text Coursera Week4编程作业1

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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, you will implement the kinematic bicycle model. The model accepts velocity and steering rate inputs and steps through the bicycle kinematic equations. Once the model is implemented, you will provide a set of inputs to drive the bicycle in a figure 8 trajectory.\n",
    "\n",
    "The bicycle kinematics are governed by the following set of equations:\n",
    "\n",
    "\\begin{align*}\n",
    "\\dot{x}_c &= v \\cos{(\\theta + \\beta)} \\\\\n",
    "\\dot{y}_c &= v \\sin{(\\theta + \\beta)} \\\\\n",
    "\\dot{\\theta} &= \\frac{v \\cos{\\beta} \\tan{\\delta}}{L} \\\\\n",
    "\\dot{\\delta} &= \\omega \\\\\n",
    "\\beta &= \\tan^{-1}(\\frac{l_r \\tan{\\delta}}{L})\n",
    "\\end{align*}\n",
    "\n",
    "where the inputs are the bicycle speed $v$ and steering angle rate $\\omega$. The input can also directly be the steering angle $\\delta$ rather than its rate in the simplified case. The Python model will allow us both implementations.\n",
    "\n",
    "In order to create this model, it's a good idea to make use of Python class objects. This allows us to store the state variables as well as make functions for implementing the bicycle kinematics. \n",
    "\n",
    "The bicycle begins with zero initial conditions, has a maximum turning rate of 1.22 rad/s, a wheelbase length of 2m, and a length of 1.2m to its center of mass from the rear axle.\n",
    "\n",
    "From these conditions, we initialize the Python class as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from notebook_grader import BicycleSolution, grade_bicycle\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "\n",
    "class Bicycle():\n",
    "    def __init__(self):\n",
    "        self.xc = 0\n",
    "        self.yc = 0\n",
    "        self.theta = 0\n",
    "        self.delta = 0\n",
    "        self.beta = 0\n",
    "        \n",
    "        self.L = 2\n",
    "        self.lr = 1.2\n",
    "        self.w_max = 1.22\n",
    "        \n",
    "        self.sample_time = 0.01\n",
    "        \n",
    "    def reset(self):\n",
    "        self.xc = 0\n",
    "        self.yc = 0\n",
    "        self.theta = 0\n",
    "        self.delta = 0\n",
    "        self.beta = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A sample time is required for numerical integration when propagating the kinematics through time. This is set to 10 milliseconds. We also have a reset function which sets all the state variables back to 0. \n",
    "\n",
    "With this sample time, implement the kinematic model using the function $\\textit{step}$ defined in the next cell. The function should take speed + angular rate as inputs and update the state variables. Don't forget about the maximum turn rate on the bicycle!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Bicycle(Bicycle):\n",
    "    def step(self, v, w):\n",
    "        # ==================================\n",
