Generating Trajectories with Python

trajectory.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  6. -15.  10.   0.   0.   0.]\n",
      "[  0.00000000e+00   1.00000000e+00   3.20000000e+01   5.13000000e+02\n",
      "   2.94400000e+03   1.06250000e+04   2.93760000e+04   6.82570000e+04\n",
      "   1.40288000e+05   2.63169000e+05   4.60000000e+05   7.60001000e+05\n",
      "   1.19923200e+06   1.82131300e+06   2.67814400e+06   3.83062500e+06\n",
      "   5.34937600e+06   7.31545700e+06   9.82108800e+06   1.29703690e+07\n",
      "   1.68800000e+07   2.16800010e+07   2.75144320e+07   3.45421130e+07\n",
      "   4.29373440e+07   5.28906250e+07   6.46093760e+07   7.83186570e+07\n",
      "   9.42618880e+07   1.12701569e+08   1.33920000e+08   1.58220001e+08\n",
      "   1.85925632e+08   2.17382913e+08   2.52960544e+08   2.93050625e+08\n",
      "   3.38069376e+08   3.88457857e+08   4.44682688e+08   5.07236769e+08\n",
      "   5.76640000e+08   6.53440001e+08   7.38212832e+08   8.31563713e+08\n",
      "   9.34127744e+08   1.04657062e+09   1.16958938e+09   1.30391306e+09\n",
      "   1.45030349e+09   1.60955597e+09]\n"
     ]
    },
    {
     "data": {
      "image/png": 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dJ1J7HK+txuuO43XVeG011FVjtVVYXRWhuirSwtWkh6tJD1eRFakkK1JJtleR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\no76yIq+FjQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c1ca9e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.linalg as alg\n",
    "\n",
    "def solve_quintic_polynomial(coeffs, num):\n",
    "    points = np.zeros(num)\n",
    "    for i in range(num):\n",
    "        points[i] = (coeffs[0]*(i**5) \n",
    "        + coeffs[1]*(i**4)\n",
    "        + coeffs[2]*(i**3)\n",
    "        + coeffs[3]*(i**2)\n",
    "        + coeffs[4]*i\n",
    "        + coeffs[5])\n",
    "    return points\n",
    "\n",
    "    \n",
    "def generate_quintic_trajectory(start, end, timestep):\n",
    "    \"\"\"\n",
    "    Creates a quintic polynomial trajectory\n",
    "    starting from [start] to [end] with [timestep]\n",
    "    intervals.\n",
    "    \"\"\"\n",
    "    t = math.ceil(end)\n",
    "    X = np.array(\n",
    "        [0,         0,         0,        0,     0, 1,\n",
    "         t**5,      t**4,      t**3,     t**2,  t, 1,\n",
    "         0,         0,         0,        0,     1, 0,\n",
    "         5*(t**4),  4*(t**3),  3*(t**2), 2*t,   1, 0,\n",
    "         0,         0,         0,        2,     0, 0,\n",
    "         20*(t**3), 12*(t**2), 6*t,      2,     0, 0]).reshape((6,6))\n",
    "    coeffs = np.transpose(alg.solve(X,np.transpose(np.array([start, end, 0, 0, 0, 0]))))\n",
    "    print(coeffs)\n",
    "    return solve_quintic_polynomial(coeffs, timestep)\n",
    "    \n",
    "s = generate_quintic_trajectory(0,1,50)\n",
    "print(s)\n",
    "plt.plot(range(50), s)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}