5_2_controlopt.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reaching multiple targets with a manipulator\n",
    "The objective of this exercise is to reach multiple targets with a manipulator.\n",
    "\n",
    "We provide a basic example for reaching one point, and you have to modify it for sequence of multiple targets. Below it is the basic example, there we'll guide you to the final result.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import magic_donotload"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will need crocoddyl as in the previous notebook, with the model of the arm of the humanoid robot Talos, a 7-dof arm. It can be found in example robot data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import crocoddyl\n",
    "import pinocchio\n",
    "import numpy as np\n",
    "import example_robot_data as robex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The optimal-control program"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's load the Pinocchio model for the Talos arm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "robot = robex.load('talos_arm')\n",
    "robot_model = robot.model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set robot model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "robot_model.armature =np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.])*5\n",
    "robot_model.q0 = np.array([3.5,2,2,0,0,0,0])\n",
    "robot_model.x0 = np.concatenate([robot_model.q0, np.zeros(robot_model.nv)])\n",
    "robot_model.gravity *= 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's add a viewer to display the model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You can open the visualizer by visiting the following URL:\n",
      "http://127.0.0.1:7001/static/\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "            <div style=\"height: 400px; width: 100%; overflow-x: auto; overflow-y: hidden; resize: both\">\n",
       "            <iframe src=\"http://127.0.0.1:7001/static/\" style=\"width: 100%; height: 100%; border: none\"></iframe>\n",
       "            </div>\n",
       "            "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from utils.meshcat_viewer_wrapper import MeshcatVisualizer\n",
    "viz = MeshcatVisualizer(robot)\n",
    "viz.display(robot_model.q0)\n",
    "viz.viewer.jupyter_cell()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "viz.addBox('world/box',[.1,.1,.1], [1.,0,0,1])\n",
    "viz.addBox('world/goal',[.1,.1,.1],[0,1,0,1])\n",
    "viz.applyConfiguration('world/goal',[0.2,0.5,.5,0,0,0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Configure the task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "FRAME_TIP = robot_model.getFrameId(\"gripper_left_fingertip_3_link\")\n",
    "goal = np.array([.2,0.5,.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a cost model per the running and terminal action model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = crocoddyl.StateMultibody(robot_model)\n",
    "runningCostModel = crocoddyl.CostModelSum(state)\n",
    "terminalCostModel = crocoddyl.CostModelSum(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we need to include a cost model (i.e. set of cost functions) in order to fully define the action model for our optimal control problem.\n",
    "For this particular example, we formulate three running-cost functions: goal-tracking cost, state and control regularization; and a terminal cost: goal cost. First, let's create the common cost functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Deprecated: Do not use FramePlacement.\n",
      "Deprecated: Do not use FrameTranslation.\n",
      "Deprecated: Do not use FrameTranslation.\n",
      "Deprecated: Do not use FrameTranslation.\n",
      "Deprecated CostModelFrameTranslation: Use ResidualModelFrameTranslation with CostModelResidual\n",
      "Deprecated CostModelState: Use ResidualModelState with CostModelResidual\n",
      "Deprecated CostModelState: Use ResidualModelState with CostModelResidual\n",
      "Deprecated CostModelControl: Use ResidualModelControl with CostModelResidual\n"
     ]
    }
   ],
   "source": [
    "### Cost for reaching the target\n",
    "Mref = crocoddyl.FramePlacement(FRAME_TIP,pinocchio.SE3(np.eye(3), goal))\n",
    "pref = crocoddyl.FrameTranslation(FRAME_TIP,goal)\n",
    "goalTrackingCost = crocoddyl.CostModelFrameTranslation(state, pref)\n",
    "weights=crocoddyl.ActivationModelWeightedQuad(np.array([1,1,1,1,1,1,1, 1,1,1,1,2,2,2.]))\n",
    "\n",
    "### Cost for regularizing the state about robot_model.x0\n",
    "xRegCost = crocoddyl.CostModelState(state,weights,robot_model.x0)\n",
