{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 確率ロボティクス2016第3回\n",
    "\n",
    "上田隆一\n",
    "\n",
    "2016年10月4日@千葉工業大学\n",
    "\n",
    "## モンテカルロ法による$bel$の計算\n",
    "\n",
    "* 発想: 前回の移動ロボットのシミュレーションをロボット（エージェント）が行う。\n",
    "  * 一挙にたくさん並列で\n",
    "  * 状態遷移のシミュレーション\n",
    "* 一つ時刻0の状態$\\boldsymbol{x}_0$を選んで、制御出力に合わせて移動\n",
    "  * 誤差を混入\n",
    "* 一つのシミュレーションの状態を、$bel$からサンプリングされる標本（サンプル）とみなすことができる\n",
    "  * 「粒子（パーティクル）」という言い方も"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## モンテカルロ法のプログラミング\n",
    "\n",
    "* 前回の移動ロボットの動作をふまえて\n",
    "  * 実際のロボットの動き（のシミュレーションを作る）\n",
    "  * パーティクルの動きを作る\n",
    "    * 数は100個にしましょう。\n",
    "\n",
    "### まず変数を準備"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from copy import copy\n",
    "import math, random\n",
    "import matplotlib.pyplot as plt                   #   for plotting data\n",
    "from matplotlib.patches import Ellipse      #  for drawing\n",
    "\n",
    "### 変数 ###\n",
    "\n",
    "# 実際の世界のシミュレーション\n",
    "actual_x = np.array([0.0,0.0,0.0])   #ロボットの実際の姿勢\n",
    "u = np.array([0.2,math.pi / 180.0 * 20]) #ロボットの移動\n",
    "\n",
    "# モンテカルロ法のための変数\n",
    "class Particle:\n",
    "    def __init__(self,w):\n",
    "        self.pose = np.array([0.0,0.0,0.0])\n",
    "        self.weight = w\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return \"pose: \" + str(self.pose) + \" weight: \" + str(self.weight)\n",
    "        \n",
    "particles = [Particle(1.0/100) for i in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pose: [ 0.  0.  0.] weight: 0.01\n"
     ]
    }
   ],
   "source": [
    "# 一個プリントしてみましょう\n",
    "print(particles[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ロボットとパーティクルを動かす関数\n",
    "\n",
    "前回のをコピペ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x_old,u):\n",
    "    pos_x, pos_y, pos_theta = x_old\n",
    "    act_fw, act_rot = u\n",
    "    \n",
    "    act_fw = random.gauss(act_fw,act_fw/10)\n",
    "    dir_error = random.gauss(0.0, math.pi / 180.0 * 3.0)\n",
    "    act_rot = random.gauss(act_rot,act_rot/10)\n",
    "    \n",
    "    pos_x += act_fw * math.cos(pos_theta + dir_error)\n",
    "    pos_y += act_fw * math.sin(pos_theta + dir_error)\n",
    "    pos_theta += act_rot\n",
    "    \n",
    "    return np.array([pos_x,pos_y,pos_theta])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これで準備OK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 動作の確認"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import copy\n",
    "\n",
    "path = [actual_x]\n",
    "particle_path = [copy.deepcopy(particles)]\n",
    "for i in range(10):\n",
    "    actual_x = f(actual_x,u)\n",
    "    path.append(actual_x)\n",
