Afrel 楕円コース PID制御 パラメータチューニング(twiddle)

twiddle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Afrel 楕円コース PID制御 パラメータチューニング(twiddle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from homework5_4.task import robot\n",
    "from math import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 楕円コース\n",
    "\n",
    "- [楕円コース | すべての商品 | | 教育版LEGO MINDSTORMS正規代理店 アフレル](http://afrel-shop.com/shopdetail/007001000018/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius = 13.5\n",
    "height = 9.0\n",
    "width = 29.0\n",
    "params = [1.0, 10.0, 0.01]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_track = [cos((t * pi / 200) + (pi / 2)) * radius + radius for t in range(100)] + \\\n",
    "          [cos((t * pi / 200) + pi) * radius + radius for t in range(100)] + \\\n",
    "          [cos((t * pi / 200) + (3.0 * pi / 2)) * radius + radius + width for t in range(100)] + \\\n",
    "          [cos((t * pi / 200)) * radius + radius + width for t in range(100)] + \\\n",
    "          [radius]\n",
    "\n",
    "y_track = [sin((t * pi / 200) + (pi / 2)) * radius + radius + height for t in range(100)] + \\\n",
    "          [sin((t * pi / 200) + pi) * radius + radius for t in range(100)] + \\\n",
    "          [sin((t * pi / 200) + (3.0 * pi / 2)) * radius + radius for t in range(100)] + \\\n",
    "          [sin((t * pi / 200)) * radius + radius + height for t in range(100)] + \\\n",
    "          [radius * 2.0 + height]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uueceunXrxvz58ylVqpTXkXKl0BY6QIsWLVi5ciWlSpWiY8eOLF++3OtIIhJC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1df56d8b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x_track, y_track, 'k-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running a robotic car"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_path = [0.0, ]\n",
    "y_path = [radius, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "myrobot = robot()\n",
    "myrobot.set(0.0, radius, pi / 2.0)\n",
    "speed = 1.0\n",
    "err = 0.0\n",
    "int_crosstrack_error = 0.0\n",
    "N = 100\n",
    "\n",
    "crosstrack_error = myrobot.cte(radius, width, height)\n",
    "\n",
    "for i in range(N * 2):\n",
    "    diff_crosstrack_error = - crosstrack_error\n",
    "    crosstrack_error = myrobot.cte(radius, width, height)\n",
    "    diff_crosstrack_error += crosstrack_error\n",
    "    int_crosstrack_error += crosstrack_error\n",
    "    steer = - params[0] * crosstrack_error \\\n",
    "            - params[1] * diff_crosstrack_error \\\n",
    "            - params[2] * int_crosstrack_error\n",
    "    myrobot = myrobot.move(steer, speed)\n",
    "    if i >= N:\n",
    "        err += crosstrack_error ** 2\n",
    "    x_path.append(myrobot.x)\n",
    "    y_path.append(myrobot.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1ZBLS6aBnvn597QdCY7PaYrkmy6nPmTOLvr600i8iMi0PPPAAr371q0mnF4W+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\nAw/IOJe7AtwyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1df360d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_track, y_track, 'k-', x_path, y_path, 'bo')\n",
    "plt.axis([-radius * 0.1, 2.1 * radius + width, -radius * 0.1, 2.1 * radius + height])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Twiddle\n",
    "- [Twiddle - Artificial Intelligence for Robotics - YouTube](https://www.youtube.com/watch?v=2uQ2BSzDvXs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run(params, printflag=False):\n",
    "    myrobot = robot()\n",
    "    myrobot.set(0.0, 1.0, 0.0)\n",
    "    speed = 1.0\n",
    "    err = 0.0\n",
    "    int_crosstrack_error = 0.0\n",
    "    N = 100\n",
    "    # myrobot.set_noise(0.1, 0.0)\n",
    "    myrobot.set_steering_drift(10.0 / 180.0 * pi)  # 10 degree steering error\n",
    "\n",
    "    crosstrack_error = myrobot.y\n",
    "\n",
    "    for i in range(N * 2):\n",
    "\n",
