Differential_Drive_Trajectory_Optimization_With_Splines.ipynb

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  "metadata": {
    "colab": {
      "name": "Differential Drive Trajectory Optimization With Splines",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nbIV8mRzocE-"
      },
      "source": [
        "#Differential Drive Trajectory Optimization\n",
        "##Steps:\n",
        "1) Generate the required model of our differential drive\n",
        "\n",
        "2) Test the model and make sure it behaves accurately\n",
        "\n",
        "3) Implement the model using `drake` which is a Non Linear Program Solver\n",
        "\n",
        "4) Graph everything"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G6W7BHniPC1L"
      },
      "source": [
        "Import Statements"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G79Izr7V7uQM"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 944,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zWpnaYrSP7tl"
      },
      "source": [
        "try:\n",
        "  import pydrake\n",
        "  import underactuated\n",
        "except ImportError:\n",
        "  !curl -s https://raw.githubusercontent.com/RussTedrake/underactuated/master/scripts/setup/jupyter_setup.py > jupyter_setup.py\n",
        "  from jupyter_setup import setup_underactuated\n",
        "  setup_underactuated()"
      ],
      "execution_count": 945,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L063_snTBWCQ"
      },
      "source": [
        "Constants:\n",
        "\n",
        "`m` - mass of robot\n",
        "\n",
        "`I` - moment of inertia of robot\n",
        "\n",
        "`r_bot` - radius of bot (width between wheels / 2)\n",
        "\n",
        "`r_wheel` - radius of wheel\n",
        "\n",
        "`k_emf` - emf constant of motor (must take into account gear ratio)\n",
        "\n",
        "`k_magnet` - constant of magnet (must take into account gear ratio)\n",
        "\n",
        "Input vector:\n",
        "\n",
        "$ \\mathbf{u} = \\begin{bmatrix}\n",
        "V_L \\\\\n",
        "V_R\n",
        "\\end{bmatrix} $\n",
        "\n",
        "State vector:\n",
        "\n",
        "$ \\mathbf{x} = \\begin{bmatrix}\n",
        "x \\\\ \n",
        "y \\\\\n",
        "\\theta \\\\\n",
        "v \\\\\n",
        "\\omega \\\\\n",
        "\\end{bmatrix} $\n",
        "\n",
        "\n",
        "$f(x, u)$ returns the derivative of x based on the input voltages\n",
        "\n",
        "$f(x, u) = \\mathbf{\\dot{x}} = \\begin{bmatrix} \\dot{x} \\\\ \\dot{y} \\\\ \\dot{\\theta}\\\\ \\dot{v} \\\\ \\dot{\\omega} \\end{bmatrix} = \\begin{bmatrix} v*cos(\\theta) \\\\ v*sin(\\theta) \\\\ \\omega \\\\ (\\tau(V_r) + \\tau(V_l)) / (r * r_{wheel} * m) \\\\ r_{wheelbase} * (\\tau(V_r) - \\tau(V_l)) / r_{wheel} \\end{bmatrix}$\n",
        "\n",
        "where $T(V)$ is a function of torque depending on $V_{applied}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "csmgoWU-pVhW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "2cea2453-5384-43b9-fdbb-3d0736e7947d"
      },
      "source": [
        "from pydrake.all import ge, eq, le, ge, MathematicalProgram, Solve, Variable\n",
        "\n",
        "#Robot constants\n",
        "m = 68.03 #kg\n",
        "r_bot = 0.5 #m\n",
        "r_wheel = 0.0762 #m\n",
        "I = (1/12.) * (2 * (2*r_bot) ** 2) * m#kg-m^2\n",
        "\n",
        "#Motor constants\n",
        "stall_torque = 3.87 #N-m\n",
        "stall_current = 185. #amp\n",
        "free_speed = 5180. #rpm (Needs to be in r/s)\n",
        "free_current = 1.2 #amp\n",
        "operating_voltage = 12. #V\n",
        "#gear_ratio = 1. / 0.096 #ul\n",
        "gear_ratio = 1. / 0.1117 #ul\n",
        "\n",
        "#Intermediate calculations\n",
        "free_speed = 2*np.pi*free_speed/60 #r/s\n",
        "k_emf = operating_voltage / free_speed\n",
        "k_magnet = stall_torque / operating_voltage\n",
        "k_emf *= gear_ratio\n",
        "k_magnet *= gear_ratio * 2\n",
        "\n",
        "print(k_emf)\n",
        "print(k_magnet)\n",
        "'''\n",
        "k_emf = 2.\n",
        "k_magnet = 2.'''"
