quad_direct_transcription.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quadrotor Direct Transcription\n",
    "by Sebastian Lopez-Cot\n",
    "\n",
    "This python notebook can be used to run the quad-ball system. The quadrotor will try to send a ball to a desired location given initial conditions and will attempt to return to its original starting point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Should end at:  [ 0.  0.]\n",
      "Number of decision vars:  320\n",
      "Solve:  SolutionResult.kSolutionFound\n"
     ]
    },
    {
     "data": {
      "image/png": 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KG0iSpcA+wIqhaxnYBcAuVfU4untMXjdwPfMqyWbAO4H9gF2AFyTZediqBnMXcGRV7QI8EXjlAt4XdzuCbmh8tAyFDedtwJ8NXcTQquqTVbWyn/wcsHTIegawO3BlVa2oqjuBM+luyFxwquqGqrq0f/5D4AoW8D1H/RfHA4D3DF3L2hgKG0CSZwDXVNVXhq5lZA4DPjZ0EfNs9Zsvr2UBHwjvlmQH4HHAPS4tX0Du/uI46hO5Y7kkdfTWciPescDr6YaOJpdtsmZzU2KSY4A7q+r9A5SoEUmyBfAh4Ii+x7DgJHk6cGNVXZpkihEfIwyFWaqqfWaan+SxwA7Al/sf7lsKfDHJ7lV10zyWOG/WtC/uluTFdN3kveeloHG5Dth+YnppP29BSrKILhBOq6pzhq5nQHsBz0hyAPAgYMskp1bVIQPXdQ9ekrqBJbkKeHxV3TZ0LUNIsj/wVuDJVfXdoeuZb0nuB3wDeCpwPd2Nly+oqisGLWwgSU4FbqmqI4euZSySPIXuVxyeMXQtM/GcwoZXjLhrOA/eAWwBXNhfenfy0AXNp6r6OfAququwvkr3i78LNRD2Ag4C9k7ypf7fw/5D16W1s6cgSWrsKUiSGkNBktQYCpKkxlCQJDWGgiSpMRQkSY2hIElqDAVJUmMoSBtQkick+XKSByTZPMnlSR4zdF3SbHlHs7SBJTme7kfPHkT3k+pvHrgkadYMBWkDS3J/4GLgx8Ce5YdMGxGHj6QNbxu6HwXcEvilgWuR7hV7CtIGluQc4APAI4Btq+rVA5ckzZr/yY60ASU5GPhZVZ2ZZDPgv5JMVdX0wKVJs2JPQZLUeE5BktQYCpKkxlCQJDWGgiSpMRQkSY2hIElqDAVJUmMoSJKa/wfXwWSNcUP5RgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb28763050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb27ec96d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb27dfb490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.          0.          0.        ]\n",
      " [-0.01        0.00319935  0.01063588]\n",
      " [-0.02144059 -0.00239676  0.02317176]\n",
      " [-0.03542539 -0.00905461  0.03698554]\n",
      " [-0.05338671 -0.00921565  0.04964751]\n",
      " [-0.07687592  0.00293359  0.06081688]\n",
      " [-0.10730806  0.0145918   0.07027966]\n",
      " [-0.14586642  0.03869719  0.07793398]\n",
      " [-0.19347141  0.07913142  0.06377319]\n",
      " [-0.24934728  0.12932746  0.04786677]\n",
      " [-0.31136649  0.17902982  0.03033952]\n",
      " [-0.37772826  0.22185658  0.01135324]\n",
      " [-0.44678599  0.25425235 -0.00890753]\n",
      " [-0.51691942  0.29488639 -0.03024704]\n",
      " [-0.58448037  0.3242977  -0.05051728]\n",
      " [-0.64770643  0.3441893  -0.06952951]\n",
      " [-0.70483972  0.35665534 -0.08711119]\n",
      " [-0.75414579  0.3638937  -0.10311338]\n",
      " [-0.79391625  0.36834464 -0.11741731]\n",
      " [-0.82244226  0.37303251 -0.12993981]\n",
      " [-0.83797918  0.38184652 -0.12169021]\n",
      " [-0.82024582  0.37541392 -0.11056336]\n",
      " [-0.79055347  0.37066305 -0.09765353]\n",
      " [-0.75032923  0.36489705 -0.08304187]\n",
      " [-0.70103682  0.35597845 -0.06684481]\n",
