From 54bce9d7a049f14eb72591bbbc45dcab79e71266 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 30 May 2015 14:44:49 -0700 Subject: [PATCH] Added EKF robot localization example. Still needs a lot of explanation; mostly the implementation is there for now. --- 11_Extended_Kalman_Filters.ipynb | 800 +++++++++++++++++++++++++++---- book_format.py | 5 +- code/ekf_internal.py | 30 ++ experiments/bicycle.py | 10 +- experiments/ekf4.py | 194 ++++++++ experiments/ekfloc.py | 290 +++++++++++ experiments/ekfloc2.py | 191 ++++++++ experiments/ekfloc3.py | 259 ++++++++++ styles/custom2.css | 2 +- 9 files changed, 1695 insertions(+), 86 deletions(-) create mode 100644 experiments/ekf4.py create mode 100644 experiments/ekfloc.py create mode 100644 experiments/ekfloc2.py create mode 100644 experiments/ekfloc3.py diff --git a/11_Extended_Kalman_Filters.ipynb b/11_Extended_Kalman_Filters.ipynb index 1cdebc7..8345ac9 100644 --- a/11_Extended_Kalman_Filters.ipynb +++ b/11_Extended_Kalman_Filters.ipynb @@ -30,7 +30,7 @@ "@import url('http://fonts.googleapis.com/css?family=Arimo');\n", "\n", " div.cell{\n", - " width: 850px;\n", + " width: 900px;\n", " margin-left: 0% !important;\n", " margin-right: auto;\n", " }\n", @@ -117,9 +117,6 @@ " font-family: 'Arimo',verdana,arial,sans-serif;\n", " line-height: 125%;\n", " font-size: 120%;\n", - " width:740px;\n", - " margin-left:auto;\n", - " margin-right:auto;\n", " text-align:justify;\n", " text-justify:inter-word;\n", " }\n", @@ -240,7 +237,10 @@ " },\n", " displayAlign: 'center', // Change this to 'center' to center equations.\n", " \"HTML-CSS\": {\n", - " scale:85,\n", + " scale:100,\n", + " availableFonts: [\"Neo-Euler\"],\n", + " preferredFont: \"Neo-Euler\",\n", + " webFont: \"Neo-Euler\",\n", " styles: {'.MathJax_Display': {\"margin\": 4}}\n", " }\n", " });\n", @@ -258,6 +258,8 @@ "source": [ "#format the book\n", "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload 2\n", "from __future__ import division, print_function\n", "import book_format\n", "book_format.load_style()" @@ -291,24 +293,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The extended Kalman filter (EKF) works by linearizing the system model for each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n", + "The extended Kalman filter (EKF) works by linearizing the system model for each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the function $f(x)=x^2−2x$. We want a linear approximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation (update) of the Kalman filter we know its current state, so if we linearize the function at that value we will have a close approximation. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n", "\n", - "\n", - "Consider the function $f(x)=x^2−2x$, which we have plotted below." + "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x−12.75 as the linearization, as in the plot below." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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LTul03hGdvnhM+ZezO32sSSb1Dx+s4bHjNXzAOPUPj5crV9MBAE6I\n0g6gW7FYLcorPq8zecd05uJRZV/KUrOlqdPHe3n4KSowTlPHp2po/7HyZW86AKAboLQDcGqGYehS\nSa7O5B3XmbxjOleQqfrG2k4f7+7qoUHRIzW8/zgNix2r/OwimUwmJQ7lvsoAgO6D0g7AqRiGoeLy\nQp3NO66z+cd1Lv+Equoqrn/gt0SHDdTQmAQNjUnQoH4jrrlvesGFYltHBgCgy1HaATiUYRi6UmHW\n2fzjOpt/Qmfzj6uypuyGzhHsH6Zh/RM0JCZBQ2LGsOUFANDjUNoB2NU3V9LP5Z+4+lF4UhXVJTd0\nDh8vfw2JHq0hMWM0JGaM+gZE8OZGAIAejdIOoEtZDavMJRd1vuCkzhVk6lxBpqpqy2/oHJ7ufTS4\n36iWkh7Zt79cTC5dlBgAAOdDaQdgUxZLsy4Wn1d24UmdLzip7MJTqm2ovqFzeLh5amDUcA2OHqX4\n6NHqHzZIrq78uAIA9F78LQjge6lrqFWO+bSyC08pu/CUcsyn1dTceEPncHfzUFzEUMXHjL5a0sMH\ny83VvYsSAwDQ/VDaAdyQsqrLyi7MulrSL51S4ZVcGYb1hs7h4d5HAyOHaXC/kRocPYqSDgDAdVDa\nAbSr2dKkgssXlH0pSxcuZSnn0mmV3+CLRiXJy9NHAyOHa1C/ERocPUoxoQPZ7gIAwA3gb00ALSqq\nS5VjPq0c82lduHRaeUXn1WS5sa0ukuTvE6RBUSM0qN9IDYoawQtHAQD4nijtQC/V2Nyg/OILLSU9\n99IZlVVfualzhQdHa1DUcMVFDtfAqOHcghEAABujtAO9gNVqUVFZgXLNZ5VbdFa5RWdUeCVXVqvl\nhs/l5uqu/mGDNTBquOKihmlg5DD58GZGAAB0KUo70MMYhqHSymJdLD6ni0VffxSfU0Nj3U2dL8A3\nRHGRQxUXOUxxkcMUHRrHi0YBALAzSjvQjRmGofLqEuUVn1de8TnlFp1TXtE51dRX3dT5XF3dFBM2\nSAMihmpAxBDFRQ5VkF+ojVMDAIAbRWkHugnDMFRWdVl5xdlfl/SrH9V1FTd9zmD/MA2IGKq4yKsl\nPapvnNzduIoOAICzobQDTshqtai4vFD5xdkquHJB+cUXlH85+6avoEuSdx8/xYbHKzYiXrHh8eof\nHi8/7wAbpgYAAF2F0g44WENjnQpLclVwOUcFV3KUfzlbhVdybvhdRb/Nw72PYsIGqX/YIPUPH6z+\n4fHc0QUAgG6M0g7YiWEYKq0qVuGVXBVeyWkp6VfKL8mQcdPndXfzUL/QuK8LerxiwgYrPChKLi6u\nNkwPAAAcidIOdIHahmpdupL7dUHPVWHJ1Y+bvYPLNzzc+yg6NE4xYYNaPsKD+lHQAQDo4SjtwPdQ\n31gnc2meLpVc1KWSizJ//bmipvR7n9vHy1/RoXGKDh149SNsoEIDIijoAAD0QpR2oBNqG6plLslX\nUWmezKV5Mpde/bq06vL3PrdJJvUNjFS/vgPUL3SA+vWNU3TYQAX4BLMHHQAASKK0Ay2u3vP8iopK\nC1RUlq+isgIVl+bLXJavypoymzxHHw9vRYXEKqpvrPqFximq7wBFhfSXp4eXTc4PAAB6Jko7ep26\nhhpdLr+k4rICFZcX6nJZoYrKC1RcVqjGpnqbPIeLi6vCg/opKiRWkX1jvy7qAxTk15er5wAA4IZR\n2tEjNTTW6XLFJV0uN+tyeaGulF+6WtTLC1VVW26z5zGZXBQaGKnI4BhFhsQqIuTq57DASLm68n8v\nAABgG7QKdEuGYai6rlJXKswqqTB//blIFwrOqqquTP/YXW3T53N1cVNYUJTCg6MVERSjiJAYRQRH\nKzQwSu5uHjZ9LgAAgO+itMNpNTTVq6SiSCWVRSqtLFZJZbFKK4tUUlGkK5VF3/v2iW3x8vBWeHCM\nwoP6KSw4WuFB/RQe1E99AyK4cg4AAByGFgKHMAxDdQ01Kq0qVmnlZZVVXVZpZbFKqy6rrPKySqsu\nq7quokue28XFVX0DIhQW1E9hgVEKC4pSaGCUwoOi5ecdwJ5zAADgdCjt6BJ1DbWqqClReVWJyqtL\nVFZ1WWXVV1RedUVl1VdUVnXFZi/6bIuLyUUh/uHqGxip0K8/vinqwf5hcuVe5wAAoBuhtOOGWCzN\nqqwtU0VNmSqqS1VRU6rKmjJVVF8t5+U1Vz93xdaV7/Jw81TfgAj1DYy4WtADIlRaXCW/PkGakTKT\n7SwAAKDHoNVAVsOqmroqVddVqKq2QlW1ZaqsKVdlbZmqastVWVOmyq8/d9WWlba4uLgqyK+vQvzC\nFBwQrhD/cIX4hynk66/9vANbbWVJT0+XJAo7AADoUWzWbP785z/rvffe0+HDh1VZWamcnBz179//\nusd98MEH+sUvfqHs7GwNGjRIL730khYuXGirWL2SxdKsmvpq1dRXqrru6kdNXaWq6ypUU1+l6toK\nVdVV/N/nukoZhtXuOd1dPRTk11dB/qEK9gtTsH+ogv3DFOwXqiC/MAX4BrONBQAAQDYs7XV1dbr9\n9tu1cOFCLV26tFPH7N27V/fdd59+/etf64c//KE++OAD3XPPPdq9e7cmTpxoq2jdktWwqr6xVvUN\ntaprqFFtQ7Vq669+rvvW17X11aqtr1LN1x+19dWqb6x1dHy5urop0DdEgT4hVz/79b1a0P1CFeh7\n9WufPn686BMAAKATbFban3nmGUn/tz2hM1auXKmZM2fq+eeflyT913/9l7Zt26aVK1fq3XfftVU0\nuzAMQ02WRjU2NaixqV4NTfUtn7/9dX1jreob61TfWKeGxjo1NNWpvuHqY3WNNaprqFFdY61d9oTf\nDJNM8vUOUIBP8NUP3yD5ewcrwDdYgb4hX3+mkAMAANiSQzf+7tu3T08//fQ1j82ZM0d//OMfOzwu\n13xGhq4WZcmQYUiGYZXVsMowjJavrVbL149ZZbFaZLVaZPn6o+VrS7Oarc2yWJrUbGmWxXr189WP\nJjU3N6rpW5+bLI1qam5UU1ODGpsb1NTc2PK5O/Py8Javd6D8vALk7xMkf59A+XkHyd87UP4+QfLz\nDpSfd6D8vQPZLw4AAGBnDm1fZrNZ4eHh1zwWHh4us9nc4XG/e/+5rozV7ZlkklcfX/n28ZOvV4B8\nvPzk4+UvX68A+Xr5yaeP/9clPODrxwLk7ubu6NgAAABoR4elffny5VqxYkWHJ0hLS9P06dNtGup6\nXnzo73Z9vh7NKtXWOH4PvK3Ex8dLkioq7HeXG3QvrBF0BusEncE6gT11WNqXLl2qJUuWdHiCmJiY\nm37yiIiIVlfVi4qKFBERcdPnBAAAAHqaDkt7SEiIQkJCuuzJJ0+erK+++ko/+9nPWh776quvNGXK\nlC57TgAAAKC7sdmedrPZLLPZrDNnzkiSMjMzVVpaqtjYWAUFBUmSZs2apeTk5JYtN88884ymT5+u\nl19+WQsWLNBHH32ktLQ07d69u9X5AwICbBUVAAAA6FZcbHWiN998U+PHj9ePf/xjmUwmzZs3T4mJ\nifrXv/7VMic7O/ua7TCTJ0/W2rVrtWrVKiUkJGjNmjVat26dJkyYYKtYAAAAQLdnMq7eNxEAAACA\nk7LZlfbvY8eOHbrrrrsUHR0tFxcX/f3v1787zPHjxzVjxgx5e3srOjpaL774oh2SwpFudJ2kpaVp\nwYIFioqKko+PjxISEvT222/bKS0c5WZ+nnzj7Nmz8vPzk5+fXxcmhKPd7BpZuXKlhg0bpj59+igq\nKqrljQHRM93MOtm4caMmTZokf39/hYaGauHChTp79qwd0sJR/ud//kcTJkxQQECAwsLCdNdddykz\nM/O6x91Mj3WK0l5TU6MxY8bo1VdflZeX13XfSbOyslKzZ89WZGSk0tPT9eqrr+qVV17R73//ezsl\nhiPc6DrZu3evEhIS9MEHHygzM1NPPPGEHn/8cb333nt2SgxHuNF18o3Gxkbdd999mjFjBu/m28Pd\nzBpZtmyZ3njjDb3yyivKysrS559/rhkzZtghLRzlRtfJuXPntHDhQt1yyy06cuSINm/erPr6es2d\nO9dOieEI27dv13/8x39o79692rp1q9zc3JSamqqysrJ2j7npHms4GV9fX+Pvf/97h3Nef/11IyAg\nwKivr2957De/+Y3Rr1+/ro4HJ9GZddKWRYsWGT/60Y+6IBGc0Y2sk2effdZ45JFHjFWrVhm+vr5d\nnAzOojNrJCsry3B3dzeysrLslArOpjPrZP369Yarq6thtVpbHtu6dathMpmMkpKSro4IJ1FdXW24\nuroan376abtzbrbHOsWV9hu1d+9eTZs2TZ6eni2PzZkzR4WFhcrNzXVgMji7iooKBQcHOzoGnMxn\nn32mzz77TH/4wx9k8DIffMcnn3yigQMHauPGjRo4cKDi4uL00EMP6fLly46OBicyZcoU+fr66i9/\n+YssFouqqqq0atUqTZw4kb93epHKykpZrdaWOye25WZ7bLcs7WazWeHh4dc89s33332zJuAbn376\nqbZu3arHH3/c0VHgRAoLC/X444/