    "        #  Implement kinematic model here\n",
    "        # ==================================\n",
    "        self.xc = self.xc + v * np.cos(self.theta + self.beta) * self.sample_time\n",
    "        self.yc = self.yc + v * np.sin(self.theta + self.beta) * self.sample_time\n",
    "        self.theta = self.theta + ((v * np.cos(self.beta) * np.tan(self.delta)/self.L)) * self.sample_time\n",
    "        self.delta = w * self.sample_time + self.delta\n",
    "        self.beta = np.arctan((self.lr / self.L) * np.tan(self.delta))\n",
    "\n",
    "        pass\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the model setup, we can now start giving bicycle inputs and producing trajectories. \n",
    "\n",
    "Suppose we want the model to travel a circle of radius 10 m in 20 seconds. Using the relationship between the radius of curvature and the steering angle, the desired steering angle can be computed.\n",
    "\n",
    "\\begin{align*}\n",
    "    \\tan{\\delta} &= \\frac{L}{r} \\\\\n",
    "    \\delta &= \\tan^{-1}(\\frac{L}{r}) \\\\\n",
    "           &= \\tan^{-1}(\\frac{2}{10}) \\\\\n",
    "           &= 0.1974\n",
    "\\end{align*}\n",
    "\n",
    "If the steering angle is directly set to 0.1974 using a simplied bicycled model, then the bicycle will travel in a circle without requiring any additional steering input. \n",
    "\n",
    "The desired speed can be computed from the circumference of the circle:\n",
    "\n",
    "\\begin{align*}\n",
    "    v &= \\frac{d}{t}\\\\\n",
    "     &= \\frac{2 \\pi 10}{20}\\\\\n",
    "     &= \\pi\n",
    "\\end{align*}\n",
    "\n",
    "We can now implement this in a loop to step through the model equations. We will also run our bicycle model solution along with your model to show you the expected trajectory. This will help you verify the correctness of your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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CH9wzEV8vT26Yv57XvznYKUeMqp6hPVv8i4GLWy4wxlxvjEk1xqTSPBfv+63d0e58e9t2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\nUm5Gg18ppdyMBr9SSrmZ/w96F95D8jAyzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 20\n",
    "model = Bicycle()\n",
    "solution_model = BicycleSolution()\n",
    "\n",
    "# set delta directly\n",
    "model.delta = np.arctan(2/10)\n",
    "solution_model.delta = np.arctan(2/10)\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    model.step(np.pi, 0)\n",
    "    \n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    solution_model.step(np.pi, 0)\n",
    "\n",
    "#     print(\"model.xc = \",model.xc)\n",
    "#     print(\"model.yc = \",model.yc)\n",
    "#     print(\"model.theta = \",model.theta)\n",
    "#     print(\"model.delta = \",model.delta)\n",
    "#     print(\"model.beta = \",model.beta)\n",
    "    \n",
    "#     print(\"------------------------------------\")\n",
    "    \n",
    "#     print(\"solution_model.xc = \",solution_model.xc)\n",
