Quadcopter_Project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Deep Drone Reinforcement Learning\n",
    "\n",
    "Design an agent to fly a drone, and then train it using a reinforcement learning algorithm of your choice! \n",
    "\n",
    "We have used Sarsa, Q-learning and DDPG. But inspired by the variations of DDPG we used DDPG to train the drone. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instructions\n",
    "\n",
    "Take a look at the files in the directory to better understand the structure of the project. \n",
    "\n",
    "- `task.py`: Define your task (environment) in this file.\n",
    "- `agents/`: Folder containing reinforcement learning agents.\n",
    "    - `policy_search.py`: A sample agent has been provided here.\n",
    "    - `agent.py`: Develop your agent here. we developed here DDPG, you can modify it like PPO or TRPO.\n",
    "- `physics_sim.py`: This file contains the simulator for the quadcopter.  **DO NOT MODIFY THIS FILE**.\n",
    "\n",
    "For this project, you can define your own task in `task.py`.  \n",
    "\n",
    "You will also design different reinforcement learning agent in `agent.py` to complete your chosen task.  \n",
    "s.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "class Basic_Agent():\n",
    "    def __init__(self, task):\n",
    "        self.task = task\n",
    "    \n",
    "    def act(self):\n",
    "        new_thrust = random.gauss(450., 25.)\n",
    "        return [new_thrust + random.gauss(0., 1.) for x in range(4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the code cell below to have the agent select actions to control the drone.  \n",
    "\n",
    "Feel free to change the provided values of `runtime`, `init_pose`, `init_velocities`, and `init_angle_velocities` below to change the starting conditions of the drone.\n",
    "\n",
    "The `labels` list below annotates statistics that are saved while running the simulation.  All of this information is saved in a text file `data.txt` and stored in the dictionary `results`.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import csv\n",
    "import numpy as np\n",
    "from tasks.base_task import Task\n",
    "\n",
    "# Modify the values below to give the quadcopter a different starting position.\n",
    "runtime = 5.                                     # time limit of the episode\n",
    "init_pose = np.array([0., 0., 10., 0., 0., 0.])  # initial pose\n",
    "init_velocities = np.array([0., 0., 0.])         # initial velocities\n",
    "init_angle_velocities = np.array([0., 0., 0.])   # initial angle velocities\n",
    "file_output = 'data.txt'                         # file name for saved results\n",
    "\n",
    "# Setup\n",
    "task = Task(init_pose, init_velocities, init_angle_velocities, runtime)\n",
    "agent = Basic_Agent(task)\n",
    "done = False\n",
    "labels = ['time', 'x', 'y', 'z', 'phi', 'theta', 'psi', 'x_velocity',\n",
    "          'y_velocity', 'z_velocity', 'phi_velocity', 'theta_velocity',\n",
    "          'psi_velocity', 'rotor_speed1', 'rotor_speed2', 'rotor_speed3', 'rotor_speed4']\n",