    "        diff_crosstrack_error = myrobot.y - crosstrack_error\n",
    "        crosstrack_error = myrobot.y\n",
    "        int_crosstrack_error += crosstrack_error\n",
    "\n",
    "        steer = - params[0] * crosstrack_error \\\n",
    "                - params[1] * diff_crosstrack_error \\\n",
    "                - int_crosstrack_error * params[2]\n",
    "        myrobot = myrobot.move(steer, speed)\n",
    "        if i >= N:\n",
    "            err += (crosstrack_error ** 2)\n",
    "        if printflag:\n",
    "            print(myrobot, steer)\n",
    "    return err / float(N)\n",
    "\n",
    "\n",
    "def twiddle(tol=0.001):  #Make this tolerance bigger if you are timing out!\n",
    "    p = [0, 0, 0]\n",
    "    dp = [1, 1, 1]\n",
    "\n",
    "    best_error = run(p)\n",
    "    n = 0\n",
    "    # sum = integral of the cross track error\n",
    "    while sum(dp) > tol:\n",
    "        print(\"Iteration {}, best error = {}\".format(n, best_error))\n",
    "        for i in range(len(p)):\n",
    "            p[i] += dp[i]\n",
    "            err = run(p)\n",
    "            if err < best_error:\n",
    "                # error is better than our best error\n",
    "                best_error = err\n",
    "                dp[i] *= 1.1\n",
    "            else:\n",
    "                # error is not better than before\n",
    "                # try other directions\n",
    "                p[i] -= 2.0 * dp[i]\n",
    "                err = run(p)\n",
    "                if err < best_error:\n",
    "                    best_error = err\n",
    "                    dp[i] *= 1.1\n",
    "                else:\n",
    "                    # did not succeed - decrease increments\n",
    "                    p[i] += dp[i]\n",
    "                    dp[i] *= 0.9\n",
    "        n += 1\n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0, best error = 8315.955485215645\nIteration 1, best error = 0.044546416135712856\nIteration 2, best error = 0.030667733375864255\nIteration 3, best error = 0.03046869606124707\nIteration 4, best error = 0.008518880324802245\nIteration 5, best error = 0.008518668206935719\nIteration 6, best error = 0.008518667701338564\nIteration 7, best error = 0.008518667701338564\nIteration 8, best error = 0.008518667701338564\nIteration 9, best error = 0.00851866770043554\nIteration 10, best error = 0.00851866770043554\nIteration 11, best error = 9.36429057863156e-13\nIteration 12, best error = 8.118576224499871e-15\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 13, best error = 8.118576224499871e-15\nIteration 14, best error = 8.118576224499871e-15\nIteration 15, best error = 8.118576224499871e-15\nIteration 16, best error = 8.118576224499871e-15\nIteration 17, best error = 8.118576224499871e-15\nIteration 18, best error = 8.118576224499871e-15\nIteration 19, best error = 5.8949635515091935e-15\nIteration 20, best error = 2.935905344458206e-18\nIteration 21, best error = 2.935905344458206e-18\nIteration 22, best error = 2.935905344458206e-18\nIteration 23, best error = 1.240039961130423e-18\nIteration 24, best error = 1.240039961130423e-18\nIteration 25, best error = 1.240039961130423e-18\nIteration 26, best error = 7.043395458551602e-19\nIteration 27, best error = 6.448015619853438e-20\nIteration 28, best error = 6.448015619853438e-20\nIteration 29, best error = 6.448015619853438e-20\nIteration 30, best error = 6.448015619853438e-20\nIteration 31, best error = 4.91946882072856e-21\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 32, best error = 4.91946882072856e-21\nIteration 33, best error = 9.615713358638735e-23\nIteration 34, best error = 9.615713358638735e-23\nIteration 35, best error = 9.615713358638735e-23\nIteration 36, best error = 9.615713358638735e-23\nIteration 37, best error = 9.615713358638735e-23\nIteration 38, best error = 9.615713358638735e-23\nIteration 39, best error = 