Simple Robot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using ForwardDiff\n",
    "using Plots\n",
    "using MeshCat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f(x,u) = [u[1]*cos(x[3]); u[1]*sin(x[3]); u[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simulate (generic function with 4 methods)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function simulate(start=0, stop=10, dt=0.01; trajectory=nothing)\n",
    "\ttimes = Vector(start:dt:stop)\n",
    "\tstates = zeros(3, length(times))\n",
    "\tstates[:, begin] = [0, 0, 1]\n",
    "\tfor t = 1:length(times)-1\n",
    "\t\tu = [1, 0]\n",
    "\t\tif trajectory != nothing \n",
    "\t\t\tu = trajectory(times[t])\n",
    "\t\tend\n",
    "\t\tx_next = states[:, t] + f(states[:, t], u)*dt\n",
    "\t\tstates[:, t+1] = x_next\n",
    "\tend\n",
    "\n",
    "\tstates\n",
    "end\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×1001 Matrix{Float64}:\n",
       " 0.0  0.00540302  0.010806   0.0162091  …  -2.41867  -2.41593  -2.41314\n",
       " 0.0  0.00841471  0.0168294  0.0252441     -2.09119  -2.1008   -2.11041\n",
       " 1.0  1.0         1.0        1.0            4.99      4.995     5.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function traj(t)\n",
    "\tt < 2 && return [1, 0]\n",
    "\t(t>=2 && t < 4) && return [-1, 1]\n",
    "\t(t>=4 && t < 6) && return [1, 0]\n",
    "\t(t>=6 && t < 10) && return [1, 0.5]\n",
    "end\n",
    "\t\n",
    "states = simulate(trajectory=traj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "  1425.78,690.346 1428.41,687.334 1431.04,684.322 1433.68,681.31 1436.31,678.298 1438.95,675.286 1441.58,672.275 1444.21,669.263 1446.85,666.251 1449.48,663.239 \n",
       "  1452.12,660.227 1454.75,657.215 1457.39,654.204 1460.02,651.192 1462.65,648.18 1465.29,645.168 1467.92,642.156 1470.56,639.144 1473.19,636.132 1475.83,633.121 \n",
       "  1478.46,630.109 1481.09,627.097 1483.73,624.085 1486.36,621.073 1489,618.061 1491.63,615.05 1494.27,612.038 1496.9,609.026 1499.53,606.014 1502.17,603.002 \n",
       "  1504.8,599.99 1507.44,596.978 1510.07,593.967 1512.7,590.955 1515.34,587.943 1517.97,584.931 1520.61,581.919 1523.24,578.907 1525.88,575.896 1528.51,572.884 \n",
       "  1531.14,569.872 1533.78,566.86 1536.41,563.848 1539.05,560.836 1541.68,557.824 1544.32,554.813 1546.95,551.801 1549.58,548.789 1552.22,545.777 1554.85,542.765 \n",
       "  1557.49,539.753 1560.12,536.742 1562.76,533.73 1565.39,530.718 1568.02,527.706 1570.66,524.694 1573.29,521.682 1575.93,518.67 1578.56,515.659 1581.19,512.647 \n",
       "  1583.83,509.635 1586.46,506.623 1589.1,503.611 1591.73,500.599 1594.37,497.587 1597,494.576 1599.63,491.564 1602.27,488.552 1604.9,485.54 1607.54,482.528 \n",
       "  1610.17,479.516 1612.81,476.505 1615.44,473.493 1618.07,470.481 1620.71,467.469 1623.34,464.457 1625.98,461.445 1628.61,458.433 1631.25,455.422 1633.88,452.41 \n",
       "  1636.51,449.398 1639.15,446.386 1641.78,443.374 1644.42,440.362 1647.05,437.351 1649.68,434.339 1652.32,431.327 1654.95,428.315 1657.59,425.303 1660.22,422.291 \n",
       "  1662.86,419.279 1665.49,416.268 1668.12,413.256 1670.76,410.244 1673.39,407.232 1676.03,404.22 1678.66,401.208 1681.3,398.197 1683.93,395.185 1686.56,392.173 \n",
       "  1689.2,389.161 1691.83,386.149 1694.47,383.137 1697.1,380.125 1699.74,377.114 1702.37,374.102 1705,371.09 1707.64,368.078 1710.27,365.066 1712.91,362.054 \n",
       "  1715.54,359.043 1718.17,356.031 1720.81,353.019 1723.44,350.007 1726.08,346.995 1728.71,343.983 1731.35,340.971 1733.98,337.96 1736.61,334.948 1739.25,331.936 \n",
       "  1741.88,328.924 1744.52,325.912 1747.15,322.9 1749.79,319.889 1752.42,316.877 1755.05,313.865 1757.69,310.853 1760.32,307.841 1762.96,304.829 1765.59,301.817 \n",
       "  1768.23,298.806 1770.86,295.794 1773.49,292.782 1776.13,289.77 1778.76,286.758 1781.4,283.746 1784.03,280.734 1786.66,277.723 1789.3,274.711 1791.93,271.699 \n",
       "  1794.57,268.687 1797.2,265.675 1799.84,262.663 1802.47,259.652 1805.1,256.64 1807.74,253.628 1810.37,250.616 1813.01,247.604 1815.64,244.592 1818.28,241.58 \n",
       "  1820.91,238.569 1823.54,235.557 1826.18,232.545 1828.81,229.533 1831.45,226.521 1834.08,223.509 1836.72,220.498 1839.35,217.486 1841.98,214.474 1844.62,211.462 \n",
       "  1847.25,208.45 1849.89,205.438 1852.52,202.426 1855.15,199.415 1857.79,196.403 1860.42,193.391 1863.06,190.379 1865.69,187.367 1868.33,184.355 1870.96,181.344 \n",
       "  1873.59,178.332 1876.23,175.32 1878.86,172.308 1881.5,169.296 1884.13,166.284 1886.77,163.272 1889.4,160.261 1892.03,157.249 1894.67,154.237 1897.3,151.225 \n",
       "  1899.94,148.213 1902.57,145.201 1905.21,142.19 1907.84,139.178 1910.47,136.166 1913.11,133.154 1915.74,130.142 1918.38,127.13 1921.01,124.118 1923.64,121.107 \n",
       "  1926.28,118.095 1928.91,115.083 1931.55,112.071 1934.18,109.059 1936.82,106.047 1939.45,103.036 1942.08,100.024 1944.72,97.0118 1947.35,94 1949.99,90.9881 \n",
       "  1952.62,87.9763 1949.99,90.9881 1947.39,94.0192 1944.84,97.0691 1942.33,100.138 1939.86,103.224 1937.44,106.329 1935.05,109.451 1932.71,112.591 1930.42,115.748 \n",
       "  1928.16,118.921 1925.95,122.111 1923.78,125.317 1921.66,128.539 1919.58,131.776 1917.54,135.028 1915.55,138.295 1913.6,141.577 1911.7,144.872 1909.84,148.182 \n",
       "  1908.03,151.505 1906.27,154.841 1904.54,158.19 1902.87,161.551 1901.24,164.924 1899.66,168.309 1898.12,171.706 1896.63,175.114 1895.18,178.532 1893.78,181.961 \n",
       "  1892.43,185.401 1891.13,188.849 1889.87,192.308 1888.66,195.775 1887.5,199.251 1886.38,202.735 1885.32,206.228 1884.3,209.728 1883.32,213.235 1882.4,216.749 \n",
       "  1881.52,220.27 1880.69,223.797 1879.91,227.331 1879.18,230.869 1878.5,234.413 1877.86,237.962 1877.27,241.515 1876.73,245.072 1876.24,248.633 1875.8,252.198 \n",
       "  1875.41,255.765 1875.06,259.336 1874.77,262.908 1874.52,266.483 1874.32,270.059 1874.17,273.637 1874.07,277.215 1874.02,280.794 1874.01,284.374 1874.06,287.953 \n",
       "  1874.15,291.531 1874.29,295.109 1874.48,298.686 1874.72,302.261 1875.01,305.834 1875.35,309.404 1875.74,312.972 1876.17,316.537 1876.65,320.099 1877.18,323.657 \n",
       "  1877.76,327.211 1878.39,330.76 1879.07,334.305 1879.79,337.844 1880.57,341.378 1881.39,344.907 1882.26,348.428 1883.17,351.944 1884.14,355.452 1885.15,358.954 \n",