      ],
      "execution_count": 946,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.19804765077818873\n",
            "5.7743957027752915\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'\\nk_emf = 2.\\nk_magnet = 2.'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 946
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pe0tCP5SEfNq"
      },
      "source": [
        "`model` is $f(x, u)$\n",
        "\n",
        "`getWheelVelocity` - returns the angular velocity of wheel (need to clarify which wheel it is)\n",
        "\n",
        "`getWheelTorque` - returns the motor torque of the wheel using `V` (voltage applied) and `vf` (surface velocity of wheel)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jm7izghmoU1Y"
      },
      "source": [
        "def model(x, u): #state and input vector: f(x, u)\n",
        "  v = x[3]\n",
        "  left_wheel_torque = getWheelTorque(u[0], getWheelVelocity(v, x[4], False))\n",
        "  right_wheel_torque = getWheelTorque(u[1], getWheelVelocity(v, x[4], True))\n",
        "  dx = np.array([\n",
        "    v * np.cos(x[2] + 0.),\n",
        "    v * np.sin(x[2] + 0.),\n",
        "    x[4],\n",
        "    (left_wheel_torque + right_wheel_torque) / (r_wheel * m),\n",
        "    r_bot * (right_wheel_torque - left_wheel_torque) / (r_wheel * I)\n",
        "  ])\n",
        "\n",
        "  return dx\n",
        "\n",
        "def getWheelVelocity(v, w, direction):\n",
        "  if direction:\n",
        "    return (v + r_bot * w) / r_wheel\n",
        "  return (v - r_bot * w) / r_wheel\n",
        "\n",
        "def getWheelTorque(V, vf):\n",
        "  voltage_eff = V - k_emf * vf #since vf is wheel speed, k_emf needs to account for the gearing. same for k_magnet\n",
        "  return k_magnet * voltage_eff\n"
      ],
      "execution_count": 947,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aEgo8L3DE6Dw"
      },
      "source": [
        "This is just a test to make sure that the above code works. It is assuming the start state is stationary and that the voltage applied is constant.\n",
        "\n",
        "In this example, left motor is applying 12V and right motor is applying 6V which, intuitively, makes the robot travel in a circle"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D2TUk8tD9wHN"
      },
      "source": [
        "x = np.array([0., 0., 0., 0., 0.])\n",
        "u_const = np.array([12., 6.])\n",
        "\n",
        "output_x = []\n",
        "output_y = []\n",
        "\n",
        "time = []\n",
        "for i in range(0, 600):\n",
        "  time.append(0.01)\n",
        "\n",
        "for i in time:\n",
        "  x = x + model(x, u_const) * 0.01\n",
        "  ans = [x[0], x[1]]\n",
        "  output_x.append(ans[0])\n",
        "  output_y.append(ans[1])\n"
      ],
      "execution_count": 948,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "Q2ikdool_X2R",
        "outputId": "d875b71c-1b34-4b2b-8064-d017d965c757"
      },
      "source": [
        "plt.plot(output_x, output_y, linewidth=4, label='trajectory')\n",
        "plt.scatter(output_x[0], output_y[0], c='green', label='start', linewidth=3)\n",
        "plt.scatter(output_x[len(output_x) - 1], output_y[len(output_y) - 1], c='red', label='end', linewidth=3)\n",
        "plt.title('Test of Trajectory', c='white')\n",
        "plt.grid()\n",
        "plt.legend()"
      ],
      "execution_count": 949,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f29e7fb8210>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 949
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bq4v6CxwGc93"
      },
      "source": [
        "`waypoints` - list of points we want the robot to go to. These are the state variables discussed above"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ia39s5dlEnO_"
      },
      "source": [
        "##This is the section where we use Splines as an initial guess"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "13c2Z4hXEr-g"
      },
      "source": [
        "'''input = [0, 2.286, 3.81, 4.572, 9.144]\n",
        "output = [2.286, 2.286, 1.524, 3.81, 3.81]'''\n",
        "'''input = [0, 4.572, 5.334, 6.868, 9.144]\n",
        "output = [2.286, 0.762, 3.048, 2.286, 2.286]'''\n",
        "'''input = [1.143, 3.81, 6.858, 5.08, 8.128, 6.858, 3.81, 1.524]\n",
        "output = [2.286, 1.143, 3.048, 3.048, 1.524, 2.286, 3.048, 2.286]'''\n",