    "weightsT=crocoddyl.ActivationModelWeightedQuad(np.array([.01,.01,.01,.01,.01,.01,.01, 1,1,1,1,2,2,2.]))\n",
    "xRegCostT = crocoddyl.CostModelState(state,weightsT,robot_model.x0)\n",
    "\n",
    "### Cost for keeping the control low\n",
    "uRegCost = crocoddyl.CostModelControl(state)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then let's added the running and terminal cost functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "runningCostModel.addCost(\"gripperPose\", goalTrackingCost, .001)\n",
    "runningCostModel.addCost(\"xReg\", xRegCost, 1e-3)\n",
    "runningCostModel.addCost(\"uReg\", uRegCost, 1e-6)\n",
    "terminalCostModel.addCost(\"gripperPose\", goalTrackingCost, 10)\n",
    "terminalCostModel.addCost(\"xReg\", xRegCostT, .01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to create an action model for running and terminal knots. The\n",
    "forward dynamics (computed using ABA) are implemented inside DifferentialActionModelFullyActuated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "actuationModel = crocoddyl.ActuationModelFull(state)\n",
    "dt = 1e-2\n",
    "runningModel = crocoddyl.IntegratedActionModelEuler(\n",
    "    crocoddyl.DifferentialActionModelFreeFwdDynamics(state, actuationModel, runningCostModel), dt)\n",
    "runningModel.differential.armature = robot_model.armature\n",
    "terminalModel = crocoddyl.IntegratedActionModelEuler(\n",
    "    crocoddyl.DifferentialActionModelFreeFwdDynamics(state, actuationModel, terminalCostModel), 0.)\n",
    "terminalModel.differential.armature = robot_model.armature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this optimal control problem, we define 250 knots (or running action\n",
    "models) plus a terminal knot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 100\n",
    "problem = crocoddyl.ShootingProblem(robot_model.x0, [runningModel] * T, terminalModel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finalize the set up by creating the DDP solver for this optimal control problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddp = crocoddyl.SolverDDP(problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Callbacks can be added, for example to at verbose output when the solver runs, or logs the data of the descent algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddp.setCallbacks([\n",
    "    crocoddyl.CallbackLogger(),\n",
    "    crocoddyl.CallbackVerbose(),\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The DDP algorithm is run by the solver with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "   0  3.00773e+00  2.02499e-07  1.38003e+01  1.00000e-09  1.00000e-09   1.0000     1\n",
      "   1  2.44328e+00  8.10451e-03  4.05595e+00  1.00000e-09  1.00000e-09   0.5000     1\n",
      "   2  2.38482e+00  1.39317e+00  4.46815e+00  1.00000e-09  1.00000e-09   0.0312     1\n",
      "   3  2.31174e+00  1.27671e+00  4.03775e+00  1.00000e-09  1.00000e-09   0.0625     1\n",
      "   4  2.20646e+00  9.48034e-01  3.65929e+00  1.00000e-09  1.00000e-09   0.0625     1\n",
      "   5  8.07975e-01  7.76175e-01  3.24833e+00  1.00000e-09  1.00000e-09   1.0000     1\n",
      "   6  7.24996e-01  5.03473e-01  8.46602e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "   7  5.74868e-01  4.17031e-01  4.91489e-01  1.00000e-09  1.00000e-09   0.2500     1\n",
      "   8  5.56593e-01  1.74155e-04  4.52707e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "   9  5.24602e-01  3.43639e-03  4.02757e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  10  4.53819e-01  9.80865e-03  4.36979e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  11  4.40213e-01  8.22974e-03  3.55627e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  12  4.25345e-01  5.16663e-02  4.54999e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  13  4.07076e-01  5.33632e-02  3.80851e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  14  3.99255e-01  5.18338e-02  1.13046e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  15  3.94406e-01  5.30757e-02  1.37113e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  16  3.92895e-01  5.20661e-02  1.71428e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  17  3.89796e-01  5.61329e-02  2.51430e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  18  3.86808e-01  5.61583e-02  3.03762e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  19  3.83998e-01  5.57339e-02  3.56409e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  20  3.81363e-01  5.41043e-02  3.90198e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  21  3.77933e-01  5.09743e-02  3.89896e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  22  3.72442e-01  4.62825e-02  3.64055e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  23  3.63702e-01  4.04253e-02  3.26512e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  24  3.48492e-01  2.14930e-02  2.58512e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  25  3.09319e-01  1.55011e-04  2.28303e-01  1.00000e-09  1.00000e-09   0.2500     1\n",