    "    \n",
    "    for p in particles:\n",
    "        p.pose = f(p.pose,u)\n",
    "    particle_path.append(copy.deepcopy(particles))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 値の確認"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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3.52443772] weight: 0.01, pose: [ 0.08259952  1.11230701  3.36883253] weight: 0.01, pose: [-0.01364817  1.03883002  3.55118194] weight: 0.01, pose: [ 0.00362118  1.11112611  3.52194495] weight: 0.01, pose: [ 0.07198805  1.17571155  3.42233676] weight: 0.01, pose: [-0.07167549  1.09892701  3.52359114] weight: 0.01, pose: [ 0.06740852  1.15074433  3.49684461] weight: 0.01, pose: [ 0.07599775  1.15525312  3.44088293] weight: 0.01, pose: [ 0.13875945  1.2644619   3.36819546] weight: 0.01, pose: [ 0.08270819  1.1609582   3.43980574] weight: 0.01, pose: [ 0.04604382  1.18831354  3.41534129] weight: 0.01, pose: [-0.11456185  1.00344149  3.56744868] weight: 0.01, pose: [ 0.00890828  1.09800655  3.38303898] weight: 0.01, pose: [-0.04861796  1.07882509  3.63858782] weight: 0.01, pose: [ 0.00546514  1.06600912  3.55540792] weight: 0.01]\n"
     ]
    }
   ],
   "source": [
    "print(path[0])\n",
    "print(particle_path[0])\n",
    "\n",
    "print(path[10])\n",
    "print(particle_path[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 描画"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw(pose,particles):    \n",
    "    fig = plt.figure(i,figsize=(8, 8))\n",
    "    sp = fig.add_subplot(111, aspect='equal')\n",
    "    sp.set_xlim(-1.0,1.0)\n",
    "    sp.set_ylim(-0.5,1.5)\n",
    "    \n",
    "    xs = [e.pose[0] for e in particles]\n",
    "    ys = [e.pose[1] for e in particles]\n",
    "    vxs = [math.cos(e.pose[2]) for e in particles]\n",
    "    vys = [math.sin(e.pose[2]) for e in particles]\n",
    "    plt.quiver(xs,ys,vxs,vys,color=\"blue\",label=\"particles\")\n",
    "    \n",
    "    plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color=\"red\",label=\"actual robot motion\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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af0dVvWAR4wEeZt/93clrXpOceWZuqu/KW+utWarlvGv31zd7ZLCtVHfPt4OqE5LcmeSC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5cab81978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c8aabd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6nOzRVndiXb40Ig4eyXYPZgj9+lBE3F6fn6sjYve2uj5fl2PFEPp2VESsbuvD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\nxCVJKpQhLklSoQxxSZIK9f8B66T1PfAbBL4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c8a847f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NEXE4sDQiHgCeHkxHI2IhsLBe3RoRqwazfyEmA/893J3YTUbr2BxXeUbr2BxX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\n/j9f+Tmw8OGabgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c89de3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c89a8780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SpEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRC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\nJleVPcUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c8981b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4\nAACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECk\nCHEAACJFiAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiFRZQtzMRpvZcjOrMbNpeZZfaGbL\nzOxZM1tgZoNTy7aY2ZLkZ1456gMAQHfQo9QdmFmVpJskjZK0StIiM5vn7stSqz0tKePuH5rZeZKu\nl3RKsmy9uw8vtR4AAHQ35bgSHyGpxt1XuPsmSXMkjU+v4O6PufuHyexCSQPL8LkAAHRr5Qjx3SWt\nTM2vSsoKOVvSA6n5rc2s2swWmtmEMtQHAIBuoeTm9NYws8mSMpI+myoe7O6rzWyopEfN7Dl3fyXP\ntlMlTZWkPfbYo0PqCwBAV1aOK/HVkgal5gcmZQ2Y2UhJl0oa5+4bs+Xuvjr5vULS45IOzvch7j7D\n3TPununfv38Zqg0AQNzKEeKLJA0zsyFm1kvSREkNepmb2cGSblUI8DWp8j5m1juZ7ifpKEnpDnEA\nAKCAkpvT3b3OzL4u6UFJVZJmufvzZnalpGp3nyfpB5K2l/Q/ZiZJf3f3cZL2kXSrmdUrfKG4tlGv\ndgAAUIC5e2fXodUymYxXV1d3djUAAGgzM1vs7plS9sGIbQAARIoQBwAgUoQ4AACRIsQBAIgUIQ4A\nQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClC\nHACASBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAg\nUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEO\nAECkCHEAACJFiAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApMoS4mY22syWm1mN\nmU3Ls7y3mf0qWf4XM9szteySpHy5mZ1QjvoAANAdlBziZlYl6SZJYyTtK2mSme3baLWzJb3r7p+U\ndIOk65Jt95U0UdJ+kkZLujnZHwAAaEY5rsRHSKpx9xXuvknSHEnjG60zXtIdyfRcSceZmSXlc9x9\no7u/Kqkm2R8AAGhGOUJ8d0krU/OrkrK867h7naT3Je3cwm0BAEAe0XRsM7OpZlZtZtW1tbWdXR0A\nADpdOUKBLP2EAAALhklEQVR8taRBqfmBSVnedcysh6QdJb3Twm0lSe4+w90z7p7p379/GaoNAEDc\nyhHiiyQNM7MhZtZLoaPavEbrzJM0JZk+WdKj7u5J+cSk9/oQScMk/bUMdQIAoOL1KHUH7l5nZl+X\n9KCkKkmz3P15M7tSUrW7z5P0c0m/NLMaSWsVgl7JendLWiapTtLX3H1LqXUCAKA7sHBBHJdMJuPV\n1dWdXQ0AANrMzBa7e6aUfUTTsQ0AADREiAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiBQh\nDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQ\nKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACASBHiAABEihAH\nACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgU\nIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSopxM2sr5k9bGYvJ7/75FlnuJk9\nZWbPm9mzZnZKatntZvaqmS1JfoaXUh8AALqTUq/Ep0la4O7DJC1I5hv7UNLp7r6fpNGSfmxmO6WW\nX+Tuw5OfJSXWBwCAbqPUEB8v6Y5k+g5JExqv4O4vufvLyfQ/JK2R1L/EzwUAoNsrNcR3cfc3kuk3\nJe1SbGUzGyGpl6RXUsVXJ83sN5hZ7yLbTjWzajOrrq2tLbHaAADEr9kQN7NHzGxpnp/x6fXc3SV5\nkf0MkPRLSWe6e31SfImkvSUdJqmvpIsLbe/uM9w94+6Z/v25kAcAoEdzK7j7yELLzOwtMxvg7m8k\nIb2mwHo7SPqdpEvdfWFq39mr+I1m9gtJ32lV7QEA6MZKbU6fJ2lKMj1F0n2NVzCzXpLukXSnu89t\ntGxA8tsU7qcvLbE+AAB0G6WG+LWSRpnZy5JGJvMys4yZzUzW+ZKkoyWdkedRsv82s+ckPSepn6Sr\nSqwPAADdhoVb2XHJZDJeXV3d2dUAAKDNzGyxu2dK2QcjtgEAEClCHACASBHiAABEihAHACBShDgA\nAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQI\ncQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACA\nSBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4\nAACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSopxM2sr5k9bGYv\nJ7/7FFhvi5ktSX7mpcqHmNlfzKzGzH5lZr1KqQ8AAN1JqVfi0yQtcPdhkhYk8/msd/fhyc+4VPl1\nkm5w909KelfS2SXWBwCAbqPUEB8v6Y5k+g5JE1q6oZmZpGMlzW3L9gAAdHelhvgu7v5GMv2mpF0K\nrLe1mVWb2UIzywb1zpLec/e6ZH6VpN1LrA8AAN1Gj+ZWMLNHJO2aZ9Gl6Rl3dzPzArsZ7O6rzWyo\npEfN7DlJ77emomY2VdLUZHajmS1tzfaR6Cfp7c6uRDup1GPjuOJTqcfGccVnr1J30GyIu/vIQsvM\n7C0zG+Dub5jZAElrCuxjdfJ7hZk9LulgSb+WtJOZ9UiuxgdKWl2kHjMkzUg+t9rdM83VPTaVelxS\n5R4bxxWfSj02jis+ZlZd6j5KbU6fJ2lKMj1F0n2NVzCzPmbWO5nuJ+koScvc3SU9JunkYtsDAID8\nSg3xayWNMrOXJY1M5mVmGTObmayzj6RqM3tGIbSvdfdlybKLJV1oZjUK98h/XmJ9AADoNpptTi/G\n3d+RdFye8mpJ5yTTT0o6oMD2KySNaMNHz2jDNjGo1OOSKvfYOK74VOqxcVzxKfnYLLRqAwCA2DDs\nKgAAkeqyIW5m/2Zmz5tZvZkV7JloZqPNbHkydOu0VHmXHNK1JUPVmtnnUsPULjGzDdnn683sdjN7\nNbVseMcfRVOVPARvC8/ZcDN7KvmbfdbMTkkt61LnrNC/mdTy3sk5qEnOyZ6pZZck5cvN7ISOrHdz\nWnBcF5rZsuT8LDCzwallef8uu4oWHNsZZlabOoZzUsumJH+7L5vZlMbbdqYWHNcNqWN6yczeSy3r\nsufMzGaZ2Ror8Ci0BTcmx/2smR2SWta68+XuXfJHoUPcXpIel5QpsE6VpFckDZXUS9IzkvZNlt0t\naWIyfYuk8zr7mJK6XC9pWjI9TdJ1zazfV9JaSdsm87dLOrmzj6OtxyVpXYHyLnm+Wnpskj4laVgy\nvZukNyTt1NXOWbF/M6l1zpd0SzI9UdKvkul9k/V7SxqS7Keqs4+pFcf1udS/o/Oyx1Xs77Ir/LTw\n2M6Q9H/zbNtX0orkd59kuk9nH1NLj6vR+hdImhXJOTta0iGSlhZYPlbSA5JM0hGS/tLW89Vlr8Td\n/QV3X97MaiMk1bj7CnffJGmOpPFmXXpI19YOVXuypAfc/cN2rVXpKnkI3maPzd1fcveXk+l/KIyZ\n0L/Dathyef/NNFonfbxzJR2XnKPxkua4+0Z3f1VSjdrWMbU9NHtc7v5Y6t/RQoWxKWLQknNWyAmS\nHnb3te7+rqSHJY1up3q2VmuPa5Kk2R1SsxK5+xMKF1+FjJd0pwcLFcZMGaA2nK8uG+IttLuklan5\n7NCtXXlI15YOVZs1UU3/cK9OmmBusOQZ/C6gkofgbdU5M7MRClcWr6SKu8o5K/RvJu86yTl5X+Ec\ntWTbztLaup2tcCWUle/vsqto6bF9Mfkbm2tmg1q5bWdocd2SWx9DJD2aKu7K56w5hY691eerpEfM\nSmVFhnR192gHfil2XOkZ96JD1Sr5ZnaApAdTxZcoBEkvhccTLpZ0Zal1bokyHddgL3EI3vZQ5nP2\nS0lT3L0+Ke60c4amzGyypIykz6aKm/xduvsr+ffQJd0vaba7bzSzcxVaUo7t5DqV00RJc919S6os\n9nNWFp0a4l5kSNcWWi1pUGo+O3TrO2rFkK7lVuy4rIVD1Sa+JOked9+c2nf2inCjmf1C0nfKUukW\nKMdxeRmG4G0P5Tg2M9tB0u8UvoQuTO27085ZHoX+zeRbZ5WZ9ZC0o8K/qZZs21laVDczG6nwxeyz\n7r4xW17g77KrBEKzx+ZhzI6smQr9OLLbHtNo28fLXsO2ac3f00RJX0sXdPFz1pxCx97q8xV7c/oi\nScMs9GzupXCi53noIdBVh3RtdqjalCb3gJIQyd5HniCpq7wIppKH4G3JsfWSdI/Cfa65jZZ1pXOW\n999Mo3XSx3uypEeTczRP0kQLvdeHSBom6a8dVO/mNHtcZnawpFsljXP3NanyvH+XHVbz5rXk2Aak\nZsdJeiGZflDS8ckx9pF0vBq27HWmlvwtysz2Vujk9VSqrKufs+bMk3R60kv9CEnvJ1/2W3++OrrX\nXkt/JJ2kcD9go6S3JD2YlO8maX5qvbGSXlL4BnZpqnyowv9gaiT9j6TenX1MSb12lrRA0suSHpHU\nNynPSJqZWm9PhW9lWzXa/lFJzykEwV2Stu/sY2rpcUn6dFL3Z5LfZ3f189WKY5ssabOkJamf4V3x\nnOX7N6PQvD8umd46OQc1yTkZmtr20mS75ZLGdPa5aeVxPZL8vyR7fuY193fZVX5acGzXSHo+OYbH\nJO2d2vas5FzWSDqzs4+lNceVzH9PYbju9HZd+pwpXHy9kfw/YZVCH4yvSvpqstwk3ZQc93NKPYHV\n2vPFiG0AAEQq9uZ0AAC6LUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACL1/wH5\nPvpo/bYD5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c894ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACA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\nIsQBAIgUIQ4AQKT+P6RZMTZc5UPDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c88a2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TnnoqhPmaNQ2vV1aWvTV2MZRpq/bWq1qofZvnA/IwdmwYVvRzn2va9ps2bV9l/v77Iciv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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c886b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ASBQhDgBAoghxAAASRYgDAJCosoS4mY01syVmttzMLi2w/DwzW2dm87LpS3nL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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c8844128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4UfrGN+peFwrwgQNju7PPjmryhhoGuFQX1mbRlez114sv16RJcR/+ppsKT68K\noG0qV+v0U5tY75LOK7DuVkm3lqMcQFs1fXoMx9qY/faTvvOdmBmsUGOyfAGeq7KyeQE+aFDMTnbA\nAXGPnhAH0pJMwzYgVW+8EZOrNFZ1vtNO0oQJ0TWtkKYCXNq4i1iuzp2jin7nnWOUuIsvLjzgC4A0\nEOLAZrRoUQyRunZt49u9/Xa0er///vzjkhcT4Lk+9rG4x7333jHP+AEHRCO4Tkx5BLQrhDiwmSxd\nGsG5cmXj2w0cGFOUHnVUtDJvqGGA9+sXXc2eeir/nOCdOkmf/3zMoEYfb6B9408c2AyWLZM++tH4\n2VCXLtLhh8e97+OOi+rtxtx9d8xkduaZUlVVDGBz2GH5A1yKavvvfz+mDb3rLqlr11LPBkBbRYgD\nZbZ6dQzcsnBh3bLevSOwR42SjjyyeZOInHVW3fOZM+MLQMOBXLbaKqrjR4yISU6qqhq/vw6gfSDE\ngTJ7990YPnXo0AjtUaNiGs/mDMWaT01NBPiiRTH2+wEH1I0FP2xYHH/6dGnsWGn0aOnyy8tyOgDa\nMEIcKLOZMyPEd9utfMd0j+rx3/8+Arxbt/rrV66MKvQbbojq9Jdekk4+WRoyJBrL/fvf0mWXla88\nANqGso3Y1pIYsQ2o85e/RPX9WzlTCZ10UkzIcscdUfVeWSnNnRtjrQNoG9rMiG0ANq/166MavW/f\neD1rVoydfsMN9bud9esn7bWX9Ne/1u8zbhat2Y8/vmXLDWDzIsSBNs49hmEdPlw64wxp8mTps5+N\nYM62UO/cOQJ87tyY6CRrhx3iKv3LX455zQG0Lwz9ALRx118f04O+805MI3rEEdKHH9YFeNeucaU+\nd27dPvvuG1Xpc+fGvXICHGifuBIH2rAHHpC+9a14fvXV0vLlG2+zenX8NIvq8osukg4+uLTpUgGk\ngRAH2qipU2N2sWzb03wBLsVMZ+eeG1OWDhnScuUD0PoIcaANmjUr7ntnr7ILOfdc6brrpG22aZly\nAWhbuCcOtDFLlkjHHhuDxjTld7+T/vGPzV8mAG0TIQ60IatWxQhvNTWNb7flljFT2dFHS08+KS1e\n3DLlA9C2UJ0OtBEbNkinnx73wnNtv720zz4x6ckxx8QgLs0Zex1A+0WIA23Et78drdH79IlpSY8+\nOiZLYZQ1AIUQ4kAbUF0d4f3ss9Lee8ec4ADQFEIcaAOqquIBAM3B930AABJFiAMAkChCHACARBHi\nAAAkihB9RzRJAAAUGUlEQVQHACBRhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAA\nJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSKEAcAIFGEOAAAiSLE\nAQBIFCEOAECiCHEAABJVlhA3s5Fm9rqZ1ZjZuDzrf2FmMzKPmWa2PGfd+px1E8tRHgAAOoIupR7A\nzDpL+pWkIyXNkzTNzCa6+yvZbdz9GznbXyBp35xDrHL3fUotBwAAHU05rsRHSKpx9znuvlbSfZJG\nN7L9qZLuLcP7AgDQoZUjxHeW9FbO63mZZRsxs4GSBkuanLO4q5lVm9lTZnZ8GcoDAECHUHJ1ejON\nkTTB3dfnLBvo7vPNbIikyWb2orvPbrijmY2VNFaSBgwY0DKlBQCgDSvHlfh8Sf1zXvfLLMtnjBpU\npbv7/MzPOZKmqP798tztxrt7lbtX9enTp9QyAwCQvHKE+DRJQ81ssJlVKoJ6o1bmZjZMUk9JU3OW\n9TSzLTLPe0s6UNIrDfcFAAAbK7k63d1rzex8SQ9J6izpVnd/2cyukFTt7tlAHyPpPnf3nN33kHSz\nmW1QfKG4KrdVOwAAKMzqZ2oaqqqqvLq6urWLAQDAJjOz6e5eVcoxGLENAIBEEeIAACSKEAcAIFGE\nOAAAiSLEAQBIFCEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBA\noghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIc\nAIBEEeIAACSKEAcAIFGEOAAAiSLEAQBIFCEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBR\nhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4A\nQKLKEuJmNtLMXjezGjMbl2f9mWa22MxmZB7n5qw7w8xmZR5nlKM8AAB0BF1KPYCZdZb0K0lHSpon\naZqZTXT3Vxps+r/ufn6DfXtJ+oGkKkkuaXpm32WllgsAgPauHFfiIyTVuPscd18r6T5Jo4vc92hJ\nD7v70kxwPyxpZBnKBABAu1eOEN9Z0ls5r+dlljV0kpm9YGYTzKx/M/eVmY01s2ozq168eHEZig0A\nQNpaqmHbXyQNcvePKa6272juAdx9vLtXuXtVnz59yl5AAABSU44Qny+pf87rfpll/+Hu77r7mszL\n30oaXuy+AAAgv3KE+DRJQ81ssJlVShojaWLuBmbWN+flKEmvZp4/JOkoM+tpZj0lHZVZBgAAmlBy\n63R3rzWz8xXh21nSre7+spldIana3SdKutDMRkmqlbRU0pmZfZea2Y8VXwQk6Qp3X1pqmQAA6AjM\n3Vu7DM1WVVXl1dXVrV0MAAA2mZlNd/eqUo7BiG0AACSKEAcAIFGEOAAAiSLEAQBIFCEOAECiCHEA\nABJFiAMAkChCHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR\n4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSKEAcAIFGEOAAA\niSLEAQBIFCEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBAoghx\nAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKLKEuJmNtLMXjezGjMbl2f9\nN83sFTN7wcweMbOBOevWm9mMzGNiOcoDAEBH0KXUA5hZZ0m/knSkpHmSppnZRHd/JWez5yRVufuH\nZvZVSddIOiWzbpW771NqOQAA6GjKcSU+QlKNu89x97WS7pM0OncDd3/U3T/MvHxKUr8yvC8AAB1a\nOUJ8Z0lv5byel1lWyDmSJuW87mpm1Wb2lJkdX4byAADQIZRcnd4cZvZFSVWSDs1ZPNDd55vZEEmT\nzexFd5+dZ9+xksZK0oABA1qkvAAAtGXluBKfL6l/zut+mWX1mNkRkr4raZS7r8kud/f5mZ9zJE2R\ntG++N3H38e5e5e5Vffr0KUOxAQBIWzlCfJqkoWY22MwqJY2RVK+VuZntK+lmRYAvylne08y2yDzv\nLelASbkN4gAAQAElV6e7e62ZnS/pIUmdJd3q7i+b2RWSqt19oqRrJW0l6fdmJkn/dvdRkvaQdLOZ\nbVB8obiqQat2AABQgLl7a5eh2aqqqry6urq1iwEAwCYzs+nuXlXKMRixDQCARBHiAAAkihAHACBR\nhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4A\nQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSKEAcAIFGEOAAAiSLEAQBIFCEOAECiCHEAABJFiAMAkChC\nHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAg\nUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSKEAcAIFGEOAAAiSLEAQBIVFlC\n3MxGmtnrZlZjZuPyrN/CzP43s/5pMxuUs+7SzPLXzezocpQHAICOoOQQN7POkn4l6RhJe0o61cz2\nbLDZOZKWufuukn4h6erMvntKGiPpI5JGSropczwAANCEclyJj5BU4+5z3H2tpPskjW6wzWhJd2Se\nT5D0aTOzzPL73H2Nu78hqSZzPAAA0IRyhPjOkt7KeT0vsyzvNu5eK2mFpO2K3BcAAOSRTMM2Mxtr\nZtVmVr148eLWLg4AAK2uHCE+X1L/nNf9MsvybmNmXST1kPRukftKktx9vLtXuXtVnz59ylBsAADS\nVo4QnyZpqJkNNrNKRUO1iQ22mSjpjMzzz0ma7O6eWT4m03p9sKShkp4pQ5kAAGj3upR6AHevNbPz\nJT0kqbOkW939ZTO7QlK1u0+UdIuku8ysRtJSRdArs939kl6RVCvpPHdfX2qZAADoCCwuiNNSVVXl\n1dXVrV0MAAA2mZlNd/eqUo6RTMM2AABQHyEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBR\nhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4A\nQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSKEAcAIFGEOAAAiSLEAQBIFCEOAECiCHEAABJFiAMAkChC\nHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAg\nUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIcAIBEEeIAACSqpBA3s15m9rCZzcr87Jlnm33M\nbKqZvWxmL5jZKTnrbjezN8xsRuaxTynlAQCgIyn1SnycpEfcfaikRzKvG/pQ0pfc/SOSRkq63sy2\nzVn/bXffJ/OYUWJ5AADoMEoN8dGS7sg8v0PS8Q03cPeZ7j4r8/xtSYsk9SnxfQEA6PBKDfEd3P2d\nzPMFknZobGMzGyGpUtLsnMU/zVSz/8LMtmhk37FmVm1m1YsXLy6x2AAApK/JEDezf5jZS3keo3O3\nc3eX5I0cp6+kuySd5e4bMosvlTRM0v6Sekm6pND+7j7e3avcvapPHy7kAQDo0tQG7n5EoXVmttDM\n+rr7O5mQXlRgu20k/U3Sd939qZxjZ6/i15jZbZIublbpAQDowEqtTp8o6YzM8zMk/bnhBmZWKemP\nku509wkN1vXN/DTF/fSXSiwPAAAdRqkhfpWkI81slqQjMq9lZlVm9tvMNidLOkTSmXm6kt1jZi9K\nelFSb0k/KbE8AAB0GBa3stNSVVXl1dXVrV0MAAA2mZlNd/eqUo7BiG0AACSKEAcAIFGEOAAAiSLE\nAQBIFCEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBRhDgAAIkixAEASBQhDgBAoghxAAAS\nRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKIIcQAAEkWIAwCQKEIcAIBEEeIA\nACSKEAcAIFGEOAAAiSLEAQBIFCEOAECiCHEAABJFiAMAkChCHACARBHiAAAkihAHACBRhDgAAIki\nxAEASBQhDgBAoghxAAASRYgDAJAoQhwAgEQR4gAAJIoQBwAgUYQ4AACJIsQBAEgUIQ4AQKJKCnEz\n62VmD5vZrMzPngW2W29mMzKPiTnLB5vZ02ZWY2b/a2aVpZQHAICOpNQr8XGSHnH3oZIeybzOZ5W7\n75N5jMpZfrWkX7j7rpKWSTqnxPIAANBhlBrioyXdkXl+h6Tji93RzEzSpyRN2JT9AQDo6EoN8R3c\n/Z3M8wWSdiiwXVczqzazp8wsG9TbSVru7rWZ1/Mk7VxieQAA6DC6NLWBmf1D0o55Vn0394W7u5l5\ngcMMdPf5ZjZE0mQze1HSiuYU1MzGShqbebnGzF5qzv6J6C1pSWsXYjNpr+fGeaWnvZ4b55We3Us9\nQJMh7u5HFFpnZgvNrK+7v2NmfSUtKnCM+Zmfc8xsiqR9JT0gaVsz65K5Gu8naX4j5RgvaXzmfavd\nvaqpsqemvZ6X1H7PjfNKT3s9N84rPWZWXeoxSq1OnyjpjMzzMyT9ueEGZtbTzLbIPO8t6UBJr7i7\nS3pU0uca2x8AAORXaohfJelIM5sl6YjMa5lZlZn9NrPNHpKqzex5RWhf5e6vZNZdIumbZlajuEd+\nS4nlAQCgw2iyOr0x7v6upE/nWV4t6dzM839J+miB/edIGrEJbz1+E/ZJQXs9L6n9nhvnlZ72em6c\nV3pKPjeLWm0AAJAahl0FACBRbTbEzezzZvaymW0ws4ItE81spJm9nhm6dVzO8jY5pGsxQ9Wa2eE5\nw9TOMLPV2f71Zna7mb2Rs26flj+LjbXnIXiL/Mz2MbOpmd/ZF8zslJx1beozK/Q3k7N+i8xnUJP5\nTAblrLs0s/x1Mzu6JcvdlCLO65tm9krm83nEzAbmrMv7e9lWFHFuZ5rZ4pxzODdn3RmZ391ZZnZG\nw31bUxHn9Yucc5ppZstz1rXZz8zMbjWzRVagK7SFGzLn/YKZ7Zezrnmfl7u3yYeiQdzukqZIqiqw\nTWdJsyUNkVQp6XlJe2bW3S9pTOb5byR9tbXPKVOWaySNyzwfJ+nqJrbvJWmppC0zr2+X9LnWPo9N\nPS9JKwssb5OfV7HnJmk3SUMzz3eS9I6kbdvaZ9bY30zONl+T9JvM8zGS/jfzfM/M9ltIGpw5TufW\nPqdmnNfhOX9HX82eV2O/l23hUeS5nSnpl3n27SVpTuZnz8zznq19TsWeV4PtL5B0ayKf2SGS9pP0\nUoH1x0qaJMkkfVzS05v6ebXZK3F3f9XdX29isxGSatx9jruvlXSfpNFmbXpI1+YOVfs5SZPc/cPN\nWqrStecheJs8N3ef6e6zMs/fVoyZ0KfFSli8vH8zDbbJPd8Jkj6d+YxGS7rP3de4+xuSarRpDVM3\nhybPy90fzfk7ekoxNkUKivnMCjla0