        "input = [1.143, 2.282, 3.048, 4.572, 6.096, 7.62, 8.763, 7.62, 6.096, 4.572, 3.048, 1.143]\n",
        "output = [0.762, 1.524, 2.08, 2.58, 2, 0.762, 1.524, 2.286, 1, 0.5, 1, 2.286] #Helix path\n",
        "\n",
        "N = len(input)\n",
        "n = N - 1"
      ],
      "execution_count": 950,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kr0i7jrEEweB"
      },
      "source": [
        "def getSpline(time, values):\n",
        "  a = [None] * N\n",
        "  for i in range(0, len(time)):\n",
        "    a[i] = (values[i])\n",
        "  print(len(a) == len(time))\n",
        "\n",
        "  b = [None] * (n)\n",
        "  d = [None] * (n)\n",
        "  h = [None] * (n)\n",
        "  \n",
        "  for i in range(0, n):\n",
        "    h[i] = time[i+1] - time[i]\n",
        "\n",
        "  alpha = [None] * (n)\n",
        "  for i in range(1, n):\n",
        "   alpha[i] = (3/h[i]) * (a[i+1] - a[i]) - (3/h[i-1]) * (a[i] - a[i-1])\n",
        "\n",
        "  c = [None] * N\n",
        "  l = [None] * N\n",
        "  u = [None] * N\n",
        "  z = [None] * N\n",
        "\n",
        "  l[0] = 1\n",
        "  u[0] = 0\n",
        "  z[0] = 0\n",
        "\n",
        "  for i in range(1, n):\n",
        "    l[i] = 2 * (time[i+1] - time[i-1]) - h[i-1] * u[i-1]\n",
        "    u[i] = h[i] / l[i]\n",
        "    z[i] = (alpha[i] - h[i-1]*z[i-1]) / l[i]\n",
        "\n",
        "  l[n] = 1\n",
        "  z[n] = 0\n",
        "  c[n] = 0\n",
        "\n",
        "  for j in range(n-1, -1, -1):\n",
        "    c[j] = z[j] - u[j]*c[j+1]\n",
        "    b[j] = (a[j+1]-a[j])/h[j] - (h[j] * (c[j+1] + 2*c[j]))/3\n",
        "    d[j] = (c[j+1] - c[j])/(3*h[j])\n",
        "\n",
        "  print(a)\n",
        "  print(b)\n",
        "  print(c)\n",
        "  print(d)\n",
        "\n",
        "  return a, b, c, d\n"
      ],
      "execution_count": 951,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hl-OACrTEy0j",
        "outputId": "cc87d51d-d05c-42ef-9916-6ff8deb5bee3"
      },
      "source": [
        "time = [None] * len(input)\n",
        "for i in range(0, len(time)):\n",
        "  time[i] = i\n",
        "\n",
        "ax, bx, cx, dx = getSpline(time, input)\n",
        "\n",
        "ay, by, cy, dy = getSpline(time, output)"
      ],
      "execution_count": 952,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "True\n",
            "[1.143, 2.282, 3.048, 4.572, 6.096, 7.62, 8.763, 7.62, 6.096, 4.572, 3.048, 1.143]\n",
            "[1.2930843127289855, 0.8308313745420288, 1.098590189102899, 1.6448078690463752, 1.4661783347116, 1.6344787921072248, -0.0030935031404999425, -1.622104779545225, -1.5094873786785996, -1.483945705740377, -1.6987297983598924]\n",
            "[0.0, -0.4622529381869566, 0.7300117527478267, -0.18379407280435048, 0.005164538469575208, 0.16313591892604962, -1.8007082141737745, 0.18169693776904947, -0.06907953690242397, 0.09462120984064638, -0.30940530246016157, 0]\n",
            "[-0.15408431272898554, 0.3974215636449278, -0.3046019418507257, 0.06298620375797523, 0.052657126818824805, -0.6546147110332746, 0.6608017173142746, -0.08359215822382449, 0.054566915581023445, -0.13467550410026932, 0.10313510082005385]\n",
            "True\n",
            "[0.762, 1.524, 2.08, 2.58, 2, 0.762, 1.524, 2.286, 1, 0.5, 1, 2.286]\n",
            "[0.8280178283358626, 0.6299643433282748, 0.6061247983510384, 0.11353646326757205, -1.3002706514213265, -0.36645385758226645, 1.3380860817503928, -0.4138904694193042, -1.254524204073176, 0.07398728571200897, 0.9585750612251402]\n",
            "[0.0, -0.1980534850075878, 0.17421394003035134, -0.6668022751138177, -0.7470048395750806, 1.6808216334141404, 0.02371830591851881, -1.7756948570882156, 0.9350611224343436, 0.3934503673508417, 0.49113740816228957, 0]\n",
            "[-0.0660178283358626, 0.12408914167931305, -0.28033873838138973, -0.02673418815375428, 0.8092754909964069, -0.5523677758318738, -0.5998043876689115, 0.9035853265075198, -0.18053691836116728, 0.03256234693714929, -0.16371246938742987]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CN1KKdgUE2d8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "919f3ef5-4806-493d-92a6-92812b623ef5"
      },
      "source": [
        "  t_2 = np.linspace(0, 1, 100)\n",
        "  t_vals = []\n",
        "  x_vals = []\n",
        "  y_vals = []\n",
        "\n",
        "  for i in range(0, n):\n",
        "    for j in t_2:\n",
        "      t = j\n",