rnXfekbe3t6PjwAllZ2crNzdX69at0z/+8Q+tXr1aWVlZmj9/\nPr/koUVkZKQ2btyo5cuXq0+fPgoMDFRmZuY1d9FDz/fMM89o3Lhxmjx5crtzbrbHdsvSzn5T3Kjd\nu3frgQce0B/+8AclJSU5Og6cyIMPPqgnnniCW82iXVarVQ0NDVq9erWmTp2qqVOnavXq1Tpw4IDS\n09MdHQ9OIjs7WwsXLtTDDz+s9PR0paWlyc/PT4sWLeKXu15i2bJl2rNnjz744IMOu+rN9thuWdoj\nIiJa/SZSVFTUMgZ8265duzR37ly9+OKL+ulPf+roOHAy27Zt0wsvvCB3d3e5u7vrscceU01Njdzd\n3fXXv/7V0fHgBCIjI+Xm5qbBgwe3PDZ48GC5urrq4sWLDkwGZ/KnP/1JMTExevnll5WQkKBp06Zp\nzZo12r59u/bu3evoeOhiS5cu1fvvv6+tW7dqwIABHc692R7bLUv75MmTtXPnTjU0NLQ89tVXX6lf\nv36KjY11YDI4mx07dmju3Ll64YUX9PTTTzs6DpzQiRMndPTo0ZaPX//61/Ly8tLRo0d19913Ozoe\nnMDUqVPV3Nys7Ozslseys7NlsVj4OwctDMOQi8u1teqb761WqyMiwU6eeeaZlsI+ZMiQ686/2R7r\nFKW9pqZGR44c0ZEjR2S1WpWbm6sjR44oLy9PkvT8888rNTW1Zf79998vb29vPfTQQ8rMzNSHH36o\nl19+WcuWLXPUHwF2cKPrJC0tTXfccYeeeOIJLV68WGazWWazmReP9XA3uk5GjBhxzUdUVJRcXFw0\nYsQIBQYGOuqPgS50o2skNTVV48eP1yOPPKIjR47o8OHDeuSRRzRp0iS22/VgN7pO7rrrLh06dEgv\nvviizp49q0OHDunhhx9W//79lZiY6Kg/BrrYk08+qVWrVumdd95RQEBAS9eoqalpmWOzHmuT+9t8\nT9u2bTNMJpNhMpkMFxeXlq8ffvhhwzAM46GHHjLi4uKuOeb48ePG9OnTjT59+hhRUVHGr3/9a0dE\nhx3d6Dp56KGHrpn3zcd31xJ6lpv5efJtb7/9tuHn52evuHCAm1kjly5dMu655x7Dz8/PCAsLM378\n4x8bxcXFjogPO7mZdbJ+/XojMTHR8PX1NcLCwowFCxYYp06dckR82Ml318c3Hy+88ELLHFv1WJNh\n8OoIAAAAwJk5xfYYAAAAAO2jtAMAAABOjtIOAAAAODlKOwAAAODkKO0AAACAk6O0AwAAAE6O0g4A\nAAA4OUo7AAAA4OQo7QAAAICT+/8BQKWT/yXokOsAAAAASUVORK5CYII=\n", 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ZE56gtITh7SE9NW64ggNDPNg14Ns8EtorKyv1l7/8RUuXLtXpp58uSXr55ZeV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\n2/a8rlLV9ZWqqXO/bnY2ebt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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -321,41 +329,10 @@ "\n", "xs = np.arange(0, 2, 0.01)\n", "ys = [x**2 - 2*x for x in xs]\n", - "plt.plot (xs, ys)\n", - "plt.xlim(1, 2)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We want a linear approximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation (update) of the Kalman filter we know its current state, so if we linearize the function at that value we will have a close approximation. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n", "\n", - "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x−12.75 as the linearization, as in the plot below." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ZE56gtITh7SE9NW64ggNDPNg14Ns8EtorKyv1l7/8RUuXLtXpp58uSXr55ZeV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\n2/a8rlLV9ZWqqXO/bnY2ebt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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ "def y(x): \n", " return 8*x - 12.75\n", + "\n", "plt.plot (xs, ys)\n", "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)])\n", "plt.xlim(1, 2)\n", @@ -379,7 +356,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -388,7 +365,7 @@ "data": { "image/png": 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Lvk9xfrmaqi+YqksvLag8b0P6iMeYGcqnjZw7F/5/2qQgtAMAACwj4UhIXa5WtfV9FP/0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\nhjqdJyd9Ti2VmJj4GQhJ0rq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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -454,7 +431,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -463,7 +440,7 @@ "data": { "image/png": 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V7tdMn25ef+01M3rrckkNGkiffirVqiX99JM0fLhUo4Y0ZIgJuA0bSsOGmSkPkuTrK11/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\nBcqP9957T0FBQTp48KD27Nn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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -669,7 +646,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -694,7 +671,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -717,7 +694,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -792,16 +769,16 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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AC2jysc1m48c//jE//vGP+7s9IiIi8i0NDQ18tmYV7k1rqD6+l5CYHmJskRAG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\nIWqSk5MTAOi91zZsI+rKnJ2d4ebmxvstGdSyZcuwZ88eHD5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OSCDh1HG+PlTNqbMDOZoyl7r6Hi22HT4QnloMcyeCn7fCgHQ+XSIYLFq0yPb3oUOHMmbM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\nn5+PefPmwcnJCcbGxrC3t8fo0aORmZnZpLazsrIwbdo0KJV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6tsrd7fV2C1HbvpyXjtq6Gh2lISIiIqKORu/Bu9wTGBiI9PR0GBoaYuLEiZgz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\nAElFTkSuQmCC\n", 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HJPrnzp1jzZo1eHt7O+J0kkWhIVDYLbV86Bj8+qf66YuIiIgURNdN9CdNmoSL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\nOe/2OpujOvd+CHhD+DwB6ptrciqkti/kW6Y7+3mE/EWUhML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U1KCsrAx5eXkYPnw4HnnkEUyaNAmvvfba9TyGAcFhQkREREQ01PXaM/Dss8/i5z//OR54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\niGzU/wA9fyKMADA/5gAAAABJRU5ErkJggg==\n", 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69OHee+9l0KBBPPfcc+dzGzpEfUOgIxARERER6Vhttgw89thj/Md//Ad33nkn0dHRPutE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\nTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -916,13 +893,15 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 9, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$" ], @@ -934,14 +913,14 @@ "⎣╲╱ x_alt + x_pos ╲╱ x_alt + x_pos ⎦" ] }, - "execution_count": 13, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy\n", - "sympy.init_printing(use_latex='mathjax')\n", + "sympy.init_printing()\n", "\n", "x_pos, x_vel, x_alt = sympy.symbols('x_pos, x_vel x_alt')\n", "\n", @@ -999,7 +978,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -1026,23 +1005,652 @@ "⎣ 2 ⎦" ] }, - "execution_count": 14, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy\n", + "from sympy import Matrix\n", "sympy.init_printing(use_latex='mathjax')\n", "w_vel, w_alt, dt = sympy.symbols('w_vel w_alt \\Delta{t}')\n", - "w = sympy.Matrix([[0, w_vel, w_alt]]).T\n", - "phi = sympy.Matrix([[1, dt, 0], [0, 1, 0], [0,0,1]])\n", + "w = Matrix([[0, w_vel, w_alt]]).T\n", + "phi = Matrix([[1, dt, 0], [0, 1, 0], [0,0,1]])\n", "\n", "q = w*w.T\n", "\n", "sympy.integrate(phi*q*phi.T, (dt, 0, dt))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Robot Localization\n", + "\n", + "So, time to try a real problem. I warn you that this is far from a simple problem. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world solution. \n", + "\n", + "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. Or, it might be one of those small robots that vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors. It doesn't matter too much. \n", + "\n", + "Our robot is wheeled, which means that it manuevers by turning it's wheels. When it does so, the robot pivots around the rear axle while moving forward. This is nonlinear behavior which we will have to account for. The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", + "\n", + "### Robot Motion Model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ekf_internal.plot_bicycle()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At a first approximation n automobile steers by turning the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modelling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. \n", + "\n", + "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. If you google bicycle model you will find that we can compute the turn angle $\\beta$ with\n", + "\n", + "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", + "\n", + "and the turning radius R is given by \n", + "\n", + "$$R = \\frac{d}{\\beta}$$\n", + "\n", + "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", + "\n", + "If we let $\\theta$ be our current orientation then we can compute the position $C$ before the turn starts as\n", + "\n", + "$$ C_x = x - R\\sin(\\theta) \\\\\n", + "C_y = y + R\\cos(\\theta)\n", + "$$\n", + "\n", + "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n", + "\n", + "$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n", + "y &= C_y - R\\cos(\\theta + \\beta) \\\\\n", + "\\theta &= \\theta + \\beta\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Once we substitute in for $C$ we get\n", + "\n", + "$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", + "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", + "\\theta &= \\theta + \\beta\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "You don't really need to understand this math in detail, as it is already a simplification of the real motion. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Design the State Variables\n", + "\n", + "For our robot we will maintain the position and orientation of the robot:\n", + "\n", + "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n", + "\n", + "I could include velocities into this model, but as you will see the math will already be quite challenging.\n", + "\n", + "Our control input $\\mathbf{u}$ is the velocity and steering angle\n", + "\n", + "$$\\mathbf{u} = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Design the System Model\n", + "\n", + "In general we model our system as a nonlinear motion model plus noise.\n", + "\n", + "$$x^- = x + f(x, u) + \\mathcal{N}(0, Q)$$\n", + "\n", + "Using the motion model for a robot that we created above, we can expand this to\n", + "\n", + "$$\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}^- = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n", + "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", + "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", + "\\beta\\end{bmatrix}$$\n", + "\n", + "We linearize this with a taylor expansion at $x$:\n", + "\n", + "$$f(x, u) \\approx \\mathbf{x} + \\frac{\\partial f(x, u)}{\\partial x}$$\n", + "\n", + "We replace $f(x, u)$ with our state estimate $\\mathbf{x}$, and the derivative is just the Jacobian of $f$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Jacobian $\\mathbf{F}$ is\n", + "\n", + "$$\\mathbf{F} = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n", + "\\frac{\\partial \\dot{x}}{\\partial x} & \n", + "\\frac{\\partial \\dot{x}}{\\partial y} &\n", + "\\frac{\\partial \\dot{x}}{\\partial \\theta}\\\\\n", + "\\frac{\\partial \\dot{y}}{\\partial x} & \n", + "\\frac{\\partial \\dot{y}}{\\partial y} &\n", + "\\frac{\\partial \\dot{y}}{\\partial \\theta} \\\\\n", + "\\frac{\\partial \\dot{\\theta}}{\\partial x} & \n", + "\\frac{\\partial \\dot{\\theta}}{\\partial y} &\n", + "\\frac{\\partial \\dot{\\theta}}{\\partial \\theta}\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "When we calculate these we get\n", + "\n", + "$$\\mathbf{F} = \\begin{bmatrix}\n", + "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n", + "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n", + "0 & 0 & 1\n", + "\\end{bmatrix}$$\n", + "\n", + "We can double check our work with SymPy." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan{\\left (a \\right )}} + \\frac{w}{\\tan{\\left (a \\right )}} \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\0 & 1 & - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan{\\left (a \\right )}} + \\frac{w}{\\tan{\\left (a \\right )}} \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\0 & 0 & 1\\end{matrix}\\right]$$" + ], + "text/plain": [ + "⎡ ⎛t⋅v⋅tan(a) ⎞⎤\n", + "⎢ w⋅cos⎜────────── + θ⎟⎥\n", + "⎢ w⋅cos(θ) ⎝ w ⎠⎥\n", + "⎢1 0 - ──────── + ─────────────────────⎥\n", + "⎢ tan(a) tan(a) ⎥\n", + "⎢ ⎥\n", + "⎢ ⎛t⋅v⋅tan(a) ⎞⎥\n", + "⎢ w⋅sin⎜────────── + θ⎟⎥\n", + "⎢ w⋅sin(θ) ⎝ w ⎠⎥\n", + "⎢0 1 - ──────── + ─────────────────────⎥\n", + "⎢ tan(a) tan(a) ⎥\n", + "⎢ ⎥\n", + "⎣0 0 1 ⎦" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sympy import symbols\n", + "a, x, y, v, w, theta, time = symbols('a, x, y, v, w, theta, t')\n", + "d = v*time\n", + "beta = (d/w)*sympy.tan(a)\n", + "R = w/sympy.tan(a)\n", + "\n", + "fxu = Matrix([[x-R*sympy.sin(theta)+R*sympy.sin(theta+beta)],\n", + " [y+R*sympy.cos(theta)-R*sympy.cos(theta+beta)],\n", + " [theta+beta]])\n", + "\n", + "fxu.jacobian(Matrix([x, y, theta]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can turn our attention to the noise. Here, the noise is in our control input, so it is in *control space*. In other words, we command a specific velocity and steering angle, but we need to convert that into errors in $x, y, \\theta$. In a real system this might vary depending on velocity, so it will need to be recomputed for every prediction. I will chose this as the noise model; for a real robot you will need to choose a model that accurately depicts the error in your system. \n", + "\n", + "$$\\mathbf{M} = \\begin{bmatrix}0.01 vel^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n", + "\n", + "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf{T}$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n", + "\n", + "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n", + "\\frac{\\partial \\dot{x}}{\\partial v} & \\frac{\\partial \\dot{x}}{\\partial \\alpha} \\\\\n", + "\\frac{\\partial \\dot{y}}{\\partial v} & \\frac{\\partial \\dot{y}}{\\partial \\alpha} \\\\\n", + "\\frac{\\partial \\dot{\\theta}}{\\partial v} & \\frac{\\partial \\dot{\\theta}}{\\partial \\alpha}\n", + "\\end{bmatrix}$$\n", + "\n", + "Let's just compute that with SymPy:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\left[\\begin{matrix}t \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} & \\frac{t v}{\\tan{\\left (a \\right )}} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right) \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) + \\frac{w}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\t \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} & \\frac{t v}{\\tan{\\left (a \\right )}} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right) \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} + \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) - \\frac{w}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\\\frac{t}{w} \\tan{\\left (a \\right )} & \\frac{t v}{w} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right)\\end{matrix}\\right]$$" + ], + "text/plain": [ + "⎡ ⎛ 2 ⎞ ⎛t⋅v⋅tan(a) ⎞ \n", + "⎢ t⋅v⋅⎝tan (a) + 1⎠⋅cos⎜────────── + θ⎟ ⎛ 2 \n", + "⎢ ⎛t⋅v⋅tan(a) ⎞ ⎝ w ⎠ w⋅⎝- tan (a) -\n", + "⎢t⋅cos⎜────────── + θ⎟ ───────────────────────────────────── - ──────────────\n", + "⎢ ⎝ w ⎠ tan(a) 2 \n", + "⎢ tan (a\n", + "⎢ \n", + "⎢ ⎛ 2 ⎞ ⎛t⋅v⋅tan(a) ⎞ \n", + "⎢ t⋅v⋅⎝tan (a) + 1⎠⋅sin⎜────────── + θ⎟ ⎛ 2 \n", + "⎢ ⎛t⋅v⋅tan(a) ⎞ ⎝ w ⎠ w⋅⎝- tan (a) -\n", + "⎢t⋅sin⎜────────── + θ⎟ ───────────────────────────────────── + ──────────────\n", + "⎢ ⎝ w ⎠ tan(a) 2 \n", + "⎢ tan (a\n", + "⎢ \n", + "⎢ ⎛ 2 \n", + "⎢ t⋅tan(a) t⋅v⋅⎝tan (a\n", + "⎢ ──────── ───────────\n", + "⎣ w w \n", + "\n", + " ⎛ 2 ⎞ ⎛t⋅v⋅tan(a) ⎞⎤\n", + " ⎞ w⋅⎝- tan (a) - 1⎠⋅sin⎜────────── + θ⎟⎥\n", + " 1⎠⋅sin(θ) ⎝ w ⎠⎥\n", + "────────── + ─────────────────────────────────────⎥\n", + " 2 ⎥\n", + ") tan (a) ⎥\n", + " ⎥\n", + " ⎛ 2 ⎞ ⎛t⋅v⋅tan(a) ⎞⎥\n", + " ⎞ w⋅⎝- tan (a) - 1⎠⋅cos⎜────────── + θ⎟⎥\n", + " 1⎠⋅cos(θ) ⎝ w ⎠⎥\n", + "────────── - ─────────────────────────────────────⎥\n", + " 2 ⎥\n", + ") tan (a) ⎥\n", + " ⎥\n", + " ⎞ ⎥\n", + ") + 1⎠ ⎥\n", + "────── ⎥\n", + " ⎦" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fxu.jacobian(Matrix([v, a]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "**authors note: explain FPF better**\n", + "\n", + "This gives us the final form of our prediction