    "#     print(\"solution_model.yc = \",solution_model.xc)\n",
    "#     print(\"solution_model.theta = \",solution_model.theta)\n",
    "#     print(\"solution_model.delta = \",solution_model.delta)\n",
    "#     print(\"solution_model.beta = \",solution_model.beta)\n",
    "    \n",
    "#     print(\"---------------------------------------------\")\n",
    "    \n",
    "    model.beta = 0\n",
    "    solution_model.beta=0\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "# plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The plot above shows the desired circle of 10m radius. The path is slightly offset which is caused by the sideslip effects due to $\\beta$. By forcing $\\beta = 0$ through uncommenting the last line in the loop, you can see that the offset disappears and the circle becomes centered at (0,10). \n",
    "\n",
    "However, in practice the steering angle cannot be directly set and must be changed through angular rate inputs $\\omega$. The cell below corrects for this and sets angular rate inputs to generate the same circle trajectory. The speed $v$ is still maintained at $\\pi$ m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0OOdSYB3QX0RyReRu4DHgKhE5AFxlv46IpInISwDGmGLgf4BN9q9H7dtUC9Xa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\nwMPOcYYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 20\n",
    "model.reset()\n",
    "solution_model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    \n",
    "    if model.delta < np.arctan(2/10):\n",
    "        model.step(np.pi, model.w_max)\n",
    "    else:\n",
    "        model.step(np.pi, 0)\n",
    "        \n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    \n",
    "    if solution_model.delta < np.arctan(2/10):\n",
    "        solution_model.step(np.pi, model.w_max)\n",
    "    else:\n",
    "        solution_model.step(np.pi, 0)    \n",
    "\n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "# plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some other example trajectories: a square path, a spiral path, and a wave path. Uncomment each section to view."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Jl0DJoVqKPjxEj9REfnLFqV7HlW4s2mP7tDbMYKuHLDjn5gPzAQoLC3VYg3R7Ow/Wcvlv\nXqe6vonR/bPITk+iPhBkd3k9dYHQ4G19slKYd84Qrp+ST5+sFK8jSzfW3vLfZ2b9w2v9/YHS8PQS\nYFCL+fIAHbIgAjz2+jZqG4M8f+s5DM3N8DqOxLn2Huq5FJgb/nkusKTF9OvCR/2cBVQc3jwkEu+2\n7q9hZN9MFb/EhBM51PMJYCUw0sxKzOxG4B5gppltAWaGbwM8C2wFioHfAl/vkNQiXVDfzGR2Hqol\nENS1d8V7bW72cc5de4y7zm9lXgfcHGkoke5o1rh+/O+aEhatKeHayTrIQbylM3xFOsmMEX04syCb\nn/79PQ3dLJ5T+Yt0koQE4/5rJuL3JfDNp9Zp8494SuUv0okG9EzlZ58ex9s7y/n1S8Vex5E4pvIX\n6WSXjOvPp08byMMvF7NNm3/EIyp/EQ98f9Yo/AnGwhXbvI4icUrlL+KBPpkpnHZKL9btLPc6isQp\nlb+IBz48UMP63RWc0jvd6ygSp6I9to9I3DtY08j/vbuHLfuqqK5vIj3ZT0aKn7REHz6f8UFpDf9Y\nvwd/gvGtC4Z7HVfilMpfJIq2llVz1aMrOVjTSFaKn6zURGobg1TVBwgEQ+MX9kpL5OKx/bj1ghEM\nyk7zOLHEK5W/SBTd++JmAsFmln5jKuMG9sDso4FuA8FmAsFm0pL0ayfe07tQJIrW76rgnBG5jM/r\n+Yn7En0JJPq0m01ig96JIlHUIzWR/VUNXscQaZPKXySKZozsw+rtB9m8r8rrKCLHpfIXiaLrPjWY\nnqmJ3PrUOhqagl7HETkmlb9IFOVkJPOLqyawYXcl976w2es4Isek8heJsplj+vL5M09h/mtbeaN4\nv9dxRFql8hfpAD+8dAxDctL5j0Xv0NikoZsl9qj8RTpAapKPH19xKrvK61j69m6v44h8gspfpIOc\nMzyHnIxkbfqRmKTyF+kgJYfqqKwLkJ2e5HUUkU+I6AxfM7sV+DLggHeB64H+wJNANvAW8EXnXGOE\nOUViSn0gyMqtB9hWVkNdIEhmip+MZD9pST4A3ttdyR/f3EFyYgJzp+R7G1akFe0ufzMbCPw7MMY5\nV2dmTwNzgEuA+51zT5rZo8CNwCNRSSsSA4pLq/jiY6vZU1F/3PnOHp7Djy4bo8HbJCZFOraPH0g1\nswCQBuwBzgM+F77/ceAnqPylG/nhX9fT0NTMgi8VMnFQL9KSfFTVN1Hd0ERdY5Bm5xiUnUaP1ESv\no4ocU7vL3zm3y8x+BewA6oAXgDVAuXOuKTxbCTAw4pQiMaK52fGv7Yf48rQCzhvV98j0lEQfuZnJ\nHiYTOTnt3uFrZr2A2UABMABIB2a1Mqs7xuPnmVmRmRWVlZW1N4ZIp0v0GQ06dl+6uEiO9rkA2Oac\nK3POBYC/AFOAnmZ2+BNFHtDqQc7OufnOuULnXGFubm4EMUQ6T0KCcWZBb559dw/1AY3dI11XJOW/\nAzjLzNIsdMWK84H3gJeBq8LzzAWWRBZRJLZ8dfoQSqsauOcf73sdRaTd2l3+zrk3gUWEDud8N/xc\n84HbgG+bWTHQG3gsCjlFYsaUoTlcPzWfhW9s5+X3S72OI9Iu5lyrm+Q7VWFhoSsqKvI6hsgJqw8E\nufLhFeyvbuD5b51D7wzt7JXOZ2ZrnHOF7XmszvAVaYeURB8PzplEZV0TP166wes4IidN5S/STiP7\nZXLT9CH8/Z09bNGVu6SLUfmLROC68NANy7XtX7oYlb9IBMprQ8NW+RPM4yQiJyfS4R1Eui3nHB+U\n1bDzUC1NQUdGsp/MFD+pST4CwWbW7ijnoeVb6JGayBUTBngdV+SkqPxFWrFlXxVf+9NbFJdWH3e+\nUf0y+e11hfTJSumkZCLRofIXOYpzjlueWEt5bSN3/9s4RvbLJMmXQFV9IDR4WyBIghnD+mQwql8m\noXMcRboWlb/IUXaV1/H+3ip+cvkYPnfmKV7HEekQ2uErcpTm8JhtKYk+b4OIdCCVv8hR8nqlkpOR\nxIvv7fM6ikiHUfmLHCUhwZj7qXyWv1/KCxv2eh1HpEOo/EVa8dXpQzl1QBa3PfMO+yqPf7lGka5I\n5S/SiiR/Ag9dO4n6QDPfefptmpu9HwBRJJpU/iLHMDQ3gx9eNprXi/fzxzc/9DqOSFSp/EWO43OT\nT2HK0N48tHyLrtwl3YrKX+Q4zIx55wxhf3UjK7ce8DqOSNSo/EXakBo+3r++UWv+0n3oDF+Je7WN\nTeyvaqTZOTJT/KQn+0n2J1AfaGbV1gP8aOl6stOTmDo8x+uoIlGj8pe49UFZNT9cvJ43tx3g6IN5\nEowj0wb0SOGxuYVkpSR2fkiRDqLyl7gUCDZz/e//RVV9gJvPHcbg3ukYUFkfoLYxSF1jkJTEBEb1\ny+KcEbkk+bWFVLqXiMrfzHoCvwPGAg64AdgEPAXkA9uBzzrnDkWUUiTK3vrwEDsO1vLw507j0vH9\nvY4j0ukiXZ15EHjOOTcKmABsBL4PLHfODQeWh2+LxJTqhiYA+vVI9jiJiDfaXf5mlgWcAzwG4Jxr\ndM6VA7OBx8OzPQ5cGWlIkWgb1T8LgBXFOnxT4lMka/5DgDLg92a21sx+Z2bpQF/n3B6A8Pc+Ucgp\nElUDe6YyfUQuv/vnVnaV13kdR6TTRVL+fuA04BHn3CSghpPYxGNm88ysyMyKysrKIogh0j7/NftU\ngs2OW59aR1Bj90iciaT8S4AS59yb4duLCP0x2Gdm/QHC30tbe7Bzbr5zrtA5V5ibmxtBDJH2Gdw7\nnf+cPZbV2w7y6KsfeB1HpFO1u/ydc3uBnWY2MjzpfOA9YCkwNzxtLrAkooQiHegzpw3k0vH9uf/F\nzazfVeF1HJFOE+nRPrcAfzKzd4CJwN3APcBMM9sCzAzfFolJZsZdV46lR2oiP3/ufa/jiHSaiI7z\nd86tAwpbuev8SJ5XpDP1TEti7pR87ntxM3sr6unXI8XrSCIdTqctigCDe6cBUFbV4HESkc6h8pe4\n4VzrR/S8W1LBfS9upm9WMiP7ZXZyKhFvaGwf6dZ2HKjl3hc38ebWg+yvbiDBjMwUP2nJPtIS/Ryq\nbaS0qoHe6UnMv+50jeEjcUPlL91WdUMTc+avpLK+iQtG92Fgr1SCzVAVHrytpqGJcXk9mJDXgysm\nDKRHmkbtlPih8pdua/nGfeyuqOfPXzmTKUM1Fr9IS/qMK91WaWVo5+2p/Xt4nEQk9qj8pdsqyEkH\nYF1JucdJRGKPyl+6rbNH5JCTkcQDyzbTFGz2Oo5ITFH5S7eV7Pdx52VjWLujnF+/VOx1HJGYovKX\nbm32xIF8etJAfv3SFoq2H/Q6jkjMUPlLt/efs09lYK9Ubn163ZEreInEO5W/dHuZKYnc99mJ7DxY\nx+/+udXrOCIxQeUvceGM/GzOH9WHP67aQbMu3CKi8pf4cdrgXuyvbqBKm35EVP4SHz48UMNT/9rJ\n0Nx0slJ0YruIfguky9tXWc+CFdtYu6OcQzWNJPkTyEzxk57kJyXRx97KetbtLCctycfC6ydjZl5H\nFvGcyl+6tIM1jcz+zQr2VzcwPq8HQ3MzCASbqawPsLeynrpAkJz0ZOadM4QvnjWYAT1TvY4sEhNU\n/tKl/W/RTvZW1vPXm6cycVBPr+OIdBna5i9d2vYDtWSnJ6n4RU6Syl+6tP49UjhY08j+al1+UeRk\nRFz+ZuYzs7Vm9vfw7QIze9PMtpjZU2aWFHlMkdZdMq4fAPNf08lbIicjGmv+3wQ2trj9c+