        "      x = ax[i] + bx[i] * t + cx[i] * t**2 + dx[i] * t**3\n",
        "      x_vals.append(x)\n",
        "      \n",
        "      y = ay[i] + by[i] * t + cy[i] * t**2 + dy[i] * t**3\n",
        "      y_vals.append(y)\n",
        "\n",
        "      t_vals.append(t + time[i])\n",
        "  print(x_vals)\n"
      ],
      "execution_count": 953,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.143, 1.1560612989034762, 1.1691216450018105, 1.182180085489861, 1.195235667562486, 1.2082874384145432, 1.221334445240891, 1.2343757352363873, 1.2474103555958904, 1.2604373535142588, 1.2734557761863496, 1.2864646708070218, 1.299463084571133, 1.3124500646735415, 1.3254246583091054, 1.338385912672683, 1.3513328749591318, 1.3642645923633105, 1.377180112080077, 1.3900784813042895, 1.402958747230806, 1.4158199570544847, 1.4286611579701836, 1.4414813971727607, 1.4542797218570744, 1.4670551792179827, 1.4798068164503435, 1.4925336807490153, 1.5052348193088558, 1.5179092793247233, 1.5305561079914758, 1.5431743525039716, 1.5557630600570689, 1.5683212778456255, 1.5808480530644995, 1.593342432908549, 1.6058034645726327, 1.6182301952516078, 1.6306216721403333, 1.6429769424336664, 1.6552950533264656, 1.6675750520135895, 1.6798159856898958, 1.6920169015502422, 1.7041768467894873, 1.7162948686024893, 1.728370014184106, 1.7404013307291955, 1.752387865432616, 1.7643286654892256, 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1.2038497089265163, 1.183567535538497, 1.1632840866454943, 1.143]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tCj5zKTJFJeo"
      },
      "source": [
        "def getLength(a, b):\n",
        "  length = 0\n",
        "  \n",
        "  first = True\n",
        "  x = 0\n",
        "  y = 0\n",
        "  if b > a:\n",
        "    for i in range(len(x_vals)):\n",
        "      if x_vals[i] >= a and x_vals[i] <= b:\n",
        "        if first:\n",
        "          x = x_vals[i]\n",
        "          y = y_vals[i]\n",
        "          first = False\n",
        "          continue\n",
        "\n",
        "        length += np.sqrt((x_vals[i] - x) ** 2 + (y_vals[i] - y) ** 2)\n",
        "        x = x_vals[i]\n",
        "        y = y_vals[i]\n",
        "  else:\n",
        "    for i in range(len(x_vals)):\n",
        "      if x_vals[i] >= b and x_vals[i] <= a:\n",
        "        if first:\n",
        "          x = x_vals[i]\n",
        "          y = y_vals[i]\n",
        "          first = False\n",
        "          continue\n",
        "\n",
        "        length += np.sqrt((x_vals[i] - x) ** 2 + (y_vals[i] - y) ** 2)\n",
        "        x = x_vals[i]\n",
        "        y = y_vals[i]\n",
        "  return length\n"
      ],
      "execution_count": 954,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "StcvYM4b_8-1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        },
        "outputId": "539290d7-9d58-495f-a6f8-28c9f6c11dc9"
      },
      "source": [
        "waypoints = []\n",
        "\n",
        "prev_x = input[0]\n",
        "prev_y = output[0]\n",
        "prev_n = 0\n",
        "\n",
        "for i in range(len(input)):\n",
        "  arc_len = getLength(prev_x, input[i])\n",
        "\n",
        "  if arc_len == 0:\n",
        "    t = 0\n",
        "  else:\n",
        "    t = arc_len / 5 #THIS WAS FOR THE DOUBLE HELIX RUN\n",
        "    #t = arc_len / (0.5/arc_len)\n",
        "    #t = arc_len / 3 #NEED TO TUNE BTW\n",
        "  print(arc_len)\n",
        "\n",
        "  #print((str)(prev_x) + \" to \" + (str)(input[i]) + \" gave \" + (str)(t))\n",
        "  if i == 0:\n",
        "    waypoints.append(\n",
        "        (np.array([input[i], output[i], np.pi/4, 0, 0]), prev_n + (int)(t/0.04))\n",
        "        )\n",
        "  elif i == len(input)-1:\n",
        "    waypoints.append(\n",
        "        (np.array([input[i], output[i], 3*np.pi/4, 0, 0]), prev_n + (int)(t/0.04)) #NOTE NEED TO CHANGE TO REFLECT ENDING STATE\n",
        "        )\n",
        "  else:\n",
        "    waypoints.append(\n",
        "        (np.array([input[i], output[i]]), prev_n + (int)(t/0.04))\n",
        "        )\n",
        "  prev_n += (int)(t/0.04)\n",
        "  prev_x = input[i]\n",
        "  \n",
        "for i in range(len(waypoints)):\n",
        "  #print(waypoints[i][1])\n",
        "  pass\n",
        "\n",
        "#Working Helix Path\n",
        "waypoints = [\n",