equations:\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{x}^- &= \\mathbf{x} + \n", + "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", + "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", + "\\beta\\end{bmatrix}\\\\\n", + "\\mathbf{P}^- &=\\mathbf{FPF}^{\\mathsf{T}} + \\mathbf{VMV}^{\\mathsf{T}}\n", + "\\end{aligned}$$\n", + "\n", + "One final point. This form of linearization is not the only way to predict $\\mathbf{x}$. For example, we could use a numerical integration technique like *Runge Kutta* to compute the position of the robot in the future. In fact, if the time step is relatively large you will have to do that. As I am sure you are realizing, things are not as cut and dried with the EKF as it was for the KF. For a real problem you have to very carefully model your system with differential equations and then determine the most appropriate way to solve that system. The correct approach depends on the accuracy you require, how nonlinear the equations are, your processor budget, and numerical stability concerns. These are all topics beyond the scope of this book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Design the Measurement Model\n", + "\n", + "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. Using $p$ be the position of a landmark, the range $r$ is\n", + "\n", + "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", + "\n", + "We assume that the sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n", + "\n", + "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n", + "\n", + "\n", + "Thus our function is\n", + "\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{x}& = h(x,p) &+ \\mathcal{N}(0, R)\\\\\n", + "&= \\begin{bmatrix}\n", + "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", + "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n", + "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n", + "\\end{aligned}$$\n", + "\n", + "This is clearly nonlinear, so we need linearize $h(x, p)$ at $\\mathbf{x}$ by taking its Jacobian. We compute that with SymPy below." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\left[\\begin{matrix}\\frac{- px + x}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & \\frac{- py + y}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & 0\\\\- \\frac{- py + y}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & - \\frac{px - x}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & -1\\end{matrix}\\right]$$" + ], + "text/plain": [ + "⎡ -px + x -py + y ⎤\n", + "⎢────────────────────────── ────────────────────────── 0 ⎥\n", + "⎢ _______________________ _______________________ ⎥\n", + "⎢ ╱ 2 2 ╱ 2 2 ⎥\n", + "⎢╲╱ (px - x) + (py - y) ╲╱ (px - x) + (py - y) ⎥\n", + "⎢ ⎥\n", + "⎢ -(-py + y) -(px - x) ⎥\n", + "⎢ ───────────────────── ───────────────────── -1⎥\n", + "⎢ 2 2 2 2 ⎥\n", + "⎣ (px - x) + (py - y) (px - x) + (py - y) ⎦" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "px, py = symbols('px, py')\n", + "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n", + " [sympy.atan2(py-y, px-x) - theta]])\n", + "z.jacobian(Matrix([x, y, theta]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Now we need to write that as a Python function. For example we might write:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from math import sqrt\n", + "\n", + "def H_of(x, p):\n", + " \"\"\" compute Jacobian of H matrix where h(x) computes the range and\n", + " bearing to a landmark for state x \"\"\"\n", + "\n", + " px = p[0]\n", + " py = p[1]\n", + " hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n", + " dist = sqrt(hyp)\n", + "\n", + " H = array(\n", + " [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n", + " [ (py - x[1, 0]) / hyp, -(px - x[0, 0]) / hyp, -1]])\n", + " return H" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We also need to define a function that converts the system state into a measurement." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from math import atan2\n", + "def Hx(x, p):\n", + " \"\"\" takes a state variable and returns the measurement that would\n", + " correspond to that state.\n", + " \"\"\"\n", + " px = p[0]\n", + " py = p[1]\n", + " dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n", + "\n", + " Hx = array([[dist],\n", + " [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n", + " return Hx" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Design Measurement Noise\n", + "\n", + "This is quite straightforward as we need to specify measurement noise in measurement space, hence it is linear. It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", + "\n", + "$$R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$\n", + "\n", + "### Implementation\n", + "\n", + "We will use `FilterPy`'s `ExtendedKalmanFilter` class to implment the filter. The prediction of $\\mathbf{x}$ is nonlinear, so we will have to override the method `predict()` to implement this. I'll want to also use this code to simulate the robot, so I'll add a method `move()` that computes the position of the robot which both `predict()` and my simulation can call. You would not need to do this for a real robot, of course.\n", + "\n", + "The matrices for the prediction step are quite large; while trying to implement this I made several errors before I finally got it working. I only found my errors by using SymPy's `evalf` function, which allows you to evaluate a SymPy `Matrix` for specific values of the variables. I decided to demonstrate this technique, and to eliminate a possible source of bugs, by using SymPy in the Kalman filter. You'll need to understand a couple of points.\n", + "\n", + "First, `evalf` uses a dictionary to pass in the values you want to use. For example, if your matrix contains an x and y, you can write\n", + "\n", + " M.evalf(subs={x:3, y:17})\n", + " \n", + "to evaluate the matrix for `x=3` and `y=17`. \n", + "\n", + "Second, `evalf` returns a `sympy.Matrix` object. You can convert it to a numpy array with `numpy.array(m)`, but the result uses type `object` for the elements in the array. You can convert the array to an array of floats with ``numpy.array(m).astype(float)`.\n", + "\n", + "So, here is the code:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from filterpy.kalman import ExtendedKalmanFilter as EKF\n", + "from numpy import dot, array, sqrt\n", + "class RobotEKF(EKF):\n", + " def __init__(self, dt, wheelbase):\n", + " EKF.__init__(self, 3, 2, 2)\n", + " self.dt = dt\n", + " self.wheelbase = wheelbase\n", + "\n", + " a, x, y, v, w, theta, time = symbols('a, x, y, v, w, theta, t')\n", + "\n", + " d = v*time\n", + " beta = (d/w)*sympy.tan(a)\n", + " r = w/sympy.tan(a)\n", + " \n", + " self.fxu = Matrix([[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n", + " [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n", + " [theta+beta]])\n", + "\n", + " self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n", + " self.V_j = self.fxu.jacobian(Matrix([v, a]))\n", + "\n", + " # save dictionary and it's variables for later use\n", + " self.subs = {x: 0, y: 0, v:0, a:0, time:dt, w:wheelbase, theta:0}\n", + " self.x_x, self.x_y, self.v, self.a, self.theta = x, y, v, a, theta\n", + "\n", + " def predict(self, u=0):\n", + " self.x = self.move(self.x, u, self.dt)\n", + "\n", + " self.subs[self.theta] = self.x[2, 0]\n", + " self.subs[self.v] = u[0]\n", + " self.subs[self.a] = u[1]\n", + "\n", + " F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n", + " V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n", + "\n", + " # covariance of motion noise in control space\n", + " M = array([[0.1*u[0]**2, 0], [0, sigma_steer**2]])\n", + "\n", + " self.P = dot(F, self.P).dot(F.T) + dot(V, M).dot(V.T)\n", + "\n", + " def move(self, x, u, dt):\n", + " h = x[2, 0]\n", + " v = u[0]\n", + " steering_angle = u[1]\n", + "\n", + " dist = v*dt\n", + "\n", + " if abs(steering_angle) < 0.0001:\n", + " # approximate straight line with huge radius\n", + " r = 1.e-30\n", + " b = dist / self.wheelbase * tan(steering_angle)\n", + " r = self.wheelbase / tan(steering_angle) # radius\n", + " sinh = sin(h)\n", + " sinhb = sin(h + b)\n", + " cosh = cos(h)\n", + " coshb = cos(h + b)\n", + " return x + array([[-r*sinh + r*sinhb],\n", + " [r*cosh - r*coshb],\n", + " [b]])\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$, which will throw off the computation of the Kalman gain. The correct angle difference in this case is $-2^\\circ$. So we will have to write code to correctly compute the bearing residual." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def residual(a,b):\n", + " \"\"\" compute residual between two measurement containing [range, bearing]. Bearing\n", + " is normalized to [0, 360)\"\"\"\n", + " y = a - b\n", + " if y[1] > np.pi:\n", + " y[1] -= 2*np.pi\n", + " if y[1] < -np.pi:\n", + " y[1] = 2*np.pi\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The rest of the code runs the simulation, and shouldn't need to much comment by now. I create a variable `map` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the EKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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FccpSI2BxJWLiWMBSPeWJiToHjs9zzD9EW02n5BQxdYOpKY0HOt7Fm+I7CWMT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\nIksnzaS9aoXSJp8bXShYoiWwHbgQQoh5VqQnJiZ48cUXZ/9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.common import plot_covariance_ellipse\n", + "from math import sqrt, tan, cos, sin, atan2\n", + "dt = 1.0\n", + "ekf = RobotEKF(dt, wheelbase=0.5)\n", + "sigma_steer = np.radians(1)\n", + "sigma_h = np.radians(1)\n", + "sigma_r = 0.1\n", + "#np.random.seed(1234)\n", + "\n", + "m = array([[5, 10],\n", + " [10, 5],\n", + " [15, 15]])\n", + "\n", + "ekf.x = array([[2, 6, .3]]).T\n", + "u = array([1.1, .01])\n", + "ekf.P = np.diag([.1, .1, .1])\n", + "ekf.R = np.diag([sigma_r**2, sigma_h**2])\n", + "c = [0, 1, 2]\n", + "\n", + "xp = ekf.x.copy()\n", + "\n", + "plt.scatter(m[:, 0], m[:, 1], marker='s', s=60)\n", + "for i in range(150):\n", + " xp = ekf.move(xp, u, dt/10.) # simulate robot\n", + " plt.plot(xp[0], xp[1], ',', color='g')\n", + "\n", + " if i % 10 == 0:\n", + " ekf.predict(u=u)\n", + "\n", + " plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10,\n", + " facecolor='b', alpha=0.08)\n", + "\n", + " for lmark in m:\n", + " d = np.sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r\n", + " a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h\n", + " z = np.array([[d], [a]])\n", + "\n", + " ekf.update(z, HJacobian=H_of, Hx=Hx, residual=residual,\n", + " args=(lmark), hx_args=(lmark))\n", + "\n", + " plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10,\n", + " facecolor='g', alpha=0.4)\n", + "\n", + " #plt.plot(ekf.x[0], ekf.x[1], 'x', color='r')\n", + "\n", + "plt.axis('equal')\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1054,21 +1662,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "**author's note: ignore this section for now. **\n", + "\n", "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'." ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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4ublRu3ZttmzZAsC3335L7dq1MRqNNGzYkP3799u8//DhwwwaNIjKlStjNBrx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AAw/cdNvLgqb4KkIIIcpb3GWV6YtU6vaHbs/B0g1FB+Bubldo3XY7Q0Ys5PmX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\nq5j3/i4824rJNxEREfDoapoaEw1CY0NhZmqGId0mQ4KEA6e341q8cjv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KA+xYBPj3Z/JN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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1095,7 +1705,10 @@ "These equations will be *very* unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n", "\n", "\n", - "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n", + "$$\\begin{aligned}\n", + "\\ddot{y} &= \\frac{0.0034ge^{-y/20000}\\dot{y}^2}{2\\beta} - g \\\\\n", + "\\ddot{x} &= \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta}\n", + "\\end{aligned}$$\n", "\n", "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag." ] @@ -1104,21 +1717,48 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is still nonlinear, so we need to linearize this equation at the current state point. If our state is position and velocity, we need an equation for some arbitrarily small change in $\\mathbf{x}$: $\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x}\\end{bmatrix}$, like so:\n", + "This is still nonlinear, so we need to linearize this equation at the current state point. If our state is position and velocity, we need an equation for some arbitrarily small change in $\\mathbf{x}$, like so:\n", "\n", - "$$ \\begin{bmatrix}\\Delta \\dot{x} \\\\ \\Delta \\ddot{x}\\end{bmatrix} = \n", - "\\begin{bmatrix}\n", - "\\frac{\\partial \\dot{x}}{\\partial x} & \\frac{\\partial \\dot{x}}{\\partial \\dot{x}} \\\\ \n", - "\\frac{\\partial \\ddot{x}}{\\partial x} & \\frac{\\partial \\ddot{x}}{\\partial \\dot{x}}\n", - "\\end{bmatrix}\n", - "\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x}\\end{bmatrix}$$\n", + "$$ \\begin{bmatrix}\\Delta \\dot{x} \\\\ \\Delta \\ddot{x} \\\\ \\Delta \\dot{y} \\\\ \\Delta \\ddot{y}\\end{bmatrix} = \n", + "\\large\\begin{bmatrix}\n", + "\\frac{\\partial \\dot{x}}{\\partial x} & \n", + "\\frac{\\partial \\dot{x}}{\\partial \\dot{x}} & \n", + "\\frac{\\partial \\dot{x}}{\\partial y} & \n", + "\\frac{\\partial \\dot{x}}{\\partial \\dot{y}} \\\\ \n", + "\\frac{\\partial \\ddot{x}}{\\partial x} & \n", + "\\frac{\\partial \\ddot{x}}{\\partial \\dot{x}}& \n", + "\\frac{\\partial \\ddot{x}}{\\partial y}& \n", + "\\frac{\\partial \\dot{x}}{\\partial \\dot{y}}\\\\\n", + "\\frac{\\partial \\dot{y}}{\\partial x} & \n", + "\\frac{\\partial \\dot{y}}{\\partial \\dot{x}} & \n", + "\\frac{\\partial \\dot{y}}{\\partial y} & \n", + "\\frac{\\partial \\dot{y}}{\\partial \\dot{y}} \\\\ \n", + "\\frac{\\partial \\ddot{y}}{\\partial x} & \n", + "\\frac{\\partial \\ddot{y}}{\\partial \\dot{x}}& \n", + "\\frac{\\partial \\ddot{y}}{\\partial y}& \n", + "\\frac{\\partial \\dot{y}}{\\partial \\dot{y}}\n", + "\\end{bmatrix}\\normalsize\n", + "\\begin{bmatrix}\\Delta x \\\\ \\Delta \\dot{x} \\\\ \\Delta \\dot{y} \\\\ \\Delta \\ddot{y}\\end{bmatrix}$$\n", "\n", + "The equations do not contain both an x and a y, so any partial derivative with both in it must be equal to zero. We also know that $\\large\\frac{\\partial \\dot{x}}{\\partial x}\\normalsize = 0$ and that $\\large\\frac{\\partial \\dot{x}}{\\partial \\dot{x}}\\normalsize = 1$, so our matrix ends up being\n", + "\n", + "$$\\mathbf{F} = \\begin{bmatrix}0&1&0&0 \\\\\n", + "\\frac{0.0034e^{-x/22000}\\dot{x}^2g}{44000\\beta}&0&0&0\n", + "\\end{bmatrix}$$\n", "\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\begin{aligned}\\ddot{x} &= -\\frac{1}{2}C_d\\rho A \\dot{x}\\\\\n", + "\\ddot{y} &= -\\frac{1}{2}C_d\\rho A \\dot{y}-g\\end{aligned}$$" + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "collapsed": false }, @@ -1133,8 +1773,8 @@ "\n", "x2 = (a*g*exp(-x/c)*(Derivative(x)**2))/(2*b) - g\n", "\n", - "pprint(x1)5\n", - "pprint(Derivative(x)*Derivative(x,n=2))\n", + "#pprint(x1)\n", + "#pprint(Derivative(x)*Derivative(x,n=2))\n", "#pprint(diff(x2, x))" ] }, @@ -1163,7 +1803,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.4.3" + "version": "3.4.1" } }, "nbformat": 4, diff --git a/book_format.py b/book_format.py index c2b573c..5b264bc 100644 --- a/book_format.py +++ b/book_format.py @@ -12,7 +12,7 @@ sys.path.insert(0,'./code') # allow us to import book_format def test_filterpy_version(): import filterpy - min_version = [0,0,10] + min_version = [0,0,18] v = filterpy.