Assignment3_2DDrone_simulation.ipynb

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    "colab": {
      "name": "Assignment3_2DDrone_simulation.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOlxcDMO1A3cTubx58iH+fU",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/amit-420/Ivlabs_summer_project-/blob/master/Assignment3_2DDrone_simulation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xo5hbS0bXvCp",
        "colab_type": "code",
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          "base_uri": "https://localhost:8080/",
          "height": 766
        },
        "outputId": "42307408-7dd4-430b-bb08-9740f42a7670"
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      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "import math\n",
        "import matplotlib.animation as animation \n",
        "\n",
        "'''\n",
        "The 2D quadcoptor model can be modelled as:\n",
        "\n",
        "z'' = -g + (u1/m) * cos(phi)Q                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \n",
        "\n",
        "y'' = -(u1/m) * sin(phi)\n",
        "\n",
        "phi'' = u2 * 1/ I_xx\n",
        "\n",
        "The values of the drone are picked up from the Aerial Robotics Course.\n",
        "'''\n",
        "##--------QUADROTOR MODEL-----------###\n",
        "\n",
        "class Quadrotor:\n",
        "    \n",
        "    \n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.MASS = 0.1800\n",
        "        self.GRAVITY = 9.81\n",
        "        self.Ixx = 0.00025\n",
        "        self.maxF = 3.5316\n",
        "        self.minF = 0.0\n",
        "        self.initial_state = [0,0,0,0,0,0]          #the initial state vector contains all the state and their dervitaive\n",
        "                                                    #The self.initial_state wil be a 1*6 vector.\n",
        "        self.current_state = self.initial_state\n",
        "    \n",
        "    def dynamics(self,state,t,u):\n",
        "        z,y,phi,zdot,ydot,phidot = state    #Unpack the state vector\n",
        "        u1 , u2 = u                         #Unpack the input vector 'u' into thrust and moment vectors\n",
        "    \n",
        "        # state_derivative = [zdot, ydot, phidot, \n",
        "        #                     -self.GRAVITY + (u1/self.MASS) * 1,\n",
        "        #                     -(u1/self.MASS)*(phi), \n",
        "        #                     u2/self.Ixx]\n",
        "\n",
        "        state_derivative = [zdot, ydot, phidot, \n",
        "                            -self.GRAVITY + (u1/self.MASS) * 1,\n",
        "                            -(u1/self.MASS)*(phi), \n",
        "                            u2/self.Ixx]\n",
        "                                            #Writing the derivative function as per the quadc model for odeint\n",
        "        return state_derivative\n",
        "    \n",
        "def simulate(TUNING_MATRIX,t):\n",
        "    solvedState = Drone.initial_state\n",
        "    timepoints = len(t)\n",
        "    Kp_z, Kd_z , Ki_z = TUNING_MATRIX[0,:]\n",
        "    Kp_y, Kd_y , Ki_y = TUNING_MATRIX[1,:]\n",
        "    Kp_th, Kd_th , Ki_th = TUNING_MATRIX[2,:]\n",
        "    # ------Added intial conditions----- # \n",
        "    int_e_z = 0\n",
        "    int_e_y = 0\n",
        "    int_e_th = 0\n",
        "    sucess = False\n",
        "    delta = 0.0075\n",
        "    #-----------------#\n",
        "\n",
        "    for i in range(1,timepoints):\n",
        "        \n",
        "        int_e_z += (des_state[0]-Drone.current_state[0])\n",
        "        u1 = Drone.MASS * ( Drone.GRAVITY + \n",
        "                            Kd_z * (des_state[2] - Drone.current_state[3]) +\n",
        "                            Kp_z * (des_state[0] - Drone.current_state[0]) + #y'' = -(u1/m) * sin(phi)\n",
        "                            Ki_z * (int_e_z)\n",
        "                            )\n",
        "        int_e_y += (des_state[1]-Drone.current_state[1])\n",
        "        phi_c = (-1/Drone.GRAVITY) * (Kd_y * (des_state[3] - Drone.current_state[4]) +\n",