        "    (np.array([1.143, 0.762, 0, 0, 0]), 0),\n",
        "    (np.array([1.62, 0.762]), 8),\n",
        "    (np.array([3.048, 2.08]), 22),\n",
        "    (np.array([6.096, 2]), 40),\n",
        "    (np.array([6.4, 2]), 45),\n",
        "    (np.array([7.62, 0.762, 0]), 78),\n",
        "    (np.array([8.763, 1.524]), 94),\n",
        "    (np.array([7.62, 2.286]), 110),\n",
        "    (np.array([6.096, 1]), 136),\n",
        "    #(np.array([3.048, 1]), 155),\n",
        "    (np.array([1.143, 2.286]), 200),\n",
        "]\n",
        "\n",
        "'''#Galactice Search Path A RED\n",
        "waypoints = [\n",
        "    (np.array([0, 2.286, 0, 0, 0]), 0),\n",
        "    (np.array([2.286, 2.286]), 20),\n",
        "    (np.array([3.81, 1.524]), 35),\n",
        "    (np.array([4.572, 3.81]), 55),\n",
        "    (np.array([9.144, 3.81, 0, 0, 0]), 86),\n",
        "]'''\n",
        "'''\n",
        "#Galactice Search Path A BLUE\n",
        "waypoints = [\n",
        "    (np.array([0, 0.762, 0, 0, 0]), 0),\n",
        "    (np.array([4.572, 0.762]), 36),\n",
        "    (np.array([5.334, 3.048]), 52),\n",
        "    (np.array([6.858, 2.286]), 69),\n",
        "    (np.array([9.144, 2.286, 0, 0, 0]), 85),\n",
        "]\n",
        "\n",
        "#Galactice Search Path B RED\n",
        "waypoints = [\n",
        "    (np.array([0, 3.048, 0, 0, 0]), 0),\n",
        "    (np.array([2.286, 3.048]), 17),\n",
        "    (np.array([3.81, 1.524]), 34),\n",
        "    (np.array([5.334, 3.048]), 53),\n",
        "    (np.array([9.144, 3.048, 0, 0, 0]), 80),\n",
        "]\n",
        "\n",
        "#Galactice Search Path B BLUE\n",
        "waypoints = [\n",
        "    (np.array([0, 1.524, 0, 0, 0]), 0),\n",
        "    (np.array([3.81, 1.524]), 27),\n",
        "    (np.array([6.096, 3.048]), 46),\n",
        "    (np.array([7.62, 1.524]), 65),\n",
        "    (np.array([9.144, 1.524, 0, 0, 0]), 77),\n",
        "]'''\n",
        "\n",
        "'''waypoints = [\n",
        "    (np.array([0, 0.762, 0, 0, 0]), 0),\n",
        "    (np.array([4.572, 0.762]), 36),\n",
        "    (np.array([5.334, 3.048]), 52),\n",
        "    (np.array([6.858, 2.286]), 69),\n",
        "    (np.array([9.144, 2.286, 0, 0, 0]), 85),\n",
        "]\n",
        "'''\n",
        "'''\n",
        "#incomplete barrel racing path\n",
        "waypoints = [\n",
        "    (np.array([1.27, 1.905, 0, 0, 0]), 0),\n",
        "    (np.array([4.445, 1.524]), 45),\n",
        "    (np.array([3.81, 1.143]), 65),\n",
        "    (np.array([3.556, 1.524]), 78),\n",
        "    (np.array([6.858, 3.302]), 150)\n",
        "\n",
        "]'''\n",
        "plt.plot(x_vals, y_vals)\n",
        "plt.scatter(input, output)"
      ],
      "execution_count": 955,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.524\n",
            "2.804086509729188\n",
            "2.9126547289606814\n",
            "5.314537438159519\n",
            "4.322494257555623\n",
            "5.523345343510055\n",
            "3.087983133025491\n",
            "3.087983133025491\n",
            "5.523345343510055\n",
            "4.322494257555623\n",
            "5.314537438159519\n",
            "5.698425296181251\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f29e7fd88d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 955
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TNwC3uJDSKZk",
        "outputId": "5a67b975-1583-4296-b08a-2cac404ede10"
      },
      "source": [
        "for i in waypoints:\n",
        "  print((str)(i[0]) + \" \" + (str)(i[1]))"
      ],
      "execution_count": 956,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.143 0.762 0.    0.    0.   ] 0\n",
            "[1.62  0.762] 8\n",
            "[3.048 2.08 ] 22\n",
            "[6.096 2.   ] 40\n",
            "[6.4 2. ] 45\n",
            "[7.62  0.762 0.   ] 78\n",
            "[8.763 1.524] 94\n",
            "[7.62  2.286] 110\n",
            "[6.096 1.   ] 136\n",
            "[1.143 2.286] 200\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Vj3q1mEGllQ"
      },
      "source": [
        "`solve` is the actual function which sets everything up and solves for the optimum solution\n",
        "\n",
        "\n",
        "`N` - is the number of intervals\n",
        "\n",
        "`T` - is the time per interval (we use this since we do linear approximation)\n",
        "\n",
        "`u` - empty list in which we will put every value in\n",