__version__ tokens = v.split('.') for i,v in enumerate(tokens): @@ -22,7 +22,8 @@ def test_filterpy_version(): i = len(tokens) - 1 if min_version[i] > int(tokens[i]): raise Exception("Minimum FilterPy version supported is {}.{}.{}.\n" - "Please install a more recent version." .format( + "Please install a more recent version.\n" + " ex: pip install filterpy --upgrade".format( *min_version)) v = int(tokens[0]*1000) diff --git a/code/ekf_internal.py b/code/ekf_internal.py index 040fe4c..862224f 100644 --- a/code/ekf_internal.py +++ b/code/ekf_internal.py @@ -38,6 +38,36 @@ def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.02): return f1 +def plot_bicycle(): + plt.clf() + plt.axes() + ax = plt.gca() + #ax.add_patch(plt.Rectangle((10,0), 10, 20, fill=False, ec='k')) #car + ax.add_patch(plt.Rectangle((21,1), .75, 2, fill=False, ec='k')) #wheel + ax.add_patch(plt.Rectangle((21.33,10), .75, 2, fill=False, ec='k', angle=20)) #wheel + ax.add_patch(plt.Rectangle((21.,4.), .75, 2, fill=True, ec='k', angle=5, ls='dashdot', alpha=0.3)) #wheel + + plt.arrow(0, 2, 20.5, 0, fc='k', ec='k', head_width=0.5, head_length=0.5) + plt.arrow(0, 2, 20.4, 3, fc='k', ec='k', head_width=0.5, head_length=0.5) + plt.arrow(21.375, 2., 0, 8.5, fc='k', ec='k', head_width=0.5, head_length=0.5) + plt.arrow(23, 2, 0, 2.5, fc='k', ec='k', head_width=0.5, head_length=0.5) + + #ax.add_patch(plt.Rectangle((10,0), 10, 20, fill=False, ec='k')) + plt.text(11, 1.0, "R", fontsize=18) + plt.text(8, 2.2, r"$\beta$", fontsize=18) + plt.text(20.4, 13.5, r"$\alpha$", fontsize=18) + plt.text(21.6, 7, "w (wheelbase)", fontsize=18) + plt.text(0, 1, "C", fontsize=18) + plt.text(24, 3, "d", fontsize=18) + plt.plot([21.375, 21.25], [11, 14], color='k', lw=1) + plt.plot([21.375, 20.2], [11, 14], color='k', lw=1) + plt.axis('scaled') + plt.xlim(0,25) + plt.axis('off') + plt.show() + +#plot_bicycle() + class BaseballPath(object): def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): """ Create baseball path object in 2D (y=height above ground) diff --git a/experiments/bicycle.py b/experiments/bicycle.py index b8cf472..21afb37 100644 --- a/experiments/bicycle.py +++ b/experiments/bicycle.py @@ -9,6 +9,7 @@ Created on Tue Apr 28 08:19:21 2015 from math import * import numpy as np import matplotlib.pyplot as plt +from matplotlib.patches import Polygon wheelbase = 100 #inches @@ -21,17 +22,17 @@ pos = np.array([0., 0.] for i in range(100): #if abs(steering_angle) > 1.e-8: - dist = vel*t turn_radius = tan(steering_angle) radius = wheelbase / tan(steering_angle) + dist = vel*t arc_len = dist / (2*pi*radius) turn_angle = 2*pi * arc_len - cx = pos[0] - (sin(orientation) * radius) - cy = pos[1] + (cos(orientation) * radius) + cx = pos[0] - radius * sin(orientation) + cy = pos[1] + radius * cos(orientation) orientation = (orientation + turn_angle) % (2.0 * pi) pos[0] = cx + (sin(orientation) * radius) @@ -41,3 +42,6 @@ for i in range(100): plt.axis('equal') + + + diff --git a/experiments/ekf4.py b/experiments/ekf4.py new file mode 100644 index 0000000..42074d3 --- /dev/null +++ b/experiments/ekf4.py @@ -0,0 +1,194 @@ +# -*- coding: utf-8 -*- +""" +Created on Sat May 30 13:24:01 2015 + +@author: rlabbe +""" + +# -*- coding: utf-8 -*- +""" +Created on Thu May 28 20:23:57 2015 + +@author: rlabbe +""" + + +from math import cos, sin, sqrt, atan2, tan +import matplotlib.pyplot as plt +import numpy as np +from numpy import array, dot +from numpy.linalg import pinv +from numpy.random import randn +from filterpy.common import plot_covariance_ellipse +from filterpy.kalman import ExtendedKalmanFilter as EKF +from sympy import Matrix, symbols +import sympy + +def print_x(x): + print(x[0, 0], x[1, 0], np.degrees(x[2, 0])) + + +def normalize_angle(x, index): + if x[index] > np.pi: + x[index] -= 2*np.pi + if x[index] < -np.pi: + x[index] = 2*np.pi + +def residual(a,b): + y = a - b + normalize_angle(y, 1) + return y + + +sigma_r = 0.1 +sigma_h = np.radians(1) +sigma_steer = np.radians(1) + +#only partway through. predict is using old control and movement code. computation of m uses +#old u. + +class RobotEKF(EKF): + def __init__(self, dt, wheelbase): + EKF.__init__(self, 3, 2, 2) + self.dt = dt + self.wheelbase = wheelbase + + a, x, y, v, w, theta, time = symbols( + 'a, x, y, v, w, theta, t') + + d = v*time + beta = (d/w)*sympy.tan(a) + r = w/sympy.tan(a) + + + self.fxu = Matrix([[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)], + [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)], + [theta+beta]]) + + self.F_j = self.fxu.jacobian(Matrix([x, y, theta])) + self.V_j = self.fxu.jacobian(Matrix([v, a])) + + self.subs = {x: 0, y: 0, v:0, a:0, time:dt, w:wheelbase, theta:0} + self.x_x = x + self.x_y = y + self.v = v + self.a = a + self.theta = theta + + + def predict(self, u=0): + + + self.x = self.move(self.x, u, self.dt) + + self.subs[self.theta] = self.x[2, 0] + self.subs[self.v] = u[0] + self.subs[self.a] = u[1] + + + F = array(self.F_j.evalf(subs=self.subs)).astype(float) + V = array(self.V_j.evalf(subs=self.subs)).astype(float) + + # covariance of motion noise in control space + M = array([[0.1*u[0]**2, 0], + [0, sigma_steer**2]]) + + self.P = dot(F, self.P).dot(F.T) + dot(V, M).dot(V.T) + + + def move(self, x, u, dt): + h = x[2, 0] + v = u[0] + steering_angle = u[1] + + dist = v*dt + + if abs(steering_angle) < 0.0001: + # approximate straight line with huge radius + r = 1.e-30 + b = dist / self.wheelbase * tan(steering_angle) + r = self.wheelbase / tan(steering_angle) # radius + + + sinh = sin(h) + sinhb = sin(h + b) + cosh = cos(h) + coshb = cos(h + b) + + return x + array([[-r*sinh + r*sinhb], + [r*cosh - r*coshb], + [b]]) + + +def H_of(x, p): + """ compute Jacobian of H matrix where h(x) computes the range and + bearing to a landmark for state x """ + + px = p[0] + py = p[1] + hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2 + dist = np.sqrt(hyp) + + H = array( + [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0], + [ (py - x[1, 0]) / hyp, -(px - x[0, 0]) / hyp, -1]]) + return H + + +def Hx(x, p): + """ takes a state variable and returns the measurement that would + correspond to that state. + """ + px = p[0] + py = p[1] + dist = np.sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2) + + Hx = array([[dist], + [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]]) + return Hx + +dt = 1.0 +ekf = RobotEKF(dt, wheelbase=0.5) + +#np.random.seed(1234) + +m = array([[5, 10], + [10, 5], + [15, 15]]) + +ekf.x = array([[2, 6, .3]]).T +u = array([1.1, .01]) +ekf.P = np.diag([.1, .1, .1]) +ekf.R = np.diag([sigma_r**2, sigma_h**2]) +c = [0, 1, 2] + +xp = ekf.x.copy() + +plt.scatter(m[:, 0], m[:, 1]) +for i in range(150): + xp = ekf.move(xp, u, dt/10.) # simulate robot + plt.plot(xp[0], xp[1], ',', color='g') + + if i % 10 == 0: + + ekf.predict(u=u) + + plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10, + facecolor='b', alpha=0.08) + + for lmark in m: + d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r + a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h + z = np.array([[d], [a]]) + + ekf.update(z, HJacobian=H_of, Hx=Hx, residual=residual, + args=(lmark), hx_args=(lmark)) + + plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10, + facecolor='g', alpha=0.4) + + #plt.plot(ekf.x[0], ekf.x[1], 'x', color='r') + +plt.axis('equal') +plt.show() + diff --git a/experiments/ekfloc.py b/experiments/ekfloc.py new file mode 100644 index 0000000..a03245d --- /dev/null +++ b/experiments/ekfloc.py @@ -0,0 +1,290 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun May 24 08:39:36 2015 + +@author: Roger +""" + +#x = x x' y y' theta + +from math import cos, sin, sqrt, atan2 +import numpy as np +from numpy import array, dot +from numpy.linalg import pinv + + +def print_x(x): + print(x[0, 0], x[1, 0], np.degrees(x[2, 0])) + + +def control_update(x, u, dt): + """ x is [x, y, hdg], u is [vel, omega] """ + + v = u[0] + w = u[1] + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + + return x + np.array([[-r*sin(x[2]) + r*sin(x[2] + w*dt)], + [ r*cos(x[2]) - r*cos(x[2] + w*dt)], + [w*dt]]) + + +a1 = 0.001 +a2 = 0.001 +a3 = 0.001 +a4 = 0.001 + +sigma_r = 0.1 +sigma_h = a_error = np.radians(1) +sigma_s = 0.00001 + +def normalize_angle(x, index): + if x[index] > np.pi: + x[index] -= 2*np.pi + if x[index] < -np.pi: + x[index] = 2*np.pi + + +def ekfloc_predict(x, P, u, dt): + + h = x[2] + v = u[0] + w = u[1] + + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + sinh = sin(h) + sinhwdt = sin(h + w*dt) + cosh = cos(h) + coshwdt = cos(h + w*dt) + + G = array( + [[1, 0, -r*cosh + r*coshwdt], + [0, 1, -r*sinh + r*sinhwdt], + [0, 0, 1]]) + + V = array( + [[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w], + [(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w], + [0, dt]]) + + + # covariance of motion noise in control space + M = array([[a1*v**2 + a2*w**2, 0], + [0, a3*v**2 + a4*w**2]]) + + + + x = x + array([[-r*sinh + r*sinhwdt], + [r*cosh - r*coshwdt], + [w*dt]]) + + P = dot(G, P).dot(G.T) + dot(V, M).dot(V.T) + + return x, P + +def ekfloc(x, P, u, zs, c, m, dt): + + h = x[2] + v = u[0] + w = u[1] + + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + sinh = sin(h) + sinhwdt = sin(h + w*dt) + cosh = cos(h) + coshwdt = cos(h + w*dt) + + F = array( + [[1, 0, -r*cosh + r*coshwdt], + [0, 1, -r*sinh + r*sinhwdt], + [0, 0, 1]]) + + V = array( + [[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w], + [(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w], + [0, dt]]) + + + # covariance of motion noise in control space + M = array([[a1*v**2 + a2*w**2, 0], + [0, a3*v**2 + a4*w**2]]) + + + x = x + array([[-r*sinh + r*sinhwdt], + [r*cosh - r*coshwdt], + [w*dt]]) + + P = dot(F, P).dot(F.T) + dot(V, M).dot(V.T) + + + R = np.diag([sigma_r**2, sigma_h**2, sigma_s**2]) + + for i, z in enumerate(zs): + j = c[i] + + q = (m[j][0] - x[0, 0])**2 + (m[j][1] - x[1, 0])**2 + + z_est = array([sqrt(q), + atan2(m[j][1] - x[1, 0], m[j][0] - x[0, 0]) - x[2, 0], + 0]) + + + H = array( + [[-(m[j, 0] - x[0, 0]) / sqrt(q), -(m[j, 1] - x[1, 0]) / sqrt(q), 0], + [ (m[j, 1] - x[1, 0]) / q, -(m[j, 0] - x[0, 0]) / q, -1], + [0, 0, 0]]) + + + + S = dot(H, P).dot(H.T) + R + + #print('S', S) + K = dot(P, H.T).dot(pinv(S)) + y = z - z_est + normalize_angle(y, 1) + y = array([y]).T + #print('y', y) + + x = x + dot(K, y) + I = np.eye(P.shape[0]) + I_KH = I - dot(K, H) + #print('i', I_KH) + + P = dot(I_KH, P).dot(I_KH.T) + dot(K, R).dot(K.T) + + return x, P + + + +def ekfloc2(x, P, u, zs, c, m, dt): + + h = x[2] + v = u[0] + w = u[1] + + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + sinh = sin(h) + sinhwdt = sin(h + w*dt) + cosh = cos(h) + coshwdt = cos(h + w*dt) + + F = array( + [[1, 0, -r*cosh + r*coshwdt], + [0, 1, -r*sinh + r*sinhwdt], + [0, 0, 1]]) + + V = array( + [[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w], + [(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w], + [0, dt]]) + + + # covariance of motion noise in control space + M = array([[a1*v**2 + a2*w**2, 0], + [0, a3*v**2 + a4*w**2]]) + + + x = x + array([[-r*sinh + r*sinhwdt], + [r*cosh - r*coshwdt], + [w*dt]]) + + + P = dot(F, P).dot(F.T) + dot(V, M).dot(V.T) + + + + R = np.diag([sigma_r**2, sigma_h**2]) + + for i, z in enumerate(zs): + j = c[i] + + q = (m[j][0] - x[0, 0])**2 + (m[j][1] - x[1, 0])**2 + + z_est = array([sqrt(q), + atan2(m[j][1] - x[1, 0], m[j][0] - x[0, 0]) - x[2, 0]]) + + H = array( + [[-(m[j, 0] - x[0, 0]) / sqrt(q), -(m[j, 1] - x[1, 0]) / sqrt(q), 0], + [ (m[j, 1] - x[1, 0]) / q, -(m[j, 0] - x[0, 0]) / q, -1]]) + + + S = dot(H, P).dot(H.T) + R + + #print('S', S) + K = dot(P, H.T).dot(pinv(S)) + y = z - z_est + normalize_angle(y, 1) + y = array([y]).T + #print('y', y) + + x = x + dot(K, y) + print('x', x) + I = np.eye(P.shape[0]) + I_KH = I - dot(K, H) + + P = dot(I_KH, P).dot(I_KH.T) + dot(K, R).dot(K.T) + + return x, P + +m = array([[5, 5], + [7,6], + [4, 8]]) + +x = array([[2, 6, .3]]).T +u = array([.5, .01]) +P = np.diag([1., 1., 1.]) +c = [0, 1, 2] + + + +import matplotlib.pyplot as plt +from numpy.random import randn +from filterpy.common import plot_covariance_ellipse +from filterpy.kalman import KalmanFilter +plt.figure() +plt.plot(m[:, 0], m[:, 1], 'o') +plt.plot(x[0], x[1], 'x', color='b', ms=20) + +xp = x.copy() +dt = 0.1 +np.random.seed(1234) + +for i in range(1000): + xp, _ = ekfloc_predict(xp, P, u, dt) + plt.plot(xp[0], xp[1], 'x', color='g', ms=20) + + if i % 10 == 0: + zs = [] + + for lmark in m: + d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r + a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h + zs.append(np.array([d, a])) + + x, P = ekfloc2(x, P, u, zs, c, m, dt*10) + + + if P[0,0] < 10000: + plot_covariance_ellipse((x[0,0], x[1,0]), P[0:2, 0:2], std=2, + facecolor='g', alpha=0.3) + + plt.plot(x[0], x[1], 'x', color='r') + +plt.axis('equal') +plt.show() diff --git a/experiments/ekfloc2.py b/experiments/ekfloc2.py new file mode 100644 index 0000000..20b7f30 --- /dev/null +++ b/experiments/ekfloc2.py @@ -0,0 +1,191 @@ +# -*- coding: utf-8 -*- +""" +Created on Mon May 25 18:18:54 2015 + +@author: rlabbe +""" + + +from math import cos, sin, sqrt, atan2 +import matplotlib.pyplot as plt +import numpy as np +from numpy import array, dot +from numpy.linalg import pinv +from numpy.random import randn +from filterpy.common import plot_covariance_ellipse +from filterpy.kalman import ExtendedKalmanFilter as EKF + + +def print_x(x): + print(x[0, 0], x[1, 0], np.degrees(x[2, 0])) + + +def normalize_angle(x, index): + if x[index] > np.pi: + x[index] -= 2*np.pi + if x[index] < -np.pi: + x[index] = 2*np.pi + +def residual(a,b): + y = a - b + normalize_angle(y, 1) + return y + + +def control_update(x, u, dt): + """ x is [x, y, hdg], u is [vel, omega] """ + + v = u[0] + w = u[1] + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + + return x + np.array([[-r*sin(x[2]) + r*sin(x[2] + w*dt)], + [ r*cos(x[2]) - r*cos(x[2] + w*dt)], + [w*dt]]) + +a1 = 0.001 +a2 = 0.001 +a3 = 0.001 +a4 = 0.001 + +sigma_r = 0.1 +sigma_h = a_error = np.radians(1) +sigma_s = 0.00001 + +def normalize_angle(x, index): + if x[index] > np.pi: + x[index] -= 2*np.pi + if x[index] < -np.pi: + x[index] = 2*np.pi + + + +class RobotEKF(EKF): + def __init__(self, dt): + EKF.__init__(self, 3, 2, 2) + self.dt = dt + + def predict_x(self, u): + self.x = self.move(self.x, u, self.dt) + + + def move(self, x, u, dt): + h = x[2, 0] + v = u[0] + w = u[1] + + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + sinh = sin(h) + sinhwdt = sin(h + w*dt) + cosh = cos(h) + coshwdt = cos(h + w*dt) + + return x + array([[-r*sinh + r*sinhwdt], + [r*cosh - r*coshwdt], + [w*dt]]) + + +def H_of(x, landmark_pos): + """ compute Jacobian of H matrix for state x """ + + mx = landmark_pos[0] + my = landmark_pos[1] + q = (mx - x[0, 0])**2 + (my - x[1, 0])**2 + + H = array( + [[-(mx - x[0, 0]) / sqrt(q), -(my - x[1, 0]) / sqrt(q), 0], + [ (my - x[1, 0]) / q, -(mx - x[0, 0]) / q, -1]]) + return H + + +def Hx(x, landmark_pos): + """ takes a state variable and returns the measurement that would + correspond to that state. + """ + mx = landmark_pos[0] + my = landmark_pos[1] + q = (mx - x[0, 0])**2 + (my - x[1, 0])**2 + + Hx = array([[sqrt(q)], + [atan2(my - x[1, 0], mx - x[0, 0]) - x[2, 0]]]) + return Hx + +dt = 1.0 +ekf = RobotEKF(dt) + +#np.random.seed(1234) + +m = array([[5, 10], + [10, 5], + [15, 15]]) + +ekf.x = array([[2, 6, .3]]).T +u = array([.5, .01]) +ekf.P = np.diag([1., 1., 1.]) +ekf.R = np.diag([sigma_r**2, sigma_h**2]) +c = [0, 1, 2] + +xp = ekf.x.copy() + +plt.scatter(m[:, 0], m[:, 1]) +for i in range(300): + xp = ekf.move(xp, u, dt/10.) # simulate robot + plt.plot(xp[0], xp[1], ',', color='g') + + if i % 10 == 0: + h = ekf.x[2, 0] + v = u[0] + w = u[1] + + if w == 0: + # approximate straight line with huge radius + w = 1.e-30 + r = v/w # radius + + sinh = sin(h) + sinhwdt = sin(h + w*dt) + cosh = cos(h) + coshwdt = cos(h + w*dt) + + ekf.F = array( + [[1, 0, -r*cosh + r*coshwdt], + [0, 1, -r*sinh + r*sinhwdt], + [0, 0, 1]]) + + V = array( + [[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w], + [(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w], + [0, dt]]) + + # covariance of motion noise in control space + M = array([[a1*v**2 + a2*w**2, 0], + [0, a3*v**2 + a4*w**2]]) + + ekf.Q = dot(V, M).dot(V.T) + + ekf.predict(u=u) + + for lmark in m: + d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r + a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h + z = np.array([[d], [a]]) + + ekf.update(z, HJacobian=H_of, Hx=Hx, residual=residual, + args=(lmark), hx_args=(lmark)) + + plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10, + facecolor='g', alpha=0.3) + + #plt.plot(ekf.x[0], ekf.x[1], 'x', color='r') + +plt.axis('equal') +plt.show() + diff --git a/experiments/ekfloc3.py b/experiments/ekfloc3.py new file mode 100644 index 0000000..3974a92 --- /dev/null +++ b/experiments/ekfloc3.py @@ -0,0 +1,259 @@ +# -*- coding: utf-8 -*- +""" +Created on Thu May 28 20:23:57 2015 + +@author: rlabbe +""" + + +from math import cos, sin, sqrt, atan2, tan +import matplotlib.pyplot as plt +import numpy as np +from numpy import array, dot +from numpy.linalg import pinv +from numpy.random import randn +from filterpy.common import plot_covariance_ellipse +from filterpy.kalman import ExtendedKalmanFilter as EKF + + +def print_x(x): + print(x[0, 0], x[1, 0], np.degrees(x[2, 0])) + + +def normalize_angle(x, index): + if x[index] > np.pi: + x[index] -= 2*np.pi + if x[index] < -np.pi: + x[index] = 2*np.pi + +def residual(a,b): + y = a - b + normalize_angle(y, 1) + return y + + +sigma_r = 0.1 +sigma_h = np.radians(1) +sigma_steer = np.radians(1) + +#only partway through. predict is using old control and movement code. computation of m uses +#old u. + +class RobotEKF(EKF): + def __init__(self, dt, wheelbase): + EKF.__init__(self, 3, 2, 2) + self.dt = dt + self.wheelbase = wheelbase + + def predict(self, u=0): + + self.x = self.move(self.x, u, self.dt) + + h = self.x[2, 0] + v = u[0] + steering_angle = u[1] + + dist = v*self.dt + + if abs(steering_angle) < 0.0001: + # approximate straight line with huge radius + r = 1.e-30 + b = dist / self.wheelbase * tan(steering_angle) + r = self.wheelbase / tan(steering_angle) # radius + + + sinh = sin(h) + sinhb = sin(h + b) + cosh = cos(h) + coshb = cos(h + b) + + F = array([[1., 0., -r*cosh + r*coshb], + [0., 1., -r*sinh + r*sinhb], + [0., 0., 1.]]) + + w = self.wheelbase + + F = array([[1., 0., (-w*cosh + w*coshb)/tan(steering_angle)], + [0., 1., (-w*sinh + w*sinhb)/tan(steering_angle)], + [0., 0., 1.]]) + + print('F', F) + + V = array( + [[-r*sinh + r*sinhb, 0], + [r*cosh + r*coshb, 0], + [0, 0]]) + + + t2 = tan(steering_angle)**2 + V = array([[0, w*sinh*(-t2-1)/t2 + w*sinhb*(-t2-1)/t2], + [0, w*cosh*(-t2-1)/t2 - w*coshb*(-t2-1)/t2], + [0,0]]) + + + t2 = tan(steering_angle)**2 + + a = steering_angle + d = v*dt + it = dt*v*tan(a)/w + h + + + + V[0,0] = dt*cos(d/w*tan(a) + h) + V[0,1] = (dt*v*(t2+1)*cos(it)/tan(a) - + w*sinh*(-t2-1)/t2 + + w*(-t2-1)*sin(it)/t2) + + + print(dt*v*(t2+1)*cos(it)/tan(a)) + print(w*sinh*(-t2-1)/t2) + print(w*(-t2-1)*sin(it)/t2) + + + + V[1,0] = dt*sin(it) + + V[1,1] = (d*(t2+1)*sin(it)/tan(a) + w*cosh/t2*(-t2-1) - + w*(-t2-1)*cos(it)/t2) + + V[2,0] = dt/w*tan(a) + V[2,1] = d/w*(t2+1) + + theta = h + + v01 = (dt*v*(tan(a)**2 + 1)*cos(dt*v*tan(a)/w + theta)/tan(a) - + w*(-tan(a)**2 - 1)*sin(theta)/(tan(a)**2) + + w*(-tan(a)**2 - 1)*sin(dt*v*tan(a)/w + theta)/(tan(a)**2)) + + print(dt*v*(tan(a)**2 + 1)*cos(dt*v*tan(a)/w + theta)/tan(a)) + print(w*(-tan(a)**2 - 1)*sin(theta)/(tan(a)**2)) + print(w*(-tan(a)**2 - 1)*sin(dt*v*tan(a)/w + theta)/(tan(a)**2)) + + '''v11 = (dt*v*(tan(a)**2 + 1)*sin(dt*v*tan(a)/w + theta)/tan(a) + + w*(-tan(a)**2 - 1)*cos(theta)/tan(a)**2 - + w*(-tan(a)**2 - 1)*cos(dt*v*tan(a)/w + theta)/tan(a)**2) + + + print(dt*v*(tan(a)**2 + 1)*sin(dt*v*tan(a)/w + theta)/tan(a)) + print(w*(-tan(a)**2 - 1)*cos(theta)/tan(a)**2) + print(w*(-tan(a)**2 - 1)*cos(dt*v*tan(a)/w + theta)/tan(a)**2) + print(v11) + print(V[1,1]) + 1/0 + + V[1,1] = v11''' + + print(V) + + + # covariance of motion noise in control space + M = array([[0.1*v**2, 0], + [0, sigma_steer**2]]) + + + fpf = dot(F, self.P).dot(F.T) + Q = dot(V, M).dot(V.T) + print('FPF', fpf) + print('V', V) + print('Q', Q) + print() + self.P = dot(F, self.P).dot(F.T) + dot(V, M).dot(V.T) + + + + def move(self, x, u, dt): + h = x[2, 0] + v = u[0] + steering_angle = u[1] + + dist = v*dt + + if abs(steering_angle) < 0.0001: + # approximate straight line with huge radius + r = 1.e-30 + b = dist / self.wheelbase * tan(steering_angle) + r = self.wheelbase / tan(steering_angle) # radius + + + sinh = sin(h) + sinhb = sin(h + b) + cosh = cos(h) + coshb = cos(h + b) + + return x + array([[-r*sinh + r*sinhb], + [r*cosh - r*coshb], + [b]]) + + +def H_of(x, p): + """ compute Jacobian of H matrix where h(x) computes the range and + bearing to a landmark for state x """ + + px = p[0] + py = p[1] + hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2 + dist = np.sqrt(hyp) + + H = array( + [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0], + [ (py - x[1, 0]) / hyp, -(px - x[0, 0]) / hyp, -1]]) + return H + + +def Hx(x, p): + """ takes a state variable and returns the measurement that would + correspond to that state. + """ + px = p[0] + py = p[1] + dist = np.sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2) + + Hx = array([[dist], + [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]]) + return Hx + +dt = 1.0 +ekf = RobotEKF(dt, wheelbase=0.5) + +#np.random.seed(1234) + +m = array([[5, 10], + [10, 5], + [15, 15]]) + +ekf.x = array([[2, 6, .3]]).T +u = array([.5, .01]) +ekf.P = np.diag([1., 1., 1.]) +ekf.R = np.diag([sigma_r**2, sigma_h**2]) +c = [0, 1, 2] + +xp = ekf.x.copy() + +plt.scatter(m[:, 0], m[:, 1]) +for i in range(300): + xp = ekf.move(xp, u, dt/10.) # simulate robot + plt.plot(xp[0], xp[1], ',', color='g') + + if i % 10 == 0: + + ekf.predict(u=u) + + plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=2, + facecolor='b', alpha=0.3) + + for lmark in m: + d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r + a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h + z = np.array([[d], [a]]) + + ekf.update(z, HJacobian=H_of, Hx=Hx, residual=residual, + args=(lmark), hx_args=(lmark)) + + plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10, + facecolor='g', alpha=0.3) + + #plt.plot(ekf.x[0], ekf.x[1], 'x', color='r') + +plt.axis('equal') +plt.show() + diff --git a/styles/custom2.css b/styles/custom2.css index e929761..ae8b315 100644 --- a/styles/custom2.css +++ b/styles/custom2.css @@ -4,7 +4,7 @@ @import url('http://fonts.googleapis.com/css?family=Arimo'); div.cell{ - width: 850px; + width: 900px; margin-left: 0% !important; margin-right: auto; }