        "                                      Kp_y * (des_state[1] - Drone.current_state[1]) +\n",
        "                                      Ki_y * (int_e_y))\n",
        "        int_e_th += (des_state[1]-Drone.current_state[1])    \n",
        "        u2 = Drone.Ixx * (Kd_th * (-1 * Drone.current_state[5]) +\n",
        "                          Kp_th * (phi_c - Drone.current_state[2]) +\n",
        "                          Ki_th * (int_e_th))  #phi'' = u2 * 1/ I_xx  z'' = -g + (u1/m) * cos(phi)Q \n",
        "\n",
        "        #-----changes for taking into account actuators have limited thrust transmission capacity ----#                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \n",
        "        if u1 >= Drone.maxF:\n",
        "          u1 = Drone.maxF\n",
        "        #----------------------------#\n",
        "        u = [u1,u2]  #The input vector 'u' into thrust and moment vectors\n",
        "        # print(u1)         \n",
        "        # temp = odeint(self.dynamics,self.current_state,t,args=(u[i],))\n",
        "        # self.current_state = temp[1,:]\n",
        "        Drone.current_state = odeint(Drone.dynamics,Drone.current_state,t,args=(u,))[1,:]\n",
        "        #solvedState = np.append(solvedState,Drone.current_state, axis=0)\n",
        "        solvedState = np.vstack((solvedState,Drone.current_state))\n",
        "        \n",
        "        #---- changes for outputing simulation success -----#\n",
        "        if des_state[0] - delta <= Drone.current_state[0] <= des_state[0]+ delta and des_state[1] - delta <= Drone.current_state[1] <= des_state[1]+ delta:\n",
        "          sucess = True\n",
        "        else:\n",
        "          sucess = False\n",
        "        \n",
        "        if sucess == True:\n",
        "          print('simulation successful')\n",
        "        # ------------------------------------#\n",
        "    return solvedState\n",
        "\n",
        "def plotResults(solvedState,t):\n",
        "    #----- Changes for animating 2D drone ------#\n",
        "    fig = plt.figure()  \n",
        "    axis = plt.axes(xlim =(-0.1,2.1 ),ylim =(-0.1, 1.2))   \n",
        "    line, = axis.plot([], [], lw = 2)\n",
        "    def init():  \n",
        "      line.set_data([], [])  \n",
        "      return line,    \n",
        "    def animate(i):\n",
        "      angle = solvedState[i,2]\n",
        "      l_cos = 0.03*np.cos(angle)\n",
        "      l_sin = 0.03*np.sin(angle)\n",
        "      line.set_data([solvedState[i,1]- l_cos,solvedState[i,1]+ l_cos],[solvedState[i,0] - l_sin,solvedState[i,0] + l_sin])\n",
        "      return line,\n",
        "\n",
        "    anim = animation.FuncAnimation(fig, animate,init_func = init, frames = 900, \n",
        "                            interval = 10,  \n",
        "                            blit = True)\n",
        "    anim.save('2DDrone.mp4', writer = 'ffmpeg', fps = 30)\n",
        "    #---------------------------------------#\n",
        "    \n",
        "    plt.plot(solvedState[:,1],solvedState[:,0],'g:',label = 'Z_Y')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "    plt.plot(t,solvedState[:,0],'b:',label = 'Z_T')\n",
        "    plt.plot(t,solvedState[:,1],'r:',label = 'Y_T')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "    \n",
        "    plt.plot(t,solvedState[:,2],'r:',label = 'Phi_T')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "    return None\n",
        "    \n",
        "# Simulation Time Parameters\n",
        "simulation_time = 20 # seconds\n",
        "time_points = simulation_time * 100 + 1\n",
        "t = np.linspace(0,simulation_time,time_points)\n",
        "\n",
        "\n",
        "des_state = np.array([1,2,0,0,0,0]) # z,y,zdot,ydot,zdotdot,y dotdot\n",
        "\n",
        "Drone = Quadrotor()\n",
        "TUNING_MATRIX = np.array([\n",
        "    [8.5,5.5,0.003], #z\n",
        "    [1.619,1.98,0.001], #y\n",
        "    [117,17,0.01]  #phi\n",
        "])\n",
        "\n",
        "solvedState = simulate(TUNING_MATRIX,t)\n",
        "\n",
        "plotResults(solvedState,t)\n",
        "\n",
        "        "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}