        "\n",
        "`x` - same as `u` except it's for all the state variables\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LY9oiTxt2UrT"
      },
      "source": [
        "The cost function it is tring to solve is defined as follows:\n",
        "\n",
        "$J(u, x) = l_w + \\int_0^{n+!}{l(x)dt}$ #This is wrong. Will fix later\n",
        "\n",
        "where $l_w$ is the final value and the integral is the value of $l(x))$, our cost function, being compared to our desired waypoints and our torque. Note, we use quadratic costs since they are guaranteed to have a minimum.\n",
        "\n",
        "Obviously, we can't actually compute this definite integral, so we solve it numerically using the approximation $f(n+1) = f(n) + f'(n) * T$ where $T$ is our change in time\n",
        "\n",
        "We also have constraints as follows:\n",
        "  - The starting point must be the same\n",
        "  - The voltage $\\in [-12, 12]$\n",
        "\n",
        "We also have costs we would like to minimize:\n",
        "  - waypoints at current location - desired current location. This is given a lot of weight since we desire this cost a lot\n",
        "  - We are also adding a cost on torque so the robot doesn't move in a way which is hard on the motors\n",
        "\n",
        "We then solve for this function, which takes a majority of the time, and get an output of $x$ and $u$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n1DNkVCCRm4K"
      },
      "source": [
        "#Note in the future may need to make all/some of waypoints constraints since intake can't even handle a few inches of error\n",
        "\n",
        "def solve():\n",
        "\n",
        "  #N = waypoints[-1, 1] + 1\n",
        "  N = waypoints[-1][1] + 1\n",
        "  T = 0.04 #Frequency robot runs at\n",
        "  prog = MathematicalProgram()\n",
        "\n",
        "  u = np.empty((2, N-1), dtype=Variable)\n",
        "  x = np.empty((5, N), dtype=Variable)\n",
        "  curvature = np.empty((1, N), dtype=Variable)\n",
        "\n",
        "  for n in range(N-1):\n",
        "    #Creating the variables that we need to solve for\n",
        "    u[:,n] = prog.NewContinuousVariables(2, 'u' + str(n))\n",
        "    x[:,n] = prog.NewContinuousVariables(5, 'x' + str(n))\n",
        "    curvature[0,n] = prog.NewContinuousVariables(1, 'c' + str(n))\n",
        "\n",
        "    #Placing initial guesses on all of them\n",
        "    prog.SetInitialGuess(u[:,n], np.zeros_like(u[:,n]))\n",
        "    prog.SetInitialGuess(x[:,n], np.zeros_like(x[:,n]))\n",
        "  x[:,N-1] = prog.NewContinuousVariables(5, 'x' + str(N))\n",
        "  prog.SetInitialGuess(u, np.ones((2,N-1))*12)\n",
        "\n",
        "  #Constrain the first point so the robot must be there\n",
        "  prog.AddBoundingBoxConstraint(waypoints[0][0], waypoints[0][0], x[:,waypoints[0][1]])\n",
        "\n",
        "  for n in range(0, N-1):\n",
        "    #Adding constraints to how far the robot can move, the max voltage, and the curvature\n",
        "    prog.AddConstraint(eq(x[:,n+1], x[:,n]+model(x[:,n], u[:,n])*T))\n",
        "    prog.AddBoundingBoxConstraint(-12, 12, u[:,n]) \n",
        "    prog.AddConstraint(eq(x[4, n], x[3, n] * curvature[0, n]))\n",
        "    prog.AddQuadraticCost(100*(curvature[0,n].dot(curvature[0,n])))\n",
        "\n",
        "    v = x[3,n]\n",
        "    torque = np.array([getWheelTorque(u[0,n], getWheelVelocity(x[3,n], x[4,n], False)), getWheelTorque(u[1,n], getWheelVelocity(x[3,n], x[4,n], True))])\n",
        "    prog.AddQuadraticCost(1000*torque.dot(torque))\n",
        "    prog.AddConstraint(ge(v, np.array([0])))\n",
        "\n",
        "  for i in range(len(waypoints)):\n",
        "    #Constaining every waypoint so the robot must land there\n",
        "    \n",
        "    #prog.AddBoundingBoxConstraint(waypoints[i][0] - np.ones(len(waypoints[i][0]))*0, waypoints[i][0]+np.ones(len(waypoints[i][0]))*0, x[:len(waypoints[i][0]),waypoints[i][1]])\n",
        "    prog.AddBoundingBoxConstraint(waypoints[i][0], waypoints[i][0], x[:len(waypoints[i][0]),waypoints[i][1]])\n",
        "    '''num = waypoints[i][0] - x[:len(waypoints[i][0]), waypoints[i][1]]\n",
        "    prog.AddQuadraticCost(100000 * (num).dot(num))'''\n",
        "\n",
        "  \n",
        "    \n",
        "  result = Solve(prog)\n",
        "\n",
        "  x_sol = result.GetSolution(x)\n",