      "  26  2.92717e-01  2.14816e-04  3.89451e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  27  2.86614e-01  1.48073e-03  2.63520e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  28  2.80809e-01  1.58761e-03  2.22596e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  29  2.76759e-01  7.09713e-04  1.91998e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  30  2.49486e-01  2.01500e-03  1.71643e-01  1.00000e-09  1.00000e-09   0.2500     1\n",
      "  31  2.34597e-01  2.80297e-02  1.72424e-01  1.00000e-09  1.00000e-09   0.2500     1\n",
      "  32  2.31131e-01  1.09873e-02  1.97054e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  33  2.22923e-01  5.90270e-03  2.70368e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  34  1.94427e-01  4.98233e-03  2.71014e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  35  1.91160e-01  2.75546e-03  2.07426e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  36  1.89313e-01  2.39734e-03  2.40411e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  37  1.86939e-01  2.04752e-03  2.87973e-01  1.00000e-09  1.00000e-09   0.0156     1\n",
      "  38  1.84469e-01  1.93610e-03  3.07535e-01  1.00000e-09  1.00000e-09   0.0156     1\n",
      "  39  1.81762e-01  1.83255e-03  3.16095e-01  1.00000e-09  1.00000e-09   0.0156     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  40  1.79504e-01  1.73882e-03  3.10131e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  41  1.73461e-01  1.52316e-03  2.85189e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  42  1.38472e-01  1.20241e-03  2.52662e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  43  1.13692e-01  9.32504e-04  1.85115e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  44  1.09150e-01  8.81085e-05  1.73874e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  45  1.05923e-01  8.52726e-05  1.76403e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  46  1.02890e-01  1.16018e-04  1.68383e-01  1.00000e-09  1.00000e-09   0.0312     1\n",
      "  47  1.01247e-01  1.76804e-04  1.56685e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  48  9.70546e-02  6.79984e-04  1.42631e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  49  9.32748e-02  1.07617e-03  1.25763e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  50  7.72414e-02  8.74717e-04  1.68407e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  51  6.52862e-02  9.19902e-04  1.32750e-01  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  52  6.31687e-02  8.21050e-04  1.10759e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  53  6.10070e-02  7.03029e-04  1.02009e-01  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  54  5.83051e-02  6.03540e-04  9.29437e-02  1.00000e-09  1.00000e-09   0.0625     1\n",
      "  55  5.57650e-02  5.18947e-04  8.36293e-02  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  56  4.92540e-02  3.68754e-04  7.36708e-02  1.00000e-09  1.00000e-09   0.2500     1\n",
      "  57  3.82447e-02  1.98115e-04  5.82544e-02  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  58  3.02991e-02  8.25491e-05  3.63770e-02  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  59  2.13443e-02  2.28805e-06  2.05291e-02  1.00000e-09  1.00000e-09   1.0000     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  60  2.09493e-02  1.60923e-04  3.53529e-03  1.00000e-09  1.00000e-09   1.0000     1\n",
      "  61  2.04860e-02  1.26044e-05  3.83314e-03  1.00000e-09  1.00000e-09   1.0000     1\n",
      "  62  1.94711e-02  8.50131e-05  3.89767e-03  1.00000e-09  1.00000e-09   1.0000     1\n",
      "  63  1.92717e-02  1.60706e-06  3.02697e-03  1.00000e-09  1.00000e-09   0.1250     1\n",
      "  64  1.90296e-02  2.34443e-06  1.92860e-03  1.00000e-09  1.00000e-09   0.2500     1\n",
      "  65  1.84753e-02  3.04108e-06  1.14209e-03  1.00000e-09  1.00000e-09   1.0000     1\n",
      "  66  1.84643e-02  1.66223e-07  6.64948e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  67  1.84598e-02  1.04465e-07  4.03756e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  68  1.84576e-02  8.30735e-08  2.80719e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  69  1.84560e-02  4.37931e-08  2.07185e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