    "results = {x : [] for x in labels}\n",
    "\n",
    "# Run the simulation, and save the results.\n",
    "with open(file_output, 'w') as csvfile:\n",
    "    writer = csv.writer(csvfile)\n",
    "    writer.writerow(labels)\n",
    "    while True:\n",
    "        rotor_speeds = agent.act()\n",
    "        _, _, done = task.step(rotor_speeds)\n",
    "        to_write = [task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(rotor_speeds)\n",
    "        for ii in range(len(labels)):\n",
    "            results[labels[ii]].append(to_write[ii])\n",
    "        writer.writerow(to_write)\n",
    "        if done:\n",
    "            break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the code cell below to visualize how the position of the drone evolved during the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OfZ1PyBeifl49yxYuY/PSzVwz/xquKb2GJfOWUBAoyOJPIeJ9CnQBkqF9JnyGkwMnOTlwkpb+lvEAPzFwgoHIwHhfn/moKa6hfl496yrXsWTeEpbMW0LDvAYqCyt1f7dIlijQ55BoPMrpodO0DrRycuDkufFgK60DrecdafvMR3VRNUvmLWFL+RaWzFtCfUk9dfPqqCuuI+jXxUmRXKNA95B4Ik7XSBetA62cGjw1PoxNdw53jt9FApDnz6O2uJa6kjo2Vm2ktiTZriupo7a4VqEtcpVRoF9FYokYncOdnBo8RdtQG6cGT3F68DRtg8l2+3D7+FNyIHkhclHhImqKa7ix+kZqimuoKa5JBnZJLRUFFTn5DZciMjMK9BwyEhuhbbCNtqE2Tg8lg3ps3DbURudw5/g3A46pKKhgcfFiVlWs4rNFn2Vx8WJqi2upKamhuqhaD1sQmUMU6LNk7HRI+1A77UPttA0lQ3ri9NjH2cf4zU9VURVVRVU0VTZRXVxNdVE1NcU1LC5eTFVRFXn+vCz9RCKSa6byxKLvknx2aKdzbmVq3kLgOaABOA78e+fc2StXZm4bjg7TPdJN10gXHUMddAwnh87hTjqGOmgfbqd7pHv8nuwxJcESqoqrqC6qZlX5KqqKqqgurmZx0WIWFy+moqBCd4yIyJRN5Qj9GWA78OyEeV8F/sU59w0z+2pq+iuZLy87RuOj9IZ76R09N/SN9nEmfIbukW56RnroHulOtsM94981MlFhoJCqoioWFS7iE9WfoLKoksrCymRoF1VTVVRFSagkCz+diHjVVB5B94qZNVww+16SzxkF+AfgZbIQ6M45Yi5GNB4lmogyEhthND5KOBYmHA8nxxPaQ9EhBqODDEYHGYok2+PzIoP0R/rpHe29aECPmZ83n/L8csoLylldsZrygvLxoaygjKrCZIjrUWUiMttmeg690jnXlmq3A5UZqueitr+xnec/fJ5oIhncYwEeTURntL6QL0RxqJiiYBHFwWKKQ8VUF1WzbOEySvNKKc0rZX7efErzSlmQv2C8XZpXqouMIpKz0r4o6pxzZuYutdzMtgHbAOrr62e0jfp59Wys2kjQHyTomzBcMJ0fyCfPn0dBoIA8fx75gfxzbX8+RaFkgCuURcSLzLlLZvG5TslTLi9MuCj6b8Dtzrk2M6sGXnbOLZtsPU1NTa65uTm9ikVE5hgz2++ca5qs30y/n/R54JFU+xHgn2e4HhERyZBJA93Mfgi8Diwzs1Yz+xLwDeAzZvY+8OnUtIiIZNFU7nL5/CUW3ZnhWkREJA16JIyIiEco0EVEPEKBLiLiEQp0ERGPUKCLiHiEAl1ExCMU6CIiHqFAFxHxCAW6iIhHKNBFRDxCgS4i4hEKdBERj1Cgi4h4hAJdRMQjFOgiIh6hQBcR8Yi0At3M/tjM3jazt8zsh2aWn6nCRERkemYc6GZWA/wR0JR6eLQfeDBThYmIyPSke8olABSYWQAoBE6nX5KIiMzEjAPdOXcK+CZwAmgD+pxzv8xUYSIiMj3pnHJZANwLLAUWA0Vm9tBF+m0zs2Yza+7q6pp5pSIiclnpnHL5NHDMOdflnIsCPwE+eWEn59zTzrkm51xTRUVFGpsTEZHLSSfQTwA3mVmhmRlwJ/BOZsoSEZHpSucc+h7gx8AB4HBqXU9nqC4REZmmQDovds59Hfh6hmoREZE06JOiIiIeoUAXEfEIBbqIiEco0EVEPEKBLiLiEQp0ERGPUKCLiHiEAl1ExCMU6CIiHqFAFxHxCAW6iIhHKNBFRDxCgS4i4hEKdBERj1Cgi4h4hAJdRMQj0gp0Mys1sx+b2btm9o6ZfSJThYmIyPSk9cQi4H8AP3fOPWBmIaAwAzWJiMgMzDjQzWw+cCvwKIBzLgJEMlOWiIhMVzqnXJYCXcD3zOwNM/u2mRVlqC4REZmmdAI9AKwD/rdzbi0wBHz1wk5mts3Mms2suaurK43NiYjI5aQT6K1Aq3NuT2r6xyQD/jzOuaedc03OuaaKioo0NiciIpcz40B3zrUDJ81sWWrWncCRjFQlIiLTlu5dLv8R+H7qDpejwO+lX5KIiMxEWoHunDsINGWoFhERSYM+KSoi4hEKdBERj1Cgi4h4hAJdRMQjFOgiIh6hQBcR8QgFuoiIRyjQRUQ8QoEuIuIRCnQREY9QoIuIeIQCXUTEIxToIiIeoUAXEfEIBbqIiEco0EVEPEKBLiLiEWkHupn5zewNM3shEwWJiMjMZOII/XHgnQysR0RE0pBWoJtZLfDvgG9nphwREZmpdI/Q/zvwF0DiUh3MbJuZNZtZc1dXV5qbExGRS5lxoJvZ3UCnc27/5fo55552zjU555oqKipmujkREZlEOkfoNwOfM7PjwI+ATWb2fzNSlYiITNuMA90595fOuVrnXAPwIPCSc+6hjFUmIiLTovvQRUQ8IpCJlTjnXgZezsS6RERkZnSELiLiEQp0ERGPUKCLiHiEAl1ExCMU6CIiHqFAFxHxCAW6iIhHKNBFRDxCgS4i4hEKdBERj1Cgi4h4hAJdRMQjFOgiIh6hQBcR8QgFuoiIRyjQRUQ8Ip2HRNeZ2S4zO2Jmb5vZ45ksTEREpiedJxbFgD91zh0wsxJgv5m96Jw7kqHaRERkGtJ5SHSbc+5Aqj0AvAPUZKowERGZnoycQzezBmAtsOciy7aZWbOZNXd1dWVicyIichFpB7qZFQP/BDzhnOu/cLlz7mnnXJNzrqmioiLdzYmIyCWkFehmFiQZ5t93zv0kMyWJiMhMpHOXiwHfAd5xzv195koSEZGZSOcI/Wbgi8AmMzuYGrZkqC4REZmmGd+26Jx7DbAM1iIiImnQJ0VFRDxCgS4i4hEKdBERj1Cgi4h4hAJdRMQjFOgiIh6hQBcR8QgFuoiIRyjQRUQ8QoEuIuIRCnQREY9QoIuIeIQCXUTEIxToIiIeoUAXEfEIBbqIiEek+0zRu8zs38zsAzP7aqaKEhGR6UvnmaJ+4H8Bm4EVwOfNbEWmChMRkemZ8SPogI3AB865owBm9iPgXuBIJgqb6N29L9J/8u30V2SXfmKec+mv3k2yjVQRk6zjguWTru+jr7Gx6YmvvWh7rJ/v/MrMUl0M8J3rZr7ka82S2zAj+axww3zJMebDxub7/Km2b/y1Zob5/Ml5PsPMP2HsG5/v8wdSbT9+f3KZz/z4/H58Pj/m9+H3BfAHgvh8hj8QwOcL4A8E8PsC+Pw6myhzTzqBXgOcnDDdCtx4YScz2wZsA6ivr5/Rhvr2/oAbu38yo9fK3JRwRhwfCXzE8RE3Hwn849MJ/CTMRxw/CUsNE9vmx5kfZ4Fk25dsY36cL4Dz+cEXGB9srO0PYv5Aaghi/hA+fwBfIIjfH8ICQfyBIP5giEAgRCB4bggG8wiEQvgDIfAHwRcEfwj8geTYF0zO909Y7tMvLjknnUCfEufc08DTAE1NTTM6Dl7+hb+jfehradVhUzkEn+Rg2JhkHc6dOzq+eIdJXz9Jh0lf40gkxwl33txz3S+2/Nx6nEukmg5wuEQi2XJgJHDO4ZwD58b7JsfJ/iTc+HRynEi+2CVIJJJtl4ifW/d4v/i51yYS4OK4RPI15uIkEsk+loinXpeARByXiI+3ScSTr3MJSMTGp0kkX4f76LS5OOZiWGo75mKYS+BzMSwRx+ci+Fwcv4snx8QmjBMEiONPDQHiBEgQIEbI4pP8W2ZGHD9xX5CEBUn4koPzBXFjoe/PS/5iCeRhwTz8gRC+YD7+YAh/MC/1yyEPAheOU8smjgP5F8zLT83Pm9DOT/5im8JflpJ56QT6KaBuwnRtal7GzV9YwfyFFVdi1SIZEU84ovEEkXiCcNwRiSWIRqOMRiNEIxHi0QjR6CixaJRoNEIsNcRjqXZklHgsQiIWJR5Lzk9EIyTiURKxURKxKMQj4+PkEIVEFItHsUSUgIsSJE7IogSJkUcs+cuFMEEbJESUEHGCxJJti5FnMUJj00QzszPMd37AX3ZccG46mJ+cDuanludDsGCSceG51/mv+PFpzktnD+wDGs1sKckgfxD4QkaqErnK+H2G3+cnP+ifMDd/VmuIxhOMROOEI3FGonGGU+ORSJy+SJzhSIzhSGr+hPbgaIzhSIzBcIzw6CiR0RGikRGio6PEImEsPkqIGHmp0M+z1Dg1hCxGgcWYF4xTEohTEohR5EtQFIhRaFEKLEZhIkp+NEpeLErIDRF0Zwm4CIF4GF8igkVHIDYKsZGZ7wBf8PzAPy/0C84fAmPticsKLzFOtUOFybE/mLl/tAybcaA752Jm9ofALwA/8F3nXAauXIrITAT9PoJ+H/PyMxs4kViCodEYg6MxBsLJ8eBolIFwbMIQ5Uw4SsuE6f6RGP0jUfpHogxFLn8KqjDkp7QgSGlxkIpCKM9PUJ7vWBhKUBZKsCAvTmkwxvxgnHmBGMX+GAVEsFgYYmGIhiE6nGoPXzA9AuE+GGhPLRtJ/uKIjiT/0pkuX/BcuI8NY9OhognTRefPX7YZSmd2HXGq0vobxTm3A9iRoVpEJAeFAj5CgRALikIzXkc0nqB/JEpfaugPx8bbfcMReoej9I5E6U21W7si9I3E6B2OEhu/3mMkIysZWwGfsaAoxMLCEAuLQpQVhygrClFWnJecntCuKM5jXkEgdVfWBIn4+b8AxodU4I+1I0MTpochMnxBewgigzDYmWqPLRti/BpW2XW5HegiIlMR9PsoK86jrDhvWq9zzjEwGqN3KMqZ4QhnhyKcGYpwdvjcuGcw2T5yup/uwVH6w7GLrivk91FWHKK8OI/ysXFJHuXFeVSU5LGopJiKkjIWleVRnHeR8J8J55J/JUSGIa84/fVNQoEuIjnLzJiXH2RefpD6ssIpvSYSS4wHfc/QKD2DEboHR+kaHKV7INnuHBjlSFs/PYORCX8BnFMQ9KdCPm98XDk/n6p5+VSOD3mUTHZ6y+zcefhZoEAXEU8JBXzjoTsZ5xy9w9HxkO8cCNM1MEpnf/IXQGf/KO93DvLaB90MXOTIvyjkHw/6qvn5LJ5fkByX5lM9v4Dq+fnMLwhm5mh/ChToIjJnmSXPwy8oCtFYWXLZvsORGB39o7T3henoTw7t/WE6+0dp6xth94c9dAyMEr/giL8g6Ke6NJ//ct8qbrqm7Er+OAp0EZGpKAwFWFoeYGl50SX7xOIJugZHaesL09Ybpq1vJNnuG6G08Mrf7qhAFxHJkIDflzrVUgBX9oaWi9IXQYiIeIQCXUTEIxToIiIeoUAXEfEIBbqIiEco0EVEPEKBLiLiEQp0ERGPMJeJpyNPdWNmXUDLJRaXA92zVkzu0/74KO2Tj9I+OZ9X98cS59ykj22b1UC/HDNrds41ZbuOXKH98VHaJx+lfXK+ub4/dMpFRMQjFOgiIh6RS4H+dLYLyDHaHx+lffJR2ifnm9P7I2fOoYuISHpy6QhdRETSMOuBbmZ3mdm/mdkHZvbViyzPM7PnUsv3mFnDbNc4m6awPx41sy4zO5gavpyNOmeLmX3XzDrN7K1LLDcz+1Zqf71pZutmu8bZNoV9cruZ9U14jzw52zXOJjOrM7NdZnbEzN42s8cv0mfOvU+A5DP1ZmsA/MCHwDVACDgErLigz38Ankq1HwSem80ac3B/PApsz3ats7hPbgXWAW9dYvkWYCdgwE3AnmzXnAP75HbghWzXOYv7oxpYl2qXAO9d5P/NnHufOOdm/Qh9I/CBc+6ocy4C/Ai494I+9wL/kGr/GLjTZusJq7NvKvtjTnHOvQKcuUyXe4FnXdJuoNTMqmenuuyYwj6ZU5xzbc65A6n2APAOUHNBtzn3PoHZP+VSA5ycMN3KR/8hxvs452JAH3Bln6yaPVPZHwC/nfqz8cdmVjc7peWsqe6zueYTZnbIzHaa2fXZLma2pE7JrgX2XLBoTr5PdFE09/0UaHDOrQZe5NxfLyJjDpD8aPga4H8C/y/L9cwKMysG/gl4wjnXn+16csFsB/opYOIRZm1q3kX7mFkAmA/0zEqdNBNmAAABTUlEQVR1s2/S/eGc63HOjaYmvw2sn6XactVU3kNzinOu3zk3mGrvAIJmVp7lsq4oMwuSDPPvO+d+cpEuc/J9MtuBvg9oNLOlZhYiedHz+Qv6PA88kmo/ALzkUlc5PGjS/XHBeb/PkTxfOJc9DzycuovhJqDPOdeW7aKyycyqxq4zmdlGkv+vvXoQROpn/Q7wjnPu7y/RbU6+TwKzuTHnXMzM/hD4Bck7PL7rnHvbzP4z0Oyce57kP9T/MbMPSF4IenA2a5xNU9wff2RmnwNiJPfHo1kreBaY2Q9J3rVRbmatwNeBIIBz7ilgB8k7GD4AhoHfy06ls2cK++QB4A/MLAaMAA96+CAI4Gbgi8BhMzuYmvdXQD3M3fcJ6JOiIiKeoYuiIiIeoUAXEfEIBbqIiEco0EVEPEKBLiLiEQp0ERGPUKCLiHiEAl1ExCP+P1/nEw/KLa+NAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x204668fe7f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(results['time'], results['x'], label='x')\n",
    "plt.plot(results['time'], results['y'], label='y')\n",
    "plt.plot(results['time'], results['z'], label='z')\n",
    "plt.legend()\n",
    "_ = plt.ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next code cell visualizes the velocity of the drone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WRqaNZFqfaYzJGEO/xH4YlEzcGsok2IUIYN9VfceKgyvILc3l26pv0WjMRjPDUofx02E/ZXTGaAYlDcJklDHo4iQJdiECjNaaDcUbWLpnKZtKNhFuCGdo6lDuG3Yfo9JGMSRliMy4KM5Jgl2IAGFvtvOv/H/x1t63OFB9gNSIVOaOmMuMvjOIM8f5uzzRiUiwC+Fnx23H+ft3f+ev3/6VSlslfRP68psJv+G6HtdJF4u4JBLsQvhJfnU+y/KWseLgCmzNNiZ0mcAdA+5gbMZYGZYo2kWCXQgf0lrzVfFXvJ33NhuKNhBuCOf7vb7PHQPuoE9CH3+XJ4KEBLsQPmB1WlmZv5J39r5Dfk0+yRHJ/HTYT/lRvx+RaEn0d3kiyEiwC9FBXNrFkdoj/PPgP3l337vUNNXQP7E/T014imt7XCsjW0SHkWAXwgsqrZXsr97P/uMnbwdrDmJ1WjEoA5O7TmbmgJmMSB0h/eeiw0mwC3ERGh2NHKg+wIHqA+4A94R5la2qZZkEcwLZCdn8IPsHZMdnMyZjDFkxMh+Q8B0JdhGyXNpFpbWSpuYm7M127C479mY7Tc1NOJod2F126ux1HKo51BLiRfVFLe+PCIugd1xvrsi6gj7xfchOyCY7IZvkiORzfKoQHU+CXYSUBkcDm4o3sbZwLeuL1lNhrTjve4zKSI/YHgxOHsy0PtPcAR6fTZeYLjIniwhIEuwi6B2tPcrawrWsK1xHblkuTpeTGFMM47uMZ3jqcCJNkZiNZsIN4ZiMJsKN4S0/R4RFkBWTJQc6RaciwS6CktaaZXnLWP7dcg7XHgagV1wvZvafycSsiQxLHSYXbxZBS4JdBJ1GRyP/veG/+bTgU0akjuCW793CxC4T6Ror85KL0CDBLoLK0dqjPLj6QfJr8nl45MPcOfBOGV4oQo4EuwgaXxZ9yYJ1C1Ao/nT1nxiXOc7fJQnhFxLsotPTWvPn3X/mxa9fJDshmxcmvSCXgxMhTYJddGqt+9On9pjKr8b9ikhTpL/LEsKvJNhFp3W09ihz18zlYPVB6U8XohUJdtEp7SjfwZwv5qC15k9X/YlxXaQ/XYgTJNhFp7OucB3z1swjJTKFV65+RYYxCnEaOR9adCorDq7gwS8epGdcT9667i0JdSHaIC120Wks2b2ERdsWMSZ9DC9MeoHo8Gh/lyREQGp3i10p1VUptVoptVcptUcpNdcbhQlxgku7WLR1EYu2LWJK9ym8dPVLEupCnIM3WuxOYJ7W+mulVAywTSn1mdZ6rxfWLUKcw+Vg4VcLWXFwBbf0u4XHRj+G0WD0d1lCBLR2B7vWugQo8TyuU0rlAV0ACXbRLo2ORh5Z+wjri9YzZ9gcZg+ZLcMZhbgAXu1jV0r1AIYDm725XhF6CusKeXT9o+yu2M0Tlz3BjL4z/F2SEJ2G14JdKRUNvA88pLWubeP12cBsgG7dunnrY0WQsTfbeXP3m7y26zUMysCiKxZxdfer/V2WEJ2KV4JdKWXCHerLtNb/19YyWutXgVcBcnJytDc+VwSXr4q/4qnNT1FQW8CU7lOYP2o+6VHp/i5LiE6n3cGu3J2efwbytNbPt78kEWrKGsp4duuzfHL4E7rHdueVq1+RM0mFaAdvtNjHA7cDu5RSOzzP/Vxr/aEX1i2CmMPl4C95f+GlHS/RrJuZM2wOdw26Sy5DJ0Q7eWNUzJeADFUQFyW/Op95a+dxoPoAE7Mm8tjox2SqXSG8RM48FT5XUl/CPZ/dQ7Ormd9P+j2Tuk6SYYxCeJEEu/CpmqYa7l11L1aHlTenvkm/xH7+LkmIoCPBLnzG6rTy089/SmFdIS9f87KEuhAdRIJd+ITT5WT+2vnsPLaT5698nlHpo/xdkhBBS6btFR1Oa82TG59kbeFafjH2F3LCkRAdTIJddLg/bP8D/zjwD+4dei8/6vcjf5cjRNCTYBcdalneMl7b9RrT+07n/qH3+7scIUKCBLvoMB8f/phntjzD5K6TeXzM4zKkUQgfkYOn4pKUN5ZTXF+MrdmGzWnD1myjydnU8rjWXsubu99keOpwnpn4DGEG+VMTwlfkf5u4YFprtpZtZVneMlYfXY1Lu865/KCkQbw4+UUsYRYfVSiEAAl2cQGsTiv/yv8Xy/KWcaD6APHmeO4aeBej0kdhCbNgMVqwhFkwG80tP5vDzJgMJn+XLkRIkmAXZ1VUX8Tyb5fz/v73qbXX0i+hH0+Oe5Lrel4nrXAhApgEuziF1WllfeF6Psj/gHWF61AoJnebzG39b2NE6gg5ACpEJyDBLnA0O/iq+Cs+OvwRq4+sptHZSJIlibsH3c3N/W6Wi10I0clIsIcop8tJbmkuHx/+mM8KPqPOXkecOY7rel7HdT2vIyctB6PB6O8yhRCXQII9RGitKawvJLc0ly2lW9hYvJEqWxVRpigmd53M1J5TuSzjMkxGOeApRGcnwR7EShtK2VK6hS0lW8gtzaW4oRiAREsiYzLGMKX7FCZ0mSAHQoUIMhLsQeJEi/zrsq/5uvxrtpZu5UjdEQDizHGMShvFnYPuZHT6aHrF9ZKDoEIEMQn2TsqlXew/vp+vy792h3nZ15RbywGIDY9lROoIbu53M2MyxpCdkI1ByewRQoQKCfYAprWmylZFYX0hRXVFFNUXUVhfSGFdIXlVedTZ6wBIi0xjZPpIRqaOZETaCHrH95YgFyKESbAHiDp7HXsq97C7Yje7K3ZTUFtAUX0RVqf1lOWSLElkxWQxpfsURqa5gzwzKlO6VoQQLSTY/cDR7GDf8X3sqtjFropd7K7YzaGaQ2g0AN1iutErvhdjM8aSFZNFVnQWXaK7kBmdSaQp0s/VCyECnQS7DzU1N/HG7jd4c/ebLS3xREsiQ5KHcH3P6xmcPJiByQOJM8f5uVIhRGcmwe4ja4+u5ektT1NYX8g13a/h2h7XMjh5MBlRGdKNIoTwKgn2Dna07ijPbHmGtYVr6RXXi9emvMbYjLH+LksIEcQk2DuIzWnjjd1v8Oddf8ZoMDJv5Dxu63+bnNkphOhwEuxeprVmzdE1PJP7DEX1RVzX4zrm5cwjLSrN36UJIUKEBLsXOVwOfrPpN7y//316x/Xmz1P+zOiM0f4uSwgRYrwS7EqpN4AbgHKt9SBvrLOzqbPXMW/NPDaWbOSewfdw37D75ApCQgi/8NbpiUuAqV5aV6dTUl/CHR/dQW5pLr8e/2seHPGghLoQwm+80mLXWq9TSvXwxro6mz2Ve5jz+RyanE386Zo/yYgXIYTfyYQi7bD6yGru+vguwg3hvH392xLqQoiA4LNgV0rNVkptVUptPXbsmK8+tsMsy1vG3NVz6R3Xm2XfX0bv+N7+LkkIIQAfBrvW+lWtdY7WOiclJcVXH+t1za5mnt7yNE9veZpJXSfxxtQ3SI5I9ndZQgjRQoY7XgRHs4MF6xaw6sgqZvafySM5j8h1QYUQAccrLXal1F+BjUA/pVShUuo/vbHeQGJz2nhw9YOsOrKK+TnzeXT0oxLqQoiA5K1RMT/2xnoCVaOjkQe+eIDc0lx+edkvmd53ur9LEkKIs5KumPOos9dx/6r72Vmxk99M+A039r7R3yUJIcQ5SbCfQ7Wtmp+s+gn7qvbx7MRnmdJjir9LEkKI85JgP4sKawWzP5tNQU0Bv5/8eyZmTfR3SUIIcUEk2NtQ1lDGrE9nUdZYxuKrFnNZ5mX+LkkIIS6YBPtpiuqLmPXJLI43HedPV/+JkWkj/V2SEEJcFAn2Vg7XHGbWp7NodDby2jWvMThlsL9LEkKIiybB7rHv+D5mfzobjebNa9+kX2I/f5ckhBCXRCYBA3ZX7Oauj+/CaDDy5lQJdSFE5xbywb61dCuzPp1FTHgMS6cupVdcL3+XJIQQ7RLSwb6haAP3rbqP1MhUlk5dSlZMlr9LEkKIdgvZYP/8yOc88MUD9IjrwZvXvikXmxZCBI2QDPaV+SuZt2Ye/ZP68/qU10mKSPJ3SUII4TUhF+zv7XuPn6//OSPTRvLqNa8SZ47zd0lCCOFVITPc0ely8uLXL/LmnjeZmDWRRVcswhJm8XdZQgjhdSER7NW2auavm8+mkk3c3O9mHh31KCajyd9lCSFEhwj6YM+rzONna37GscZjPDnuSaZlT/N3SUII0aGCOthX5q9k4VcLiTfHs/S6pQxKHuTvkoQQosMFZbA7XA6e3/o87+S9Q05aDs9d8ZyMfBFChIygC/ZKayXz180ntzSXmf1n8nDOw5gM0p8uhAgdQRXsm0o28d8b/pvjtuM8NeEpuYydECIkBUWwl9SX8OzWZ/ms4DO6xXTj7evepn9Sf3+XJYQQftGpg93ebGfJniW8tvM1AB4Y/gD/MfA/MBvNfq5MCCH8p9MG+7rCdTyz5RmO1B3hmu7XMD9nPhnRGf4uSwgh/K7TBfvRuqP8bsvvWFO4hh6xPXjlmlcYlznO32UJIUTA6FTBvnTPUl78+kWMBiMPj3yYmf1nyhmkQghxmk4V7FGmKK7qfhXzRs6TaXaFEOIsOlWw/zD7h0zvO93fZQghREDrVNP2KqX8XYIQQgQ8rwS7UmqqUuo7pdQBpdRj3linEEKIS9PuYFdKGYE/AtcBA4AfK6UGtHe9QgghLo03WuyjgQNa63yttR34G/