9.615713358638735e-23\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 40, best error = 9.615713358638735e-23\nIteration 41, best error = 9.615713358638735e-23\nIteration 42, best error = 9.615713358638735e-23\nIteration 43, best error = 9.615713358638735e-23\nIteration 44, best error = 9.615713358638735e-23\nIteration 45, best error = 9.615713358638735e-23\nIteration 46, best error = 9.615713358638735e-23\nIteration 47, best error = 9.615713358638735e-23\nIteration 48, best error = 9.615713358638735e-23\nIteration 49, best error = 9.615713358638735e-23\nIteration 50, best error = 9.615713358638735e-23\nIteration 51, best error = 9.615713358638735e-23\nIteration 52, best error = 9.615713358638735e-23\nIteration 53, best error = 9.615713358638735e-23\nIteration 54, best error = 9.615713358638735e-23\nIteration 55, best error = 9.615713358638735e-23\nIteration 56, best error = 9.615713358638735e-23\nIteration 57, best error = 9.615713358638735e-23\nIteration 58, best error = 9.615713358638735e-23"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\nIteration 59, best error = 9.615713358638735e-23\nIteration 60, best error = 9.615713358638735e-23\nIteration 61, best error = 9.615713358638735e-23\nIteration 62, best error = 9.615713358638735e-23\nIteration 63, best error = 9.615713358638735e-23\nIteration 64, best error = 9.615713358638735e-23\nIteration 65, best error = 9.615713358638735e-23\nIteration 66, best error = 9.615713358638735e-23\nIteration 67, best error = 9.615713358638735e-23\nIteration 68, best error = 9.615713358638735e-23\nIteration 69, best error = 9.615713358638735e-23\nIteration 70, best error = 8.52429893895755e-23\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 71, best error = 8.52429893895755e-23\nIteration 72, best error = 6.89583556100888e-23\nIteration 73, best error = 6.89583556100888e-23\nIteration 74, best error = 6.89583556100888e-23\nIteration 75, best error = 4.145006145539035e-23\nIteration 76, best error = 4.145006145539035e-23\nIteration 77, best error = 4.145006145539035e-23\nIteration 78, best error = 4.145006145539035e-23\nIteration 79, best error = 2.5204962731676635e-23\nIteration 80, best error = 2.5204962731676635e-23\nIteration 81, best error = 2.5204962731676635e-23\nIteration 82, best error = 2.2815797166143525e-23\nIteration 83, best error = 2.2815797166143525e-23\nIteration 84, best error = 1.8528427475010002e-23\nIteration 85, best error = 1.692511989245343e-23\nIteration 86, best error = 1.4714089527272985e-23\nIteration 87, best error = 1.4714089527272985e-23\nIteration 88, best error = 1.4714089527272985e-23\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 89, best error = 1.0446065646529456e-23\nIteration 90, best error = 1.0446065646529456e-23\nIteration 91, best error = 7.068232261492995e-24\nIteration 92, best error = 6.284762759979449e-24\nIteration 93, best error = 6.284762759979449e-24\nIteration 94, best error = 5.217848562917681e-24\nIteration 95, best error = 4.838097998336666e-24\nIteration 96, best error = 4.352319633069647e-24\nIteration 97, best error = 4.352319633069647e-24\nIteration 98, best error = 4.352319633069647e-24\nIteration 99, best error = 3.25800247296385e-24\nIteration 100, best error = 3.115690350598778e-24\nIteration 101, best error = 1.7799813352217147e-24\nIteration 102, best error = 1.7799813352217147e-24\nIteration 103, best error = 1.7799813352217147e-24\nIteration 104, best error = 1.6110446580330185e-24\nIteration 105, best error = 1.444549485191908e-24\nIteration 106, best error = 1.444549485191908e-24\nIteration 107, best error = 9.355395139345826e-25\nIteration 108, best error = 9.355395139345826e-25\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1.666025810674142, 7.575994288835168, 0.1650652674944419]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = twiddle()\n",
    "params"
   ]
  }
 ],
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