      " [-0.64419913  0.34205747 -0.04920877]\n",
      " [-0.58140655  0.32130342 -0.0303038 ]\n",
      " [-0.51430038  0.29183696 -0.01031628]\n",
      " [-0.44454461  0.25204508  0.00860821]\n",
      " [-0.37569544  0.22131544  0.02627656]\n",
      " [-0.30926835  0.18063321  0.04250699]\n",
      " [-0.2467639   0.13276856  0.05714067]\n",
      " [-0.18975494  0.08268505  0.07005534]\n",
      " [-0.1400096   0.03843557  0.07687726]\n",
      " [-0.09924791  0.01034308  0.06622305]\n",
      " [-0.06757392  0.00297102  0.05389167]\n",
      " [-0.04352305 -0.00644972  0.0401027 ]\n",
      " [-0.02540281 -0.00344453  0.02520414]\n",
      " [-0.01142302  0.00275639  0.01163051]\n",
      " [ 0.          0.          0.        ]]\n"
     ]
    }
   ],
   "source": [
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "\n",
    "from pydrake.all import MathematicalProgram\n",
    "from pydrake.symbolic import (sin,cos,tanh)\n",
    "\n",
    "from quad_direct_transcription import (QuadDirectTranscription)\n",
    "from IPython.display import HTML\n",
    "\n",
    "# Define the min and max time for the problem\n",
    "time_used = 4.0\n",
    "\n",
    "# Quad initial conditions\n",
    "initial_quad_state = np.zeros(6)\n",
    "initial_quad_state[0] = 0.0\n",
    "initial_quad_state[1] = 0.0\n",
    "initial_quad_state[2] = 0.0\n",
    "initial_quad_state[3] = 0.0\n",
    "initial_quad_state[4] = 0.0\n",
    "initial_quad_state[5] = 0.0\n",
    "\n",
    "final_quad_state = np.zeros(6)\n",
    "final_quad_state[0] = 0.0 #np.random.choice(np.arange(-4.0, 4.0, 0.1))\n",
    "final_quad_state[1] = 0.0 #np.random.choice(np.arange(1.0, 5.0, 0.1))\n",
    "final_quad_state[2] = 0.0 #np.random.choice(np.arange(-np.pi/6.0, np.pi/6.0, 0.1))\n",
    "final_quad_state[3] = 0.0\n",
    "final_quad_state[4] = 0.0\n",
    "final_quad_state[5] = 0.0\n",
    "\n",
    "print \"Should end at: \", final_quad_state[0:2]\n",
    "\n",
    "# System params\n",
    "quad_mass = 0.1\n",
    "ball_mass = 0.01\n",
    "g = -9.81\n",
    "beta = 1.0\n",
    "\n",
    "# Run the solver\n",
    "qdt = QuadDirectTranscription(quad_mass, g)\n",
    "quad_traj, input_traj, time_array = qdt.solve(initial_quad_state, final_quad_state, time_used)\n",
    "\n",
    "# Visualize the results\n",
    "plt.figure()\n",
    "plt.title(\"Quad trajectory\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.xlim(-5,5)\n",
    "plt.ylim(-10,10)\n",
    "plt.plot(quad_traj[:,0], quad_traj[:,1])\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.title(\"Quad y position\")\n",
    "plt.xlim(-20,10)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(time_array[0:40], quad_traj[:,1])\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.title(\"Quad y velocity\")\n",
    "plt.xlim(-20,10)\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.plot(time_array[0:40], quad_traj[:,4])\n",
    "plt.show()\n",
    "\n",
    "#print input_traj\n",
    "print quad_traj[:,0:3]\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}