BvXlivEEKIS+CNg6ddgKOtfi4ExnhhvWfY9M6viCv4GI27r10DtDxWLc+7Wu4N6BP32v28ezkDLhQuz/taltMGzzKt3qPc9+7lWr3W6jM1oHWrxyg45XjAiZ89tSrlOV7gfl6deF0Z3He4H2MwopQBDAb3vTKiDAbPLQxlDMNgNGEwhmEIcz82hpkwGk0YTSbCTBZMZjOmcAumcAvhlgjM4WbMlgjMlggio2IwR0SjjJ3qGLoQ4jx89j9aKTUbmA3QrVu3S1uJMQyXIdzzw4kYp3W8tjxv8MS70p57dTLSaXldnxL1aDDQ7F6+1ToN2tXqczzv0yc/S6HBs340rWo58RiUS7equ9Xr+pTdgfvzOLGsb9gJw4YZuzJjN1hwGMw4DRE4wyJpNkXjCo+B8GiUJQajJRZjRCzhUXGYo+KwRCcQGRNPeGQcmGPBHANh4ef/UCFEh/FGsBcBXVv9nOV57hRa61eBVwFycnIuKbnG/vhx4PFLeWvno7Xn1gzaderN5XnO5Tzl1ux04rA34XDYabLbcdht2Jts2JusOO1NOOw2nPYmmh02mu1Wmu1WtL0RHFa0w4rB6b4Zm22ENVsx22sx61IidSPRWInGhkGd/5/OjgmbIRKrMZYmcyJOSxI6KoWwmBTMcWlEJmYSnZiOIToFIpMhIgEMnWqAlhABzRvBngtkK6V64g70W4BbvbDe0KZOdN9ceOAZPTcLEOPFUlwuTYPdSYnVQX19Dda6Gqx1VTQ11GJvrMFprcFlrcVlq0M11aHsdYQ56wm31xBVV0187T6S1FYSqWtzx+DCQIMxFlt4Ak5zIq7IJIzRKZhiU4lMysQSn4GKyYDoVIhKBZNchFyIc2l3sGutnUqpOcAnuHPlDa31nnZXJgKGwaCIsZiIsZggIRK4uMnWGpqcVNQ3cbimkerKMhqqSmiqKcVZWw6NlRitlYQ3VRHZUE18Qy1JVSUkqlriaWhzR2ALi6XJkowrKg1jbBoRCZmY4jIgOg1i0tz30WnubwJy7oMIQV7pY9dafwh86I11ieATZQ4jyhxG96Qo6JUCtH3tWa01tVYnx+ptfFdnp6K2gZqKEhqqinBUl6DrygizlhPVVEFyUw2ptZWklBzEpKoxKfsZ62s2mGiOSEZFJhEWk4KKTIKoZIhMOvUWkXDyZoqQnYHo9GQ4hAgYSiniIk3ERZrokwqQBJx5oN3R7KK8romSais7qq0UH7dSUVVBQ2UxjpoSqCsjtrmKVFVNkr2WxNpaksoKSTHmkUAdUbrh7EUYzacG/YlbZOufEz3PJbbaIUTKDkEEDAl20emYjAa6xEfQJT6CnJZn+7Q8OtHyL6xupLjaRnGNldxqKyXVNoqrrRyrrqOproJ4XUvejzxLAAANg0lEQVSCqiOOBuJVPWmmRrqENZFOI0n2RuIdDcRU78firMVkr0E5rWcvqvUOoSXw4907gcjEM78lRCaBJV4OGosOIcEugs7Jln8cAzPj2lym2aUpr3MHfXG1jaJqK8XVVvZUWyny7ABqrI5T3pMe4WJAgot+sU56RtvpHmEjPdxKapiVCGcNWI9DYxVYq6HqEFir3D83N52lUINnR9A68NvYCZzYOUQkyM5AXBAJdhGSjAZFRlwEGXERjOze9jL1TU6KjlspqGygoLKRQ5UNFFQ2sKK0keIaK1rHtiybHB1O75RoeqdG0yfLc58aTUasBYPTCo2V0Fjhua/y3HtuDRXunUJVPhTmup9zOdsuShnc4R6ZeGqX0ImdQsTpOwbPMnLdgpAiwS7EWUSbw+iXHkO/9DMHjzY5mzlaZeVwRQP5FfUcKK/n4LEG/rWz5JSWfoTJSN+0aAZkxjEwM5GBmT34XrdYIsKNZ/9graGp1rMDqHLvEFq+DVSdel9XAmV73D87Gs++zogE91DR6NSTw0ajU9yjh055nCI7gSCgtPbtWY7gPkFp69atPv9cITqa1pqKejsHj7nD/kB5Pd+W1rK3uJZam7sVblDQKyWagZmxnlscg7PiiLW0M1Ad1lO/DZwI/8ZKaDgG9eXuW0M51B8De13b64lI9AwZTTk5dDQqpdUt+eS9KaJ9NYuLopTaprXOOe9yEuxCdDytNYXHrewprmVvcQ17S2rZU1xLSY2tZZleyVEMyYpjSFY8Q7u6jw9YTOdo2beXvfFkyDeUQ32Z+3F9mefm2QnUlcHZDhyHR58M+shkiEry3Lf1XIqcXNZOEuxCdAKV9U3sLq5l59FqvimsYWdhNeV17oOtRoOib1oMQz1hPyQrjn7pMZiMPj54qjXY693HAhoq3K3/hmPuLqLWPzdUnnzO5Wh7XeEx7m8CZ7T+U9zHBFrOM/Dcy7xDp5BgF6KTKqu18c3RanYW1vBNofv+RL99eJiBARmxp4R9r5RojIYAGkOvNdhqTh4YPhH2rXcE9eUnHzdWuOc+aos59rQhorFgiTvzZo51H1SO8BxYNscF5eghCXYhgoTWmiNVjXxTWMOuQnfLfndRDY32ZgCiwo0MyYpneLd4hndLYFjXeFJizH6u+iK4XJ7jAa12BI2VJ78BtIwcqgJbrXunYatxT5B3VspzHsFpJ5pZ4tveMZy4BfiQUgl2IYJYs0tz8Fi9u1V/tJodR6vJK6nF6ZkeOishoiXkh3eLZ1BmHOFhgRlWl0RrsDe4A77JE/bWarBVtxpBdPy0W6sdw7l2CqefX3D6SWbRqe6uoxOji6KSwdCBx0JalybBLkRosTma2V1Uw/Yj7qDffuQ4xZ6DsxEmI6N6JjK+dxLj+yQzICMWQyB13/hS652CrfrkN4ATO4aWcww83yKsx08+13zmnESgTg38qOSTB5Bbjhskn7xvxzTVEuxCCMpqbWw/cpxN+VVsOFDB/vJ6AOIjTVzWK4lxfZIZ3zuJnslRnqt6ibPSGprqWh0jODF89Nip940V7m6kppq21/Pj5dBv6iWVcKHBLicoCRHE0mItTB2UwdRB7qmWy2ptfHWwgg0HKvnqQAUf7S4FIDPOwoTsZC7PTmF8n2QSo2Q0yhmU8hy8jYWk3udf3mk/ecZxQ6sDyGkDO75UabELEZq01hyubGTDgYqWW63NiVIwuEscl2cnM6FPCiO7JwRX/3wnJl0xQoiL4mx2sauohvX7K1i//xhfH6mm2aWJDDcypmci4/skM653Mt9Ljwnd/nk/k2AXQrRLnc3BxoOVfHmggi/3V5Bf4Z7HPikqnLG9kxjfO5nxfZLolhgp/fM+In3sQoh2ibGYmDIwnSkD0wEorrby1UF33/yGgxX8a2cJAF3iIxjfJ6mlRd+pxtAHKWmxCyEumtaa/IoGd8gfqGRjfmXL2bHfS49hfB93a350zySizdJ+9BbpihFC+EyzS7OnuIYNByrZcKCCLYersDtdhBkUw7vFM653Mlf2S2FoVrz0z7eDBLsQwm9sjma2FRznS89om11FNWgNydFmrvpeKlcPSGNCn+Rzz0svziB97EIIv7GYjJ7umGQAjjfYWbOvnFV55Xy4q4TlW49iDjMwoU8yV/VP46r+qaTFypS+3iItdiGET9mdLrYcqmJVXhmr8sooPO6e631oVpz7YO2ANPqkRstImzZIV4wQIuBprdlXVs+qvDI+3VvGN0erAfdFR64ZmMa1A9MZJv3yLSTYhRCdTmmNjc/yyvh0TykbD1bidGlSYsxcMyCNa/qnMbpnIlEhPMpGgl0I0anVWB2s+a6cT/aUsua7YzTam08ZZTMhO5mhWfEhNd2BBLsQImjYHM3kHq5yT1528OQom8hwI6N7JnrOgk2mf0ZMUPfNy6gYIUTQsJiMXJ6dwuXZKQDUNDrYmF/pmamygt98lwe4z4Kd4umbz+meQJivrw8bINrVYldKzQAWAv2B0VrrC2qGS4tdCOFNpTU21u07xqd7S1m3vwK700VCpImr+7tDfkJ2MhZT5x8z75OuGKVUf8AFvAI8IsEuhPC3hiYna/cd49M9pXz+bTl1NieR4Uau6JvCpH6pTOybQnpc5xwz75OuGK11nufD2rMaIYTwmihzGNcPzuD6wRnYnS42H6rkkz2lfLa3rOXCIv3SYpjYN5mJfVMY1SMxKFrzrXnl4KlSag3SYhdCBDCtNd+W1rFu3zHW7T9G7qHj2JtdWEwGxvZKYmJ2CtcMSKNrYqS/Sz0rr3XFKKVWAeltvPS41vqfnmXWcJ5gV0rNBmYDdOvWbWRBQcH5ahNCiA7TaHeyOb+KtfuOsW7fsZb55od2jefGIe4Wf2Z8hJ+rPJVPhztKi10I0dkdqWzkw90lrNxZzO6iWgByuidww5AMrh+SQWqM//vlJdiFEOISHapoYOU3xazcWcJ3ZXUYFIzpmcS/D8/kxqGZRIb7Z6S4r0bFTAP+AKQA1cAOrfW153ufBLsQorPYX1bHBztLWPlNMfkVDcRYwvjhiCxuG9ON7LQYn9YiZ54KIYQXaa3ZWnCcdzYV8NGuUuzNLsb0TGTm2O5cOzDdJ1MbSLALIUQHqaxv4u9bC/nLlgKOVllJjjZz86gsfjy6G1kJHTeqRoJdCCE6mMulWbv/GMs2FfDFt+Vo4Mq+Kdw6pjuT+qV4fUoDCXYhhPChomorf9tyhOW5RymvayI91sKPRnXl5lFd6eKlYZMS7EII4QfOZhdffFvOX7YcYe2+Y4D3WvES7EII4WeFxxtZnnv0lFb88z8ayjjPtWAvlkzbK4QQfpaVEMm8Kf2Ye1U2X3xbzl+3HKF7clSHf64EuxBCdLAwo8F9oe6Bbc3O4n2hOQu9EEIEMQl2IYQIMhLsQggRZCTYhRAiyEiwCyFEkJFgF0KIICPBLoQQQUaCXQghgoxfphRQSh0DznbR02SgwoflBDrZHmeSbXIm2SanCtbt0V1rnXK+hfwS7OeilNp6IXMhhArZHmeSbXIm2SanCvXtIV0xQggRZCTYhRAiyARisL/q7wICjGyPM8k2OZNsk1OF9PYIuD52IYQQ7ROILXYhhBDt4LdgV0pNVUp9p5Q6oJR6rI3XzUqp5Z7XNyulevi+St+5gO1xp1LqmFJqh+c2yx91+opS6g2lVLlSavdZXldKqRc922unUmqEr2v0tQvYJlcqpWpa/Y084esafUkp1VUptVoptVcptUcpNbeNZULu7wQArbXPb4AROAj0AsKBb4ABpy1zP/Cy5/EtwHJ/1BpA2+NOYLG/a/XhNpkIjAB2n+X164GPAAWMBTb7u+YA2CZXAiv9XacPt0cGMMLzOAbY18b/m5D7O9Fa+63FPho4oLXO11rbgb8B/3baMv8GLPU8fg+4SimlfFijL13I9ggpWut1QNU5Fvk34C3ttgmIV0pl+KY6/7iAbRJStNYlWuuvPY/rgDygy2mLhdzfCfivK6YLcLTVz4Wc+Q/SsozW2gnUAEk+qc73LmR7APzQ83XyPaVUV9+UFrAudJuFmsuUUt8opT5SSg30dzG+4umqHQ5sPu2lkPw7kYOnnccHQA+t9RDgM05+mxHihK9xn3I+FPgD8P/8XI9PKKWigfeBh7TWtf6uJxD4K9iLgNYtzizPc20uo5QKA+KASp9U53vn3R5a60qtdZPnx9eBkT6qLVBdyN9QSNFa12qt6z2PPwRMSqlkP5fVoZRSJtyhvkxr/X9tLBKSfyf+CvZcIFsp1VMpFY774OiK05ZZAfyH5/F04AvtORoShM67PU7rF7wJd39iKFsB3OEZ9TAWqNFal/i7KH9SSqWfOA6llBqN+/93sDaG8PyufwbytNbPn2WxkPw7CfPHh2qtnUqpOcAnuEeEvKG13qOUehLYqrVegfsf7G2l1AHcB4xu8UetvnCB2+NBpdRNgBP39rjTbwX7gFLqr7hHeSQrpQqBXwImAK31y8CHuEc8HAAagbv8U6nvXMA2mQ7cp5RyAlbgliBuDAGMB24Hdimldnie+znQDUL37wTkzFMhhAg6cvBUCCGCjAS7EEIEGQl2IYQIMhLsQggRZCTYhRAiyEiwCyFEkJFgF0KIICPBLoQQQeb/AwPD7wNlHXDUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2046c85b208>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results['time'], results['x_velocity'], label='x_hat')\n",
    "plt.plot(results['time'], results['y_velocity'], label='y_hat')\n",
