Simulateur du robot de GEL-3014 / GLO-3013

Design 3 -- Simulateur Robot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "\n",
    "import numpy as np\n",
    "from numpy import maximum as max, minimum as min, cos, sin, ones, zeros\n",
    "from matplotlib.pyplot import figure, plot, subplot, grid, xlabel, ylabel, show\n",
    "from scipy.integrate import ode, odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eqns_diff(x, t, U1, U2, U3, U4):\n",
    "\n",
    "    # La sortie doit être un vecteur colonne\n",
    "    d_x = zeros((8,))\n",
    "\n",
    "    # Paramètres\n",
    "    R = 0.032\n",
    "    Ktheta = 8\n",
    "    tautheta = .0025\n",
    "    J = Ktheta*tautheta # inertie du robot en rotation\n",
    "    Kth = 1/Ktheta      # coeff friction en rotation\n",
    "    K1 = 0.14           # gain de (vit ang roue 1)/(PWM 1) \n",
    "    K2 = 0.16           # gain de (vit ang roue 2)/(PWM 2) \n",
    "    K3 = 0.14           # gain de (vit ang roue 3)/(PWM 3) \n",
    "    K4 = 0.15           # gain de (vit ang roue 4)/(PWM 4) \n",
    "    Tau1 = 0.22         # constante de temps de (vit ang roue 1)/(PWM 1) \n",
    "    Tau2 = 0.24         # constante de temps de (vit ang roue 2)/(PWM 2)  \n",
    "    Tau3 = 0.25         # constante de temps de (vit ang roue 3)/(PWM 3) \n",
    "    Tau4 = 0.24         # constante de temps de (vit ang roue 4)/(PWM 4)   \n",
    "    Kw = 1e-2           # coefficient définissant la force appliqué par les roues sur le robot: Fi = Kw*wi\n",
    "    usat = 100          # niveau de saturation des signaux PWM\n",
    "\n",
    "    # Saturation des signaux PWM\n",
    "    U1 = max(min(U1, usat), -usat)\n",
    "    U2 = max(min(U2, usat), -usat)\n",
    "    U3 = max(min(U3, usat), -usat)\n",
    "    U4 = max(min(U4, usat), -usat)\n",
    "\n",
    "    # Équations d'états\n",
    "    d_x[0]=(1/Tau1)*(K1*U1-x[0])\n",
    "    d_x[1]=(1/Tau2)*(K2*U2-x[1])\n",
    "    d_x[2]=(1/Tau3)*(K3*U3-x[2])\n",
    "    d_x[3]=(1/Tau4)*(K4*U4-x[3])\n",
    "    Vt = 0.5*R*(-x[0] + x[2])\n",
    "    Vn = 0.5*R*(x[3] - x[1])\n",
    "    d_x[4] = x[5]\n",
    "    d_x[5] = Kw*(x[0] + x[1] + x[2] + x[3])/J - Kth*x[5]/J;\n",
    "    d_x[6] = Vt*cos(x[4]) - Vn*sin(x[4])\n",
    "    d_x[7] = Vt*sin(x[4]) + Vn*cos(x[4])\n",
    "\n",
    "    return d_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simuler():\n",
    "\n",
    "    # Paramètres de simulation\n",
    "    Ts = 0.01                           # Période D'échantillonnage [s]\n",
    "    Tf = 10                             # Durée de la simulation [s]\n",
    "    temps = np.arange(0, Tf + Ts, Ts)   # Vecteur temps\n",
    "    N = len(temps)                      # Nombre de points de la simulation\n",
    "    R = 0.032                           # Rayon des roues\n",
    "\n",
    "    # Signaux PWM [%]\n",
    "    u1 = np.concatenate((zeros((5,)), -50*ones((N-5,))))\n",
    "    u2 = np.concatenate((zeros((5,)), 0*ones((N-5,))))\n",
    "    u3 = np.concatenate((zeros((5,)), 50*ones((N-5,))))\n",
    "    u4 = np.concatenate((zeros((5,)), 0*ones((N-5,))))\n",
    "    \n",
    "    # Initialisation\n",
    "    CI = zeros((8,))\n",
    "    data = zeros((8, N))\n",
    "\n",
    "    # Boucle de simulation\n",
    "    for i in range(N):\n",
    "        U1, U2, U3, U4 = u1[i], u2[i], u3[i], u4[i]\n",
    "\n",
    "        #solver = ode(fun).set_integrator('dopri5') # Utiliser Runge-Kutta ordre (4)5\n",
    "\n",
    "        sol = odeint(eqns_diff, CI, temps[i:i+2], args=(U1, U2, U3, U4))\n",
    "        CI = sol[-1,:]\n",
    "        data[:, i] = CI\n",
    "\n",
    "    return temps, u1, u2, u3, u4, data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def figures(temps, u1, u2, u3, u4, data):\n",
    "\n",
    "    posx = data[6,:]\n",
    "    posy = data[7,:]\n",
    "    theta = data[4,:]\n",
    "    theta_point = data[5,:]\n",
    "    w1 = data[0,:]\n",
    "    w2 = data[1,:]\n",
    "    w3 = data[2,:]\n",
    "    w4 = data[3,:]\n",
    "\n",
    "    figure(1)\n",
    "    subplot(4,1,1); plot(temps,u1); grid(); xlabel('Temps'); ylabel('U1')\n",
    "    subplot(4,1,2); plot(temps,u2); grid(); xlabel('Temps'); ylabel('U2')\n",
    "    subplot(4,1,3); plot(temps,u3); grid(); xlabel('Temps'); ylabel('U3')\n",
    "    subplot(4,1,4); plot(temps,u4); grid(); xlabel('Temps'); ylabel('U4')\n",
    "\n",
    "    figure(2)\n",
    "    subplot(4,1,1); plot(temps,w1); grid(); xlabel('Temps'); ylabel('w1')\n",
    "    subplot(4,1,2); plot(temps,w2); grid(); xlabel('Temps'); ylabel('w2')\n",
    "    subplot(4,1,3); plot(temps,w3); grid(); xlabel('Temps'); ylabel('w3')\n",
    "    subplot(4,1,4); plot(temps,w4); grid(); xlabel('Temps'); ylabel('w4')\n",
    "\n",
    "    figure(3)\n",
    "    subplot(3,1,1); plot(temps,theta); grid(); xlabel('Temps'); ylabel('theta')\n",
    "    subplot(3,1,2); plot(temps,posx); grid(); xlabel('Temps'); ylabel('x')\n",
    "    subplot(3,1,3); plot(temps,posy); grid(); xlabel('Temps'); ylabel('y')\n",
    "\n",
    "    figure(4)\n",
    "    plot(posx,posy); grid(); xlabel('x'); ylabel('y')\n",
    "\n",
    "    show()\n",
    "\n",
    "\n",
    "def ecrire_csv(temps, u1, u2, u3, u4, data):\n",
    "\n",
    "    with open('simulation.csv', 'w', newline='') as csvfile:\n",
    "        w = csv.writer(csvfile)\n",
    "        w.writerow([\"temps\", \"u1\", \"u2\", \"u3\", \"u4\", \"w1\", \"w2\", \"w3\", \"w4\", \"theta\", \"theta_point\", \"posx\", \"posy\"])\n",
    "        for i in range(len(temps)):\n",
    "            w.writerow([temps[i], u1[i], u2[i], u3[i], u4[i]] + data[:,i].tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7f0925908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7f0d1e7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7f0e0c1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7f0ea9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def main():\n",
    "    simulation = simuler()\n",
    "\n",
    "    ecrire_csv(*simulation)\n",
    "    figures(*simulation)\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
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