       "  1886.21,362.447 1887.32,365.933 1888.47,369.41 1889.68,372.879 1890.93,376.339 1892.22,379.789 1893.57,383.23 1894.96,386.66 1896.39,390.08 1897.88,393.49 \n",
       "  1899.41,396.888 1900.98,400.276 1902.61,403.651 1904.27,407.014 1905.99,410.365 1907.75,413.703 1909.55,417.028 1911.4,420.34 1913.3,423.637 1915.24,426.921 \n",
       "  1917.22,430.19 1919.25,433.445 1921.32,436.685 1923.44,439.909 1925.6,443.117 1927.81,446.31 1930.05,449.486 1932.35,452.645 1934.68,455.788 1937.06,458.913 \n",
       "  1939.48,462.021 1941.94,465.11 1944.44,468.182 1946.98,471.234 1949.57,474.269 1952.2,477.283 1954.87,480.279 1957.58,483.255 1960.33,486.21 1963.12,489.146 \n",
       "  1965.95,492.061 1968.82,494.954 1971.72,497.827 1974.67,500.678 1977.66,503.507 1980.68,506.315 1983.74,509.1 1986.85,511.862 1989.98,514.601 1993.16,517.318 \n",
       "  1996.37,520.01 1999.62,522.679 2002.9,525.325 2006.22,527.945 2009.58,530.542 2012.97,533.113 2016.4,535.66 2019.86,538.181 2023.35,540.677 2026.88,543.147 \n",
       "  2030.44,545.591 2034.04,548.008 2037.67,550.4 2041.33,552.764 2045.02,555.101 2048.74,557.412 2052.5,559.694 2056.28,561.949 2060.1,564.176 2063.95,566.375 \n",
       "  2067.82,568.546 2071.73,570.688 2075.66,572.802 2079.63,574.886 2083.62,576.941 2087.64,578.967 2091.69,580.963 2095.76,582.929 2099.86,584.865 2103.99,586.771 \n",
       "  2108.14,588.647 2112.32,590.492 2116.52,592.307 2120.75,594.09 2125,595.842 2129.27,597.563 2133.57,599.253 2137.89,600.911 2142.24,602.537 2146.6,604.131 \n",
       "  2150.99,605.693 2155.4,607.223 2159.82,608.72 2164.27,610.185 2168.74,611.616 2173.23,613.016 2177.73,614.382 2182.26,615.715 2186.8,617.014 2191.36,618.28 \n",
       "  2195.94,619.513 2200.53,620.712 2205.14,621.877 2209.77,623.009 2214.41,624.106 2219.07,625.169 2223.73,626.198 2228.42,627.193 2233.11,628.153 2237.82,629.079 \n",
       "  2242.55,629.97 2247.28,630.826 2252.03,631.647 2256.78,632.434 2261.55,633.186 2266.33,633.903 2271.11,634.584 2275.91,635.231 2280.71,635.842 2285.52,636.418 \n",
       "  2290.34,636.958 2285.52,636.453 2280.69,635.948 2275.86,635.443 2271.04,634.938 2266.21,634.433 2261.38,633.927 2256.56,633.422 2251.73,632.917 2246.9,632.412 \n",
       "  2242.08,631.907 2237.25,631.402 2232.42,630.897 2227.6,630.392 2222.77,629.887 2217.94,629.381 2213.12,628.876 2208.29,628.371 2203.46,627.866 2198.64,627.361 \n",
       "  2193.81,626.856 2188.98,626.351 2184.16,625.846 2179.33,625.341 2174.5,624.836 2169.68,624.33 2164.85,623.825 2160.02,623.32 2155.2,622.815 2150.37,622.31 \n",
       "  2145.54,621.805 2140.72,621.3 2135.89,620.795 2131.06,620.29 2126.24,619.784 2121.41,619.279 2116.58,618.774 2111.76,618.269 2106.93,617.764 2102.1,617.259 \n",
       "  2097.28,616.754 2092.45,616.249 2087.62,615.744 2082.8,615.239 2077.97,614.733 2073.14,614.228 2068.31,613.723 2063.49,613.218 2058.66,612.713 2053.83,612.208 \n",
       "  2049.01,611.703 2044.18,611.198 2039.35,610.693 2034.53,610.187 2029.7,609.682 2024.87,609.177 2020.05,608.672 2015.22,608.167 2010.39,607.662 2005.57,607.157 \n",