B+59xw\n4BBwYxReQ6RVw/pkMueMQfz2n1tZ+cEBr+OIdBkRlb+Z5QGXAr8L3zbgPGBReJbHgSsjeQ2Rttx5\n2RgKeqfz7afXUV7b6HUckS4h0jX/B4DvAYcHS+8NlDvnDp9CWQIMjPA1RI4rPdnPg3MmUVbVwA//\nuh7nNHyDSFvaXf5mdhlQ6pxb03JyK7O2+ptoZvPMrMjMisrKytobQwSAcXk9uHXmCP7+zh5eL97v\ndRyRmBfJmv9U4Aoz2w48SWhzzwNATzM7fP5AHrC7tQc75+Y75wqdc4W5ubkRxBAJ+fLZBfTLSuGx\n17d5HUUk5rW7/J1ztzvn8pxz+cAc4CXn3OeBl4GrwrPNBZZEnFLkBCT7fUwbnsO7JRVeRxGJeR1x\nnP9twLfNrJjQPoDHOuA1RD5hX2U9K4r3MzQ3w+soIjEvKsM7OOdeAV4J/7wVmByN5xU5rKI2wJK3\nd7F+VwWVdU2kJfnITPGTmuQnyWfsOFjLso2lBJsdj3xhtNdxRWKexvaRmLevsp4rH17Bnop6cjKS\n6JWWRF0gSFV9E3WNQRqDzfTJTObCMX35+rnDGNZHa/4ibVH5S8yb/9pW9lc3sOimT3H64F6fGJK5\nudmRkKBhmkVOhspfYt7GPZWMHdiDwvzsVu9X8YucPA3sJjGvV1oSpZUNOnlLJIpU/hLzzhvVh13l\ndSzbWOp1FJFuQ+UvMe+yCf0Z3ieDOxa/ywEN3SwSFSp/iXnJfh8PXTuJitoAtz3zjjb/iESByl+6\nhNH9s7ht1iiWbSzlz6t3eB1HpMtT+UuXcf2UfKYNy+Gnf99IWZU2/4hEQuUvXUZCgvFfs0+loSnI\nH1Zu9zqOSJem8pcuZUhuBuPzerJq60Gvo4h0aSp/6VLKqhr48EANuVnJXkcR6dJ0hq/EjPpAkBXF\n+9m8r5qahibSkn1kpiSSlujDl2AUl1bzVNFOahuDfG36UK/jinRpKn+JCXsq6pgzfxUfHqgFwAyO\nPqLTDKYM7c3ts0YzdmAPD1KKdB8qf4kJP//H+5RVNfDb6wqZMrQ3aUk+6gPNVDUEqGsMEgg6BvRM\nIS1Jb1mRaNBvksSEf20/xPmj+zJzTN8j01KTfKQm+TxMJdJ9aYevxISUxATqGpu8jiESN1T+EhOm\nDsvhtc372VdZ73UUkbig8peYcMPUAszge4veoblZY/eIdDSVv8SE/Jx0fnjpaF7dXMbCN7Z7HUek\n22t3+ZvZIDN72cw2mtkGM/tmeHq2mb1oZlvC33tFL650Z184azAXjO7DPf94n017q7yOI9KtRbLm\n3wR8xzk3GjgLuNnMxgDfB5Y754YDy8O3RdpkZtzzmfFkpfr5zv+u0+YfkQ7U7vJ3zu1xzr0V/rkK\n2AgMBGYDj4dnexy4MtKQEj9yMpK5fdZo1u+q5OVNunKXSEeJyjZ/M8sHJgFvAn2dc3sg9AcC6BON\n15D4MXviADKT/bz0vspfpKNEXP5mlgE8A3zLOVd5Eo+bZ2ZFZlZUVlYWaQzpRg7WNNIQbCYlUSd4\niXSUiM7wNbNEQsX/J+fcX8KT95lZf+fcHjPrD7S6+uacmw/MBygsLNTG3TjhnGPzvmq27a+hPhAk\nI9lPRoqftCQfzsGG3ZU8+uoHJBhcO3mQ13FFuq12l7+ZGfAYsNE5d1+Lu5YCc4F7wt+XRJRQuo2S\nQ7V8+fEi3m/jSJ7hfTL4441nMqxPZiclE4k/kaz5TwW+CLxrZuvC0+4gVPpPm9mNwA7g6sgiSndx\nx+L17DpUx93/No7xeT1ITfJRXd9EdUMTdY1BHJDfO41hfTIIrVuISEdpd/k7514HjvUben57n1e6\np0CwmX9uKWPeOUP43JmneB1HJO7pDF/pFM6F1hQSE/SWE4kF+k2UTpHkT2B8Xk+e27CXoE7eEvGc\nyl86zZfPLqC4tJpHXin2OopI3FP5S6e5dFx/Lp8wgPuXbWHdznKv44jENZW/dBoz46dXjqVfVgrf\nenIttbp4i4hnVP7SqXqkJnLvZyew/UAtv3x+k9dxROKWyl863VlDenPt5FP446oP2VuhK3eJeEHl\nL574ytkFBIKOF9/b63UUkbik8hdP+BJC5wc2BnXYp4gXIhrYTeRYqhua2HWojoamIIaRkBAqfJ8Z\nJYfquPvZjaQl+bh4bD+vo4rEJZW/RNXu8jr+Y9HbvPHBAdxxVur7ZCbzu+sKGdgztfPCicgRKn+J\nGuccX//TWxSXVnPLucMY0S+TFL8PBwSbHc3O0dTsyErx86mhvUn2a7x+Ea+o/CVqSg7VsW5nOXde\nNoYbpxV4HUdEjkM7fCVqahuDAORkJHmcRETaovKXqBncO42MZD+vbtZlOUVincpfoiYl0cdnCwex\neO0u3vhgv9dxROQ4VP4SVd+9aAT5vdP57tNvU1EX8DqOiByDyl+iKi3JzwPXTGRfVQM/WrLe6zgi\ncgwqf4m6CYN68s3zh7Nk3W6Wxfz2AAAEp0lEQVSeW6/hG0RikcpfOsTXZgxlVL9M7vnHRpp15S6R\nmNNh5W9mF5vZJjMrNrPvd9TrSGxK9CXwtRlD2X6gljU7DnkdR0SO0iHlb2Y+4GFgFjAGuNbMxnTE\na0ns6t8jNHTDwZpGj5OIyNE6as1/MlDsnNvqnGsEngRmd9BrSYxxzrF+VwU/WrKejGQ/ZxZkex1J\nRI7SUcM7DAR2trhdApzZQa8lMWLjnkpueWItB6obOFQbICvFz8OfP42eaTrjVyTWdFT5WyvTPrbX\nz8zmAfMATjnllA6KIZ0pI9nP8D4ZnFmQzZgBWVwytj+90lX8IrGoo8q/BBjU4nYesLvlDM65+cB8\ngMLCQh0O0g0Myk7jkS+c7nUMETkBHbXN/1/AcDMrMLMkYA6wtINeS0RETlKHrPk755rM7BvA84AP\nWOCc29ARryUiIievw8bzd849CzzbUc8vIiLtpzN8RUTikMpfRCQOqfxFROKQyl9EJA6p/EVE4pA5\n5/35VWZWBnzodY4TlAPoGoXHp2V0fFo+bdMyalsOkO6cy23Pg2Oi/LsSMytyzhV6nSOWaRkdn5ZP\n27SM2hbpMtJmHxGROKTyFxGJQyr/kzff6wBdgJbR8Wn5tE3LqG0RLSNt8xcRiUNa8xcRiUMq/xNg\nZj8xs11mti78dUmL+24PX6R+k5ld5GVOr5nZxeHlUGxm3/c6T6wws+1m9m74vVMUnpZtZi+a2Zbw\n915e5+xMZrbAzErNbH2Laa0uEwt5KPy+esfMTvMueec4xvKJag+p/E/c/c65ieGvZwHCF6WfA5wK\nXAz8d/ji9XEn/O9+GJgFjAGuDS8fCTk3/N45fGje94HlzrnhwPLw7XiykNDvTEvHWiazgOHhr3nA\nI52U0UsL+eTygSj2kMo/MrOBJ51zDc65bUAxoYvXx6PJQLFzbqtzrhF4ktDykdbNBh4P//w4cKWH\nWTqdc+414OBRk4+1TGYD/+NCVgE9zax/5yT1xjGWz7G0q4dU/ifuG+GPnAtafERv7UL1Azs/WkzQ\nsjg2B7xgZmvC164G6Ouc2wMQ/t7Hs3Sx41jLRO+tj0Sth1T+YWa2zMzWt/I1m9DHzKHARGAPcO/h\nh7XyVPF6+JSWxbFNdc6dRmjzxc1mdo7XgboYvbdCotpDHXYlr67GOXfBicxnZr8F/h6+2eaF6uOI\nlsUxOOd2h7+XmtliQh/J95lZf+fcnvAmjFJPQ8aGYy0TvbcA59y+wz9Ho4e05n8Cjtq++G/A4T3w\nS4E5ZpZsZgWEdkit7ux8MeJfwHAzKzCzJEI7oJZ6nMlzZpZuZpmHfwYuJPT+WQrMDc82F1jiTcKY\ncqxlshS4LnzUz1lAxeHNQ/Ek2j2kNf8T8wszm0joo9R24KsAzrkNZvY08B7QBNzsnAt6ltJDzrkm\nM/sG8DzgAxY45zZ4HCsW9AUWmxmEft/+7Jx7zsz+BTxtZjcCO4CrPczY6czsCWAGkGNmJcCPgXto\nfZk8C1xCaEdmLXB9pwfuZMdYPjOi2UM6w1dEJA5ps4+ISBxS+YuIxCGVv4hIHFL5i4jEIZW/iEgc\nUvmLiMQhlb+ISBxS+YuIxKH/D7Ccnz2c4Ta+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 60\n",
    "model.reset()\n",
    "solution_model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "x_solution = np.zeros_like(t_data)\n",
    "y_solution = np.zeros_like(t_data)\n",
    "\n",
    "# maintain velocity at 4 m/s\n",
    "v_data = np.zeros_like(t_data)\n",
    "v_data[:] = 4 \n",
    "\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "# ==================================\n",
    "#  Square Path: set w at corners only\n",
    "# ==================================\n",
    "# w_data[670:670+100] = 0.753\n",
    "# w_data[670+100:670+100*2] = -0.753\n",
    "# w_data[2210:2210+100] = 0.753\n",
    "# w_data[2210+100:2210+100*2] = -0.753\n",
    "# w_data[3670:3670+100] = 0.753\n",
    "# w_data[3670+100:3670+100*2] = -0.753\n",
    "# w_data[5220:5220+100] = 0.753\n",
    "# w_data[5220+100:5220+100*2] = -0.753\n",
    "\n",
    "# ==================================\n",
    "#  Spiral Path: high positive w, then small negative w\n",
    "# ==================================\n",
    "# w_data[:] = -1/100\n",
    "# w_data[0:100] = 1\n",
    "\n",
    "# ==================================\n",
    "#  Wave Path: square wave w input\n",
    "# ==================================\n",
    "w_data[:] = 0\n",
    "w_data[0:100] = 1\n",
    "w_data[100:300] = -1\n",
    "w_data[300:500] = 1\n",
    "w_data[500:5700] = np.tile(w_data[100:500], 13)\n",
    "w_data[5700:] = -1\n",
    "\n",
    "# ==================================\n",
    "#  Step through bicycle model\n",
    "# ==================================\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc\n",
    "    y_data[i] = model.yc\n",
    "    model.step(v_data[i], w_data[i])\n",
    "\n",
    "    x_solution[i] = solution_model.xc\n",
    "    y_solution[i] = solution_model.yc\n",