      "  70  1.84547e-02  2.89873e-08  1.51796e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  71  1.84539e-02  1.50243e-08  1.07605e-05  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  72  1.84533e-02  9.18402e-09  7.70062e-06  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  73  1.84530e-02  4.81285e-09  5.43949e-06  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  74  1.84527e-02  2.82934e-09  3.90509e-06  1.00000e-09  1.00000e-09   0.5000     1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  75  1.84525e-02  1.50275e-09  2.79244e-06  1.00000e-09  1.00000e-09   0.5000     1\n",
      "  76  1.84524e-02  8.64158e-10  2.02615e-06  1.00000e-09  1.00000e-09   0.5000     1\n"
     ]
    }
   ],
   "source": [
    "ddp.solve([],[],1000)  # xs_init,us_init,maxiter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now look at the results, either in Gepetto-viewer by running the trajectory, or by plotting it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load -r 103-104 tp5/arm_example.py\n",
    "import tp5.croco_utils as crocutils\n",
    "crocutils.displayTrajectory(viz,ddp.xs,ddp.problem.runningModels[0].dt,12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plotting..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load -r 97-99 tp5/arm_example.py\n",
    "log = ddp.getCallbacks()[0]\n",
    "crocoddyl.plotOCSolution(log.xs, log.us, figIndex=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some elements describing the solver convergence can also been plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x576 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "crocoddyl.plotConvergence(log.costs, log.u_regs, log.x_regs, log.grads, log.stops, log.steps, figIndex=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. DifferentialActionModel for Pinocchio ABA\n",
    "This scenario uses an action model that computes 2nd order differential dynamics with Pinocchio. Note that it can accept several cost models. This action model is tailored for robot applications, and at the same time, it's modular since:\n",
    " - you can modify the robot dynamics by changing Pinocchio model, and\n",
    " - you can formulate any cost function by simply adding running a terminal costs.\n",
    "\n",
    "## II. Cost models\n",
    "\n",
    "A cost model computes a scalar cost value and its gradient and Hessian. All the models implemented are computing a cost residual and are computing the Hessian with the Gauss approximation.\n",
    "\n",
    "We implemented reusable cost models for controlling \n",
    " - a frame placement (translation or velocity),\n",
    " - the center of mass position, and \n",
    " - state  and control spaces.\n",
    "\n",
    "In the example above, we used the CostModelFrameTranslation which defines a 3d position task, and the state and control regularizers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All functions are defined by their *model*, which is const, i.e none of its fields is modified by the *calc* and *calcDiff* calls. Temporary buffers are defined in a companion *data*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataCollector = crocoddyl.DataCollectorMultibody(robot.data)\n",
    "trackData = goalTrackingCost.createData(dataCollector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.a Frame position cost\n",
    "\n",
    "You define a frame ID and the reference position as a 3D array. The cost is the distance between the frame and the target. This cost depends on $\\mathbf{x}$ (specifically the configuration $\\mathbf{q}$). You can double check the 0s in its gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lx =  [-0.07596597  0.03892435  0.13087767 -0.01389783 -0.01787752  0.05840131\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.        ]\n",
      "Lu =  [0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "x = ddp.xs[1].copy()\n",
    "q = x[:state.nq]\n",
    "pinocchio.updateFramePlacements(robot.model, robot.data)\n",
    "pinocchio.computeJointJacobians(robot.model, robot.data, q)\n",
    "goalTrackingCost.calc(trackData, x)\n",
    "goalTrackingCost.calcDiff(trackData, x)\n",
    "print('Lx = ',trackData.Lx)\n",
    "print('Lu = ',trackData.Lu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.b State cost\n",
    "In this part of the tutorial you must define a State model. It defines \n",
    " - the dimension of the state and its tangent, and\n",
    " - the exponential/integrate and difference/log operators.\n",
    "The operators can described using Pinocchio functions. And the exercite consists on adding them into your State class. Please note crocoddyl has abstract functions for this.\n",
    "\n",
    "The state cost uses a reference in state space (State.zero() by default). The cost is the distance, computed with state.difference between the current state and the reference. Hence, with this cost, we regularize both position and velocity.\n",
