plot([ e[:3] for e in herr])\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (m)')\n",
    "plt.subplot(212)\n",
    "plt.plot([ e[3:] for e in herr])\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (rad)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse kinematics for two tasks\n",
    "We yet controlled the robot with a single task (either the 3d position or the 6d placement errors). Let's see how to take into account a second task. Let's first introduce a second task. \n",
    "\n",
    "#### Introducing a second task: control the gaze\n",
    "The robot has an additional frame named F_gaze, attached to the head and located 40 cm in front of the cameras. The task will be to position (3d) the center of this frame on an object of interest (a red ball)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You can open the visualizer by visiting the following URL:\n",
      "http://127.0.0.1:7007/static/\n"
     ]
    }
   ],
   "source": [
    "robot = loadTiago(addGazeFrame=True)\n",
    "viz = MeshcatVisualizer(robot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "IDX_GAZE = robot.model.getFrameId('framegaze')\n",
    "\n",
    "# Add a small ball as a visual target to be reached by the robot\n",
    "ball = np.array([ 1.2,0.5,1.1 ])\n",
    "viz.addSphere('ball', .05, [ .8,.1,.5, .8] )\n",
    "viz.applyConfiguration('ball', list(ball)+[0,0,0,1])\n",
    "\n",
    "# Add the box again\n",
    "oMgoal = pin.SE3(pin.Quaternion(-0.5, 0.58, -0.39, 0.52).normalized().matrix(),\n",
    "                np.array([1.2, .4, .7]))\n",
    "viz.addBox('goal', [.1,.1,.1], [ .1,.1,.5, .6] )\n",
    "viz.applyConfiguration('goal',oMgoal)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <div style=\"height: 400px; width: 100%; overflow-x: auto; overflow-y: hidden; resize: both\">\n",
       "            <iframe src=\"http://127.0.0.1:7007/static/\" style=\"width: 100%; height: 100%; border: none\"></iframe>\n",
       "            </div>\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "viz.display(q0)\n",
    "viz.viewer.jupyter_cell()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Controlling this point can be done by achieving a simple variation of the control law for positioning (3d) the robot tool. Here is the solution if you need it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load tp3/generated/control_head_gaze_loop\n",
    "q = q0.copy()\n",
    "herr = [] # Log the value of the error between gaze and ball.\n",
    "# Loop on an inverse kinematics for 200 iterations.\n",
    "for i in range(500):  # Integrate over 2 second of robot life\n",
    "\n",
    "    # Run the algorithms that outputs values in robot.data\n",
    "    pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "    pin.computeJointJacobians(robot.model,robot.data,q)\n",
    "\n",
    "    # Placement from world frame o to frame f oMgaze\n",
    "    oMgaze = robot.data.oMf[IDX_GAZE]\n",
    "\n",
    "    # 6D jacobian in local frame\n",
    "    o_Jgaze3 = pin.computeFrameJacobian(robot.model, robot.data, q, IDX_GAZE,pin.LOCAL_WORLD_ALIGNED)[:3,:]\n",
    "\n",
    "    # vector from gaze to ball, in world frame\n",
    "    o_GazeBall = oMgaze.translation-ball\n",
    "    \n",
    "    vq = -pinv(o_Jgaze3) @ o_GazeBall\n",
    "\n",
    "    q = pin.integrate(robot.model,q, vq * DT)\n",
    "    viz.display(q)\n",
    "    time.sleep(1e-3)\n",
    "\n",
    "    herr.append(o_GazeBall) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Performing 2 tasks\n",
    "\n",
    "We now have two tasks (e1,J1) controlling the tool placement and (e2,J2) controlling the gaze position.\n",
    "\n",
    "We use the previous technique to compute:\n",
    "$$vq_1 = J_1^+ v_1^*$$\n",
    "the optimal (in a least square sense) control for task 1. Then we can add any vector which is in the null space of $J_1$ to perform the second task. We search for $vq = vq_1 + dvq$ where $dvq$ gives an optimal control for task 2.\n",