        "  u_sol = result.GetSolution(u)\n",
        "\n",
        "  assert(result.is_success()), \"Optimization failed\"\n",
        "\n",
        "  return x_sol, u_sol, N, T\n",
        "\n",
        "  print(x_sol)\n",
        "  print(u_sol)"
      ],
      "execution_count": 957,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qF0qnTOBRqy8"
      },
      "source": [
        "x_sol, u_sol, N, T = solve()"
      ],
      "execution_count": 958,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-1oUtWFvG9uH"
      },
      "source": [
        "Here we are splitting `x_sol` into it's x and y parts (note: it has more information but for a graph, this is enough)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aopOYEmqRrYf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        },
        "outputId": "da32c27b-f595-49e2-ab28-da7062e4662a"
      },
      "source": [
        "x_coords = []\n",
        "y_coords = []\n",
        "theta = []\n",
        "velocity = []\n",
        "angular_velocity = []\n",
        "\n",
        "for i in range(N):\n",
        "  x_coords.append((float)(\"%.4f\" % (3.28084 * x_sol[0,i])))\n",
        "  y_coords.append((float)(\"%.4f\" % (3.28084 * x_sol[1,i])))\n",
        "  theta.append(x_sol[2,i])\n",
        "  velocity.append(x_sol[3,i])\n",
        "  angular_velocity.append(x_sol[4,i])\n",
        "#print(x_coords)\n",
        "#print(y_coords)\n",
        "\n",
        "x_points = []\n",
        "y_points = []\n",
        "for i in range(len(waypoints)):\n",
        "  x_points.append(3.28084 * waypoints[i][0][0])\n",
        "  y_points.append(3.28084 * waypoints[i][0][1])\n",
        "\n",
        "\n",
        "#print(u_sol)\n",
        "plt.plot(x_coords, y_coords, linewidth=2, label='trajectory')\n",
        "plt.title('Robot Trajectory in terms of x and y', c='white', fontsize=20)\n",
        "plt.xlabel(\"x position of robot\", c='white', fontsize=15) \n",
        "plt.ylabel(\"y position of robot\", c='white', fontsize=15) \n",
        "plt.scatter(x_points, y_points)\n",
        "print(\"Time taken: \" + str(T * waypoints[-1][1]) + \" seconds\")\n",
        "plt.xlim(0, 30)\n",
        "plt.ylim(0, 15)\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "\n",
        "prev = 0\n",
        "for i in x_coords:\n",
        "  #print(i-prev)\n",
        "  prev = i"
      ],
      "execution_count": 959,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Time taken: 8.0 seconds\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0SyCxL7-HIGq"
      },
      "source": [
        "This is doing the same thing but now for `u_sols`. It graphs the voltage each motor needs to apply at each time interval"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NXoKmnelj3Ep",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "outputId": "07ce0b3e-8383-4893-d01a-d17e4a5fb528"
      },
      "source": [
        "left = []\n",
        "right = []\n",
        "\n",
        "for i in range(N-1):\n",
        "  left.append((float)(\"%.4f\" % u_sol[0, i]))\n",
        "  right.append((float)(\"%.4f\" % u_sol[1, i]))\n",
        "\n",
        "time = []\n",
        "for i in range(N-1):\n",
        "  time.append(i * T)\n",
        "\n",
        "plt.plot(time, left, label=\"Left Motor\", linewidth=2)\n",
        "plt.plot(time, right, label=\"Right Motor\", linewidth=2)\n",
        "\n",
        "\n",
        "plt.title(\"Voltage each motor must apply\", fontsize=20, c='white')\n",
        "plt.xlabel('Time', fontsize=15, c='white')\n",
        "plt.ylabel('Voltage', fontsize=15, c='white')\n",
        "plt.legend()\n",
        "plt.grid()\n"
      ],
      "execution_count": 960,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pgke5PG4rB3U",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "e9f9e9c6-48be-4ddb-a357-c9933db57854"
      },
      "source": [
        "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=False, sharey=False)\n",
        "\n",
        "ax1.plot(time, left, label=\"Left Motor\", linewidth=2)\n",
        "ax1.plot(time, right, label=\"Right Motor\", linewidth=2)\n",
        "\n",
        "time_2 = time.copy()\n",
        "time_2.append((N-1) * T)\n",
        "ax2.plot(time_2, theta)\n",
        "\n",
        "ax3.plot(time_2, velocity)\n",
        "\n",
        "ax4.plot(time_2, angular_velocity)\n",
        "\n",
        "print(\"Time taken: \" + (str)(time_2[-1]))\n",