    "    solution_model.step(v_data[i], w_data[i])\n",
    "    \n",
    "#     print(\"model.xc = \",x_data[i])\n",
    "#     print(\"model.yc = \",y_data[i])\n",
    "#     print(\"model.theta = \",model.theta)\n",
    "#     print(\"model.delta = \",model.delta)\n",
    "#     print(\"model.beta = \",model.beta)\n",
    "    \n",
    "#     print(\"------------------------------------\")\n",
    "    \n",
    "#     print(\"solution_model.xc = \",x_solution[i])\n",
    "#     print(\"solution_model.yc = \",y_solution[i])\n",
    "#     print(\"solution_model.theta = \",solution_model.theta)\n",
    "#     print(\"solution_model.delta = \",solution_model.delta)\n",
    "#     print(\"solution_model.beta = \",solution_model.beta)\n",
    "    \n",
    "#     print(\"---------------------------------------------\")\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data,label='Learner Model')\n",
    "# plt.plot(x_solution, y_solution,label='Solution Model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We would now like the bicycle to travel a figure eight trajectory. Both circles in the figure eight have a radius of 8m and the path should complete in 30 seconds. The path begins at the bottom of the left circle and is shown in the figure below:\n",
    "\n",
    "![title](figure8.png)\n",
    "\n",
    "Determine the speed and steering rate inputs required to produce such trajectory and implement in the cell below. Make sure to also save your inputs into the arrays v_data and w_data, these will be used to grade your solution. The cell below also plots the trajectory generated by your own model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hW3HWTgXHBrMON0kAQgxSVLB0NRa2FernhadBUdNitEt5LpkAPAzKIavrCPcS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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 30\n",
    "model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "v_data = np.zeros_like(t_data)\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "v_data[:] = (16 * np.pi)/15\n",
    "\n",
    "# ==================================\n",
    "#  Learner solution begins here\n",
    "# ==================================\n",
    "model.xc = 0\n",
    "model.yc = 0\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    x_data[i] = model.xc \n",
    "    y_data[i] = model.yc\n",
    "    \n",
    "    if i < 352 or i > 1800:\n",
    "        if model.delta < np.arctan(2/8):\n",
    "            model.step(v_data[i], model.w_max)\n",
    "            w_data[i] = model.w_max\n",
    "        else:\n",
    "            model.step(v_data[i], 0)\n",
    "            w_data[i] = 0\n",
    "    else:\n",
    "        if model.delta > -np.arctan(2/8):\n",
    "            model.step(v_data[i],-model.w_max)\n",
    "            w_data[i] = -model.w_max\n",
    "        else:\n",
    "            model.step(v_data[i],0)\n",
    "            w_data[i] = 0\n",
    "    \n",
    "#     print(\"i = \",i)\n",
    "#     print(\"model.xc = \",x_data[i])\n",
