Generating Trajectories in Python

trajectory_fixed.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.00000000e+00   8.24178404e-05   6.39036520e-04   2.08936182e-03\n",
      "   4.79554936e-03   9.06495351e-03   1.51526763e-02   2.32641161e-02\n",
      "   3.35575171e-02   4.61465174e-02   6.11026986e-02   7.84581342e-02\n",
      "   9.82079389e-02   1.20312817e-01   1.44701612e-01   1.71273856e-01\n",
      "   1.99902314e-01   2.30435542e-01   2.62700425e-01   2.96504736e-01\n",
      "   3.31639676e-01   3.67882430e-01   4.04998712e-01   4.42745315e-01\n",
      "   4.80872659e-01   5.19127341e-01   5.57254685e-01   5.95001288e-01\n",
      "   6.32117570e-01   6.68360324e-01   7.03495264e-01   7.37299575e-01\n",
      "   7.69564458e-01   8.00097686e-01   8.28726144e-01   8.55298388e-01\n",
      "   8.79687183e-01   9.01792061e-01   9.21541866e-01   9.38897301e-01\n",
      "   9.53853483e-01   9.66442483e-01   9.76735884e-01   9.84847324e-01\n",
      "   9.90935046e-01   9.95204451e-01   9.97910638e-01   9.99360963e-01\n",
      "   9.99917582e-01   1.00000000e+00]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8511c0d68>"
      ]
     },
     "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(start, end, coeffs, step_range):\n",
    "    points = np.zeros(step_range)\n",
    "    timesteps = np.linspace(start,end,step_range)\n",
    "    for i,e in enumerate(timesteps):\n",
    "        points[i] = (coeffs[0]*(e**5) \n",
    "        + coeffs[1]*(e**4)\n",
    "        + coeffs[2]*(e**3)\n",
    "        + coeffs[3]*(e**2)\n",
    "        + coeffs[4]*e\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 = alg.solve(X, np.array([start, end, 0, 0, 0, 0]))\n",
    "    #print(coeffs)\n",
    "    return solve_quintic_polynomial(start, end, 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
}