       "  2000.74,606.652 1995.91,606.147 1991.09,605.641 1986.26,605.136 1981.43,604.631 1976.61,604.126 1971.78,603.621 1966.95,603.116 1962.13,602.611 1957.3,602.106 \n",
       "  1952.47,601.601 1947.65,601.096 1942.82,600.59 1937.99,600.085 1933.17,599.58 1928.34,599.075 1923.51,598.57 1918.69,598.065 1913.86,597.56 1909.03,597.055 \n",
       "  1904.21,596.55 1899.38,596.044 1894.55,595.539 1889.73,595.034 1884.9,594.529 1880.07,594.024 1875.25,593.519 1870.42,593.014 1865.59,592.509 1860.77,592.004 \n",
       "  1855.94,591.499 1851.11,590.993 1846.29,590.488 1841.46,589.983 1836.63,589.478 1831.81,588.973 1826.98,588.468 1822.15,587.963 1817.33,587.458 1812.5,586.953 \n",
       "  1807.67,586.447 1802.85,585.942 1798.02,585.437 1793.19,584.932 1788.37,584.427 1783.54,583.922 1778.71,583.417 1773.89,582.912 1769.06,582.407 1764.23,581.902 \n",
       "  1759.41,581.396 1754.58,580.891 1749.75,580.386 1744.93,579.881 1740.1,579.376 1735.27,578.871 1730.45,578.366 1725.62,577.861 1720.79,577.356 1715.97,576.85 \n",
       "  1711.14,576.345 1706.31,575.84 1701.49,575.335 1696.66,574.83 1691.83,574.325 1687.01,573.82 1682.18,573.315 1677.35,572.81 1672.53,572.305 1667.7,571.799 \n",
       "  1662.87,571.294 1658.05,570.789 1653.22,570.284 1648.39,569.779 1643.57,569.274 1638.74,568.769 1633.91,568.264 1629.09,567.759 1624.26,567.253 1619.43,566.748 \n",
       "  1614.61,566.243 1609.78,565.738 1604.95,565.233 1600.13,564.728 1595.3,564.223 1590.47,563.718 1585.65,563.213 1580.82,562.707 1575.99,562.202 1571.17,561.697 \n",
       "  1566.34,561.192 1561.51,560.687 1556.69,560.182 1551.86,559.677 1547.03,559.172 1542.21,558.667 1537.38,558.162 1532.55,557.656 1527.73,557.151 1522.9,556.646 \n",
       "  1518.07,556.141 1513.25,555.636 1508.42,555.131 1503.59,554.626 1498.77,554.121 1493.94,553.616 1489.11,553.11 1484.29,552.605 1479.46,552.1 1474.63,551.595 \n",
       "  1469.81,551.09 1464.98,550.585 1460.15,550.08 1455.33,549.575 1450.5,549.07 1445.67,548.565 1440.85,548.059 1436.02,547.554 1431.19,547.049 1426.37,546.544 \n",
       "  1421.54,546.039 1416.71,545.534 1411.89,545.029 1407.06,544.524 1402.23,544.019 1397.41,543.513 1392.58,543.008 1387.75,542.503 1382.93,541.998 1378.1,541.493 \n",
       "  1373.27,540.988 1368.45,540.483 1363.62,539.978 1358.79,539.473 1353.97,538.968 1349.14,538.462 1344.31,537.957 1339.49,537.452 1334.66,536.947 1329.83,536.442 \n",
       "  1325.01,535.937 1320.18,535.432 1315.35,534.944 1310.52,534.475 1305.68,534.023 1300.84,533.589 1296,533.172 1291.15,532.774 1286.3,532.393 1281.45,532.03 \n",
       "  1276.6,531.685 1271.75,531.357 1266.89,531.048 1262.03,530.756 1257.17,530.482 1252.31,530.226 1247.44,529.988 1242.57,529.768 1237.71,529.565 1232.84,529.381 \n",
       "  1227.97,529.214 1223.1,529.065 1218.22,528.934 1213.35,528.821 1208.48,528.726 1203.6,528.649 1198.73,528.589 1193.85,528.548 1188.98,528.524 1184.1,528.519 \n",
       "  1179.23,528.531 1174.35,528.561 1169.48,528.609 1164.6,528.675 1159.73,528.758 1154.85,528.86 1149.98,528.98 1145.11,529.117 1140.24,529.272 1135.37,529.446 \n",
       "  1130.5,529.637 1125.63,529.846 1120.77,530.072 1115.9,530.317 1111.04,530.58 1106.18,530.86 1101.32,531.158 1096.47,531.474 1091.61,531.808 1086.76,532.16 \n",