    "\n",
    "### II.c Control cost\n",
    "\n",
    "The control cost uses a control reference as in the state cost. The cost is the distance the current control and the reference. Hence the cost regularizes torque commands."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.d Add cost models to the differential action model\n",
    "Each time we want to include a new cost function, we use addCost function inside our DAM. In this function you're also able its weight."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Create the problem with integrated action model\n",
    "Differential action models describe cost and dynamics in continuous-time, however our optimal control solvers work in discrete-time. We have created the integrated action model in order to deal with this.\n",
    "\n",
    "In the previous code, we have used an abstract class that uses simpletic Euler rules. In the cartpole exercise you have learnt how to use integrated action models for your problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Callbacks\n",
    "\n",
    "Callback functions are needed for analysing and debugging the performance of the solver for your specific problem.\n",
    "For problems defined with Pinocchio, you can display the robot trajectory per each iterate by including CallbackDisplay. With this callback, you can display robot motions with different rates. Additionally, CallbackVerbose prints a message that allows us to understand the behaviour of the solver.\n",
    "\n",
    "Generally speaking, an user is able to describe any callback function. This function will be run once per iterate and it has access to all data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VI. Modifying the example\n",
    "\n",
    "Start by defining several targets (let's say 4 targets, all at x=0.4, and at y and z being either 0 or 0.4), and display then in the viewer.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shooting problem will be composed of 4 sequences of action models. Each sequence consists on T shooting \"running\" nodes and 1 terminal node. The running nodes mostly have regularization terms, while the terminal nodes have a strong cost toward the respective target.\n",
    "\n",
    "[ R1,R1,R1 ... R1,T1, R2,R2 .... R2, T2, R3 ... R3, T3, R4 ... R4 ] , T4\n",
    "\n",
    "First create 4 running models and 4 terminal models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then you need to add a position cost, and state and control regularization to each running action model. Please  note that for terminal action model is only needed the position cost. Additionally, in the running models, the position cost should be low, and it should be high in the terminal models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create a shooting problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq0 = [runningModels[0]]*T + [terminalModels[0]]\n",
    "seq1 = [runningModels[1]]*T + [terminalModels[1]]\n",
    "seq2 = [runningModels[2]]*T + [terminalModels[2]]\n",
    "seq3 = [runningModels[3]]*T \n",
    "problem = crocoddyl.ShootingProblem(x0,seq0+seq1+seq2+seq3,terminalmodel[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a DDP solver for this problem and run it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddp = crocoddyl.SolverDDP(problem)\n",
    "ddp.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, it should not work, at least no on the first shot. The DDP solver is likely not strong enough to accept the random weights that you have selected. \n",
    "\n",
    "If it is working nicely from the first shot, display it in the viewer and go take a coffee. But you will likely have to tweak the gains to make it work.\n",
    "\n",
    "**It is suggested to first optimize only sequence 1. When you are happy with it, add sequence 2 and optimize again, etc.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. Penalty\n",
    "The solver works with double precisions, so it is quite robust to high weight. 10000 is likely to be accepted for example. But if you make the problem too difficult, the solver will break. \n",
    "\n",
    "In that case, you can implement a simple penalty solver by setting the weight to be 10**i, and creating a for loop to explore i from 0 to 5. At each iteration of the loop, run the solver from the previous solution and for few iterations only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1,6):\n",
    "    for m in terminalModels:\n",
    "        m.costs.costs['gripperPose'].weight = 10**i\n",
    "    ddp.solve(ddp.xs, ddp.us, 10)"
   ]
  }
 ],
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