    "\n",
    "The orthogonal null space projector of $J_1$ can be computed using the pseudoinverse.\n",
    "$$P_1 = I_{nq} - J_1^+ J_1$$\n",
    "Finally, the control law to perform task 1 and task 2 in the null space of task 1 is:\n",
    "\n",
    "$$vq_2 = vq_1 + (J_2 P_1)^+ ( v_2^* - J_2 vq_1)$$\n",
    "\n",
    "You can now implement a control law solving the two tasks, i.e positioning the tool while controlling the gaze. Where we use $dvq$ being a solution of the minimisation problem:\n",
    "$$\\min_{x\\in Ker(J_1)} \\|J_2 (vq_1 + x) - v_2^*\\|_2^2$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = q0.copy()\n",
    "herr = [] # Log the value of the error between tool and goal.\n",
    "herr2 = [] # Log the value of the error between gaze and ball."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load tp3/generated/control_head_multi\n",
    "q = q0.copy()\n",
    "herr = [] # Log the value of the error between tool and goal.\n",
    "herr2 = [] # Log the value of the error between gaze and ball.\n",
    "# Loop on an inverse kinematics for 200 iterations.\n",
    "for i in range(500):  # Integrate over 2 second of robot life\n",
    "\n",
    "    # Run the algorithms that outputs values in robot.data\n",
    "    pin.framesForwardKinematics(robot.model,robot.data,q)\n",
    "    pin.computeJointJacobians(robot.model,robot.data,q)\n",
    "\n",
    "    # Tool task\n",
    "    oMtool = robot.data.oMf[IDX_TOOL]\n",
    "    tool_Jtool = pin.computeFrameJacobian(robot.model,robot.data,q,IDX_TOOL,pin.LOCAL)\n",
    "    tool_nu = pin.log(oMtool.inverse()*oMgoal).vector\n",
    "\n",
    "    # Gaze task\n",
    "    oMgaze = robot.data.oMf[IDX_GAZE]\n",
    "    o_Jgaze3 = pin.computeFrameJacobian(robot.model, robot.data, q, IDX_GAZE,pin.LOCAL_WORLD_ALIGNED)[:3,:]\n",
    "    o_GazeBall = oMgaze.translation-ball\n",
    "\n",
    "    vq = pinv(tool_Jtool) @ tool_nu\n",
    "    Ptool = np.eye(robot.nv)-pinv(tool_Jtool) @ tool_Jtool\n",
    "    vq += pinv(o_Jgaze3 @ Ptool) @ (-o_GazeBall - o_Jgaze3 @ vq)\n",
    "\n",
    "    q = pin.integrate(robot.model,q, vq * DT)\n",
    "    viz.display(q)\n",
    "    time.sleep(1e-3)\n",
    "\n",
    "    herr.append(tool_nu)\n",
    "    herr2.append(o_GazeBall) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(311)\n",
    "plt.plot([ e[:3] for e in herr])\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (m)')\n",
    "plt.subplot(312)\n",
    "plt.plot([ e[3:] for e in herr])\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (rad)');\n",
    "plt.subplot(313)\n",
    "plt.plot([ e for e in herr2])\n",
    "plt.xlabel('control cycle (iter)')\n",
    "plt.ylabel('error (rad)');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A third task can be implemented as well by computing the null space of the two first tasks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "Pgaze = Ptool - pinv(o_Jgaze3 @ Ptool) @ o_Jgaze3 @ Ptool"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Load an extra cube in the viewer to figure a table. First control the robot hand to reach an arbitrary point on the table (don't mind for the collision). Then implement a control law to control three tasks:\n",
    "* the tool frame should be kept on the table (i.e. only the z component of the error matter, select only the 3rd row of the matrix).\n",
    "* the gaze should be control to reach the position of a ball object positionned on the table.\n",
    "* the center of the basis frame should reach a given target on the floor. For this task, only the x- and y- component of the task matter, select only the 2 first rows.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code"
   ]
  }
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