       "  1081.91,532.529 1077.06,532.916 1072.22,533.321 1067.38,533.744 1062.54,534.185 1057.7,534.643 1052.87,535.119 1048.04,535.613 1043.22,536.125 1038.4,536.654 \n",
       "  1033.58,537.201 1028.76,537.765 1023.95,538.348 1019.15,538.948 1014.34,539.565 1009.55,540.2 1004.75,540.853 999.963,541.524 995.178,542.211 990.399,542.917 \n",
       "  985.624,543.64 980.854,544.381 976.089,545.139 971.329,545.914 966.575,546.707 961.826,547.518 957.083,548.345 952.345,549.191 947.613,550.053 942.888,550.933 \n",
       "  938.168,551.831 933.454,552.745 928.747,553.677 924.046,554.626 919.352,555.593 914.664,556.577 909.983,557.577 905.309,558.596 900.642,559.631 895.982,560.683 \n",
       "  891.329,561.752 886.683,562.839 882.045,563.942 877.415,565.063 872.792,566.2 868.177,567.355 863.57,568.526 858.971,569.714 854.381,570.92 849.798,572.141 \n",
       "  845.224,573.38 840.658,574.636 836.101,575.908 831.553,577.197 827.013,578.503 822.483,579.825 817.961,581.164 813.449,582.52 808.946,583.892 804.452,585.28 \n",
       "  799.968,586.685 795.494,588.107 791.029,589.545 786.574,590.999 782.129,592.47 777.694,593.956 773.27,595.46 768.855,596.979 764.451,598.515 760.058,600.066 \n",
       "  755.675,601.634 751.303,603.218 746.941,604.818 742.591,606.434 738.252,608.066 733.924,609.714 729.607,611.377 725.301,613.057 721.008,614.752 716.725,616.463 \n",
       "  712.455,618.19 708.196,619.932 703.949,621.69 699.714,623.463 695.491,625.252 691.281,627.057 687.083,628.877 682.897,630.712 678.724,632.563 674.563,634.429 \n",
       "  670.415,636.31 666.28,638.206 662.159,640.118 658.05,642.045 653.954,643.986 649.872,645.943 645.803,647.915 641.747,649.902 637.705,651.903 633.677,653.919 \n",
       "  629.662,655.95 625.662,657.996 621.675,660.057 617.702,662.132 613.744,664.221 609.8,666.325 605.87,668.444 601.955,670.577 598.054,672.724 594.168,674.886 \n",
       "  590.297,677.062 586.441,679.252 582.6,681.456 578.773,683.674 574.962,685.906 571.166,688.152 567.386,690.412 563.62,692.686 559.871,694.974 556.137,697.275 \n",
       "  552.419,699.591 548.716,701.919 545.03,704.262 541.359,706.617 537.705,708.987 534.066,711.369 530.444,713.765 526.839,716.175 523.25,718.597 519.677,721.033 \n",
       "  516.121,723.481 512.582,725.943 509.059,728.418 505.554,730.905 502.065,733.406 498.594,735.919 495.139,738.445 491.702,740.983 488.283,743.534 484.88,746.098 \n",
       "  481.495,748.674 478.128,751.263 474.779,753.863 471.447,756.476 468.133,759.102 464.837,761.739 461.559,764.389 458.299,767.05 455.057,769.723 451.833,772.409 \n",
       "  448.628,775.106 445.441,777.815 442.273,780.535 439.123,783.267 435.992,786.011 432.88,788.766 429.786,791.532 426.711,794.31 423.656,797.099 420.619,799.899 \n",
       "  417.601,802.71 414.603,805.533 411.624,808.366 408.664,811.21 405.723,814.065 402.802,816.931 399.901,819.808 397.019,822.695 394.157,825.592 391.315,828.5 \n",
       "  388.492,831.419 385.69,834.348 382.907,837.287 380.145,840.236 377.402,843.195 374.68,846.165 371.978,849.144 369.297,852.133 366.635,855.132 363.995,858.141 \n",