        "#ax1.title(\"Voltage each motor must apply\", fontsize=20, c='white')\n",
        "ax1.set(xlabel='Time', ylabel='Voltage')\n",
        "ax2.set(xlabel='Time', ylabel='Theta')\n",
        "ax3.set(xlabel='Time', ylabel='Velocity')\n",
        "ax4.set(xlabel='Time', ylabel='Angular Velocity')\n",
        "#ax1.xlabel('Time', fontsize=15, c='white')\n",
        "#ax1.ylabel('Voltage', fontsize=15, c='white')\n",
        "ax1.legend()\n",
        "ax1.grid()\n",
        "\n",
        "for i in range(len(x_coords)):\n",
        "  x_temp = x_coords[i]\n",
        "  x_coords[i] = -y_coords[i]\n",
        "  y_coords[i] = x_temp\n"
      ],
      "execution_count": 961,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Time taken: 8.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EhOhh1hH0HF1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "outputId": "a7d95731-e13b-44d7-df67-8d5522441fa2"
      },
      "source": [
        "plt.plot(x_coords, y_coords)\n",
        "print(x_coords[0])\n",
        "print(y_coords[0])\n",
        "x_0 = x_coords[0]\n",
        "y_0 = y_coords[0]"
      ],
      "execution_count": 962,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-2.5\n",
            "3.75\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qx4tjc0zHOpB"
      },
      "source": [
        "with open('Slalom_new.tsv', 'w') as writefile:\n",
        "    for i in range(len(x_coords)):\n",
        "      writefile.write(\"%.4f\" %(x_coords[i] - x_0) + \"\\t\" + \"%.4f\" %(y_coords[i] - y_0)  + \"\\t\" + (\"%.2f\" % (T*i)) + \"\\n\")\n",
        "      x_coords[i] = x_coords[i] - x_0\n",
        "      y_coords[i] = y_coords[i] - y_0\n",
        "      #print((str)(x_coords[i]) + \", \" + (str)(y_coords[i])  + \", \" + (str)(\"%.2f\" % (T*i)) + \"\\n\")\n",
        "    \n",
        "with open('voltages.txt', 'w') as writefile:\n",
        "    for i in range(len(left)):\n",
        "      writefile.write((str)(left[i]) + \", \" + (str)(right[i])  + \", \" + \"\\n\")"
      ],
      "execution_count": 963,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pD8ynvWze_VC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "62ef6a58-8599-4895-b274-7c8737638005"
      },
      "source": [
        "plt.scatter(x_coords, y_coords)"
      ],
      "execution_count": 964,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f29e7c6ef90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 964
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m9EpokvzyxT0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f0e28704-8ac7-4d68-8515-808aeb0f58a7"
      },
      "source": [
        "print(\"Summary: \")\n",
        "print(\"\\t drive train info:\")\n",
        "print(\"\\t\\tMotors used: Falcons\")\n",
        "print(\"\\t\\tGear ratio: \" + str(gear_ratio))\n",
        "print(\"\\t\\tMOI: \" + str(I))\n",
        "print(\"\\t\\tWheel radius: \" + str(r_wheel))\n",
        "print(\"\\t\\tBot radius: \" + str(r_bot))\n",
        "print(\"\\t\\tMass: \" + str(m))\n",
        "print(\"\\t Performance info:\")\n",
        "print(\"\\t\\tNumber of waypoints: \" + str(len(waypoints)))\n",
        "print(\"\\t\\tSteps taken: \" + str(waypoints[-1][1]))\n",
        "print(\"\\t\\tTime taken: \" + str(time_2[-1]) + \" seconds\")\n",
        "print(\"\\t\\tEnding velocity: \" + str(x_sol[3,-1]) + \" m/s\")\n",
        "print(\"\\t\\tEnding Angular Velocity: \" + str(x_sol[4,-1]) + \" r/s\")\n",
        "print(\"\\t\\tEnding Angule (radians): \" + str(x_sol[2,-1]) + \" r\")"
      ],
      "execution_count": 965,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Summary: \n",
            "\t drive train info:\n",
            "\t\tMotors used: Falcons\n",
            "\t\tGear ratio: 8.952551477170994\n",
            "\t\tMOI: 11.338333333333333\n",
            "\t\tWheel radius: 0.0762\n",
            "\t\tBot radius: 0.5\n",
            "\t\tMass: 68.03\n",
            "\t Performance info:\n",
            "\t\tNumber of waypoints: 10\n",
            "\t\tSteps taken: 200\n",
            "\t\tTime taken: 8.0 seconds\n",
            "\t\tEnding velocity: 2.4550335731573316 m/s\n",
            "\t\tEnding Angular Velocity: -0.3936833258340126 r/s\n",
            "\t\tEnding Angule (radians): 2.2416875298110384 r\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L2IMWP0KuU_h"
      },
      "source": [
        ""
      ],
      "execution_count": 965,
      "outputs": []
    }
  ]
}