    "#     print(\"model.yc = \",y_data[i])\n",
    "    \n",
    "    model.beta = 0\n",
    "    \n",
    "    \n",
    "# ==================================\n",
    "#  Learner solution ends here\n",
    "# ==================================\n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now run your speed and angular rate inputs through our bicycle model solution. This is to ensure that your trajectory is correct along with your model. The cell below will display the path generated by our model along with some waypoints on a desired figure 8. Surrounding these waypoints are error tolerance circles with radius 1.5m, your solution will pass the grader if the trajectory generated stays within 80% of these circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assessment passed! Your trajectory meets 100.0% of the waypoints.\n"
     ]
    },
    {
     "data": {
      "image/png": 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vHnI68rTJypQRnhcrIxHZBdzKJGgC8C3wXE1ehMaE4lXUxLtPndsC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WrTpHgTWpdpnaDoukbas9t7NzUK1cAum53+nU7MBgtrddlQD+oUqcPjiMdUK1iNHTd38EnFT16d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\nEDQ0NDQ0AG1A0NDQ0NCI438AAdKwrBf0nAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grade_bicycle(t_data,v_data,w_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The cell below will save the time and vehicle inputs as text file named $\\textit{figure8.txt}$. To locate the file, change the end of your web directory to $\\textit{/notebooks/Course_1_Module_4/figure8.txt}$\n",
    "\n",
    "Once you are there, you can download the file and submit to the Coursera grader to complete this assessment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = np.vstack([t_data, v_data, w_data]).T\n",
    "np.savetxt('figure8.txt', data, delimiter=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations! You have now completed the assessment! Feel free to test the bicycle model with different inputs in the cell below, and see what trajectories they form. For example, try moving in an equilateral triangle. You'll find that it's rather difficult to generate desired trajectories by pre-setting the inputs. The next module on vehicle control will show you an easier and more accurate method. See you there!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample_time = 0.01\n",
    "time_end = 30\n",
    "model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "x_data = np.zeros_like(t_data)\n",
    "y_data = np.zeros_like(t_data)\n",
    "v_data = np.zeros_like(t_data)\n",
    "w_data = np.zeros_like(t_data)\n",
    "\n",
    "# ==================================\n",
    "#  Test various inputs here\n",
    "# ==================================\n",
    "for i in range(t_data.shape[0]):\n",
    "\n",
    "    model.step(v_data[i], w_data[i])\n",
    "    \n",
    "plt.axis('equal')\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()"
   ]
  }
 ],
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