       "  361.374,861.16 358.775,864.188 356.196,867.225 353.638,870.272 351.1,873.328 348.583,876.394 346.088,879.469 343.613,882.553 341.159,885.645 338.727,888.747 \n",
       "  336.315,891.858 333.925,894.978 331.556,898.106 329.208,901.243 326.882,904.389 324.577,907.543 322.294,910.705 320.032,913.876 317.792,917.055 315.574,920.242 \n",
       "  313.377,923.438 311.202,926.641 309.049,929.853 306.918,933.072 304.809,936.299 302.722,939.533 300.656,942.776 298.613,946.026 296.593,949.283 294.594,952.548 \n",
       "  292.618,955.82 290.663,959.099 288.732,962.385 286.822,965.679 284.936,968.979 283.071,972.286 281.229,975.6 279.41,978.921 277.614,982.248 275.84,985.582 \n",
       "  274.088,988.923 272.36,992.269 270.654,995.623 268.972,998.982 267.312,1002.35 265.675,1005.72 264.061,1009.1 262.47,1012.48 260.902,1015.87 259.358,1019.26 \n",
       "  257.836,1022.66 256.338,1026.07 254.863,1029.48 253.411,1032.9 251.982,1036.32 250.577,1039.75 249.195,1043.18 247.836,1046.62 246.501,1050.06 245.189,1053.51 \n",
       "  243.901,1056.96 242.637,1060.42 241.396,1063.88 240.178,1067.34 238.984,1070.81 237.814,1074.29 236.667,1077.77 235.545,1081.25 234.445,1084.74 233.37,1088.23 \n",
       "  232.319,1091.72 231.291,1095.22 230.287,1098.73 229.307,1102.23 228.351,1105.74 227.419,1109.25 226.51,1112.77 225.626,1116.29 224.766,1119.81 223.929,1123.34 \n",
       "  223.117,1126.87 222.329,1130.4 221.565,1133.94 220.825,1137.47 220.109,1141.02 219.417,1144.56 218.749,1148.1 218.105,1151.65 217.486,1155.2 216.891,1158.75 \n",
       "  216.32,1162.31 215.773,1165.87 215.25,1169.42 214.752,1172.98 214.278,1176.55 213.828,1180.11 213.403,1183.68 213.001,1187.24 212.625,1190.81 212.272,1194.38 \n",
       "  211.944,1197.95 211.64,1201.53 211.36,1205.1 211.105,1208.67 210.874,1212.25 210.667,1215.82 210.485,1219.4 210.327,1222.98 210.193,1226.56 210.084,1230.14 \n",
       "  210,1233.71 209.939,1237.29 209.903,1240.87 209.891,1244.45 209.904,1248.03 209.941,1251.61 210.003,1255.19 210.089,1258.77 210.199,1262.35 210.333,1265.92 \n",
       "  210.492,1269.5 210.676,1273.08 210.883,1276.65 211.115,1280.23 211.372,1283.8 211.653,1287.38 211.958,1290.95 212.287,1294.52 212.641,1298.09 213.019,1301.66 \n",
       "  213.421,1305.23 213.848,1308.79 214.299,1312.35 214.774,1315.92 215.273,1319.48 215.797,1323.04 216.345,1326.59 216.917,1330.15 217.513,1333.7 218.133,1337.25 \n",
       "  218.778,1340.8 219.447,1344.34 220.14,1347.89 220.857,1351.43 221.598,1354.96 222.363,1358.5 223.153,1362.03 223.966,1365.56 224.803,1369.09 225.665,1372.61 \n",
       "  226.55,1376.13 227.459,1379.65 228.393,1383.16 229.35,1386.67 230.331,1390.17 231.336,1393.68 232.365,1397.18 233.417,1400.67 234.494,1404.16 235.594,1407.65 \n",
       "  236.718,1411.13 237.865,1414.61 239.037,1418.08 240.232,1421.55 241.45,1425.02 242.692,1428.48 243.958,1431.94 245.247,1435.39 246.56,1438.84 247.896,1442.28 \n",
       "  249.256,1445.72 \n",
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(states[1, :], states[2, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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