sPuvtTdl0l6WNLIzVTO5mrueZ0q6d4WKVmJ3P0xxcVXIaMl\n3enhKcWYKX21CZ9Xmw3xIu0s6a2c19mhW9vykK7FDlWbNUYb/+L+NFMF8wvL9MFvA9rzELzN+szM\nbITiymJ2zuK28pkV+pvJu03mM1mh+IyK2be1NLds5yiuhLLy/V62FcWe20mZ37EJZta/mfu2hqLL\nlrn1MVjS5JzFbfkza0qhc2/251VSF7NSWSNDurp7sgO/NHZeuS/cGx2qVplvZh+V9FDO4ksVQVKp\n6J5wiaQrSi1zMcp0XgO9xCF4N4cyf2Z3STrD3TdkFrfaZ4aNmdkXJVVJOjRn8Ua/l+4+O/8R2qS/\nSLrX3deY2ZcVNSmfauUyldMYSRPcfX3OstQ/s7Jo1RD3RoZ0LdJ8Sf1zXmeHbn1XzRjStdwaOy8r\ncqjajJMl/dHd1+UcO3tFuMbMbpN0cVkKXYRynJeXYQjezaEc52Zm20j6m+JL6FM5x261zyyPQn8z\n+baZZ2ZdJPVQ/E0Vs29rKapsZnaE4ovZoe6+Jru8wO9lWwmEJs/NY8yOrN8q2nFk9z2swb5Tyl7C\nTdOc36cxks7LXdDGP7OmFDr3Zn9eqVenT5M01KJlc6Xig57o0UKgrQ7p2uRQtTk2ugeUCZHsfeTj\nJbWViWDa8xC8xZxbpaQ/Ku5zTWiwri19Znn/Zhpsk3u+n5M0OfMZTZQ0xqL1+mBJQyU900LlbkqT\n52Vm+0q6WdIod1+Uszzv72WLlbxpxZxb35yXoyS9mnn+kKSjMufYU9JRql+z15qK+V2UmQ1TNPKa\nmrOsrX9mTZko6UuZVuofl7Qi82W/+Z9XS7faK/Yh6QTF/YA1khZKeiizfCdJD+Zsd6ykmYpvYN/N\nWT5E8R9MjaTfS9qitc8pU67tJD0iaZakf0jqlVleJem3OdsNUnwr69Rg/8mSXlQEwd2Stmrtcyr2\nvCR9MlP25zM/z2nrn1czzu2LktZJmpHz2Kctfmb5/mYU1fujMs+7Zj6DmsxnMiRn3+9m9ntd0jGt\n/dk087z+kfm/JPv5TGzq97KtPIo4tyslvZw5h0clDcvZ9+zMZ1kj6azWPpfmnFfm9Q8Vw3Xn7tem\nPzPFxdc7mf8T5inaYHxF0lcy603SrzLn/aJyemA19/NixDYAABKVenU6AAAdFiEOAECiCHEAABJF\niAMAkChCHACARBHiAAAkihAHACBRhDgAAIn6/7zLFeyqldagAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5c88107b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i,p in enumerate(path):\n",
    "    draw(path[i],particle_path[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数式での表現\n",
    "\n",
    "### パーティクルの定義\n",
    "\n",
    "* $\\Xi = \\{\\xi^{(i)} = (\\boldsymbol{x}^{(i)}, w^{(i)}) | i = 1,2,\\dots,N \\}$\n",
    "* パーティクルは次のように$bel$を近似しなければならない\n",
    "  * $Bel(X) = \\int_{\\boldsymbol{x} \\in X} bel(\\boldsymbol{x}) d\\boldsymbol{x} \\approx \\sum_{i=1}^N \\delta(\\boldsymbol{x}^{(i)} \\in X) w^{(i)}$\n",
    "   * $Bel(X)$: $X$の中に真の状態が存在する確率\n",
    "     * 密度関数$bel$を積分すると確率になる\n",
    "   * $\\forall X \\subset \\mathcal{X}$ \n",
    "   * $\\delta$: カッコの中が真なら1、そうでなければ0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### motion update\n",
    "\n",
    "* 先ほどのシミュレーション\n",
    "* 各パーティクルを$p(\\boldsymbol{x} | \\boldsymbol{x}_{t-1}, \\boldsymbol{u}_t)$に従って動かす\n",
    "  * $\\boldsymbol{x}^{(i)}_t \\sim p(\\boldsymbol{x} | \\boldsymbol{x}_{t-1}, \\boldsymbol{u}_t) \\quad (i=1,2,\\dots,N)$\n",
    "    * 時刻$t$における$i$番目のパーティクルの状態を、状態遷移の確率分布にしたがって一つランダムに選ぶ\n",
    "    * 今のところ、全パーティクルをひとつずつ選んで動かすだけでよい"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## まとめ\n",
    "\n",
    "* $bel$をモンテカルロ法（パーティクル）で近似計算\n",
    "* ロボットの動きを雑音つきの状態方程式で表現してロボットに実装\n",
    "* ロボットの中でパーティクルの数だけロボットの動作のシミュレーション"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}