    "plt.plot(results['time'], results['z_velocity'], label='z_hat')\n",
    "plt.legend()\n",
    "_ = plt.ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, you can plot the Euler angles (the rotation of the drone over the $x$-, $y$-, and $z$-axes),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2046c8a63c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results['time'], results['phi'], label='phi')\n",
    "plt.plot(results['time'], results['theta'], label='theta')\n",
    "plt.plot(results['time'], results['psi'], label='psi')\n",
    "plt.legend()\n",
    "_ = plt.ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "before plotting the velocities (in radians per second) corresponding to each of the Euler angles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2046ca4a898>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results['time'], results['phi_velocity'], label='phi_velocity')\n",
    "plt.plot(results['time'], results['theta_velocity'], label='theta_velocity')\n",
    "plt.plot(results['time'], results['psi_velocity'], label='psi_velocity')\n",
    "plt.legend()\n",
    "_ = plt.ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, you can use the code cell below to print the agent's choice of actions.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2046ca722e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results['time'], results['rotor_speed1'], label='Rotor 1 revolutions / second')\n",
    "plt.plot(results['time'], results['rotor_speed2'], label='Rotor 2 revolutions / second')\n",
    "plt.plot(results['time'], results['rotor_speed3'], label='Rotor 3 revolutions / second')\n",
    "plt.plot(results['time'], results['rotor_speed4'], label='Rotor 4 revolutions / second')\n",
    "plt.legend()\n",
    "_ = plt.ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When specifying a task, you will derive the environment state from the simulator.  Run the code cell below to print the values of the following variables at the end of the simulation:\n",
    "- `task.sim.pose` (the position of the drone in ($x,y,z$) dimensions and the Euler angles),\n",
    "- `task.sim.v` (the velocity of the drone in ($x,y,z$) dimensions), and\n",
    "- `task.sim.angular_v` (radians/second for each of the three Euler angles)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.76159199 -0.39583263 15.          6.25521245  0.14154246  0.        ]\n",
      "[-1.26953805 -0.47872507  4.07771581]\n",
      "[0.00449113 0.16387469 0.        ]\n"
     ]
    }
   ],
   "source": [
    "# the pose, velocity, and angular velocity of the drone at the end of the episode\n",
    "print(task.sim.pose)\n",
    "print(task.sim.v)\n",
    "print(task.sim.angular_v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Agent\n",
    "\n",
    "The sample agent given in `agents/policy_search.py` uses a very simplistic linear policy to directly compute the action vector as a dot product of the state vector and a matrix of weights. Then, it randomly perturbs the parameters by adding some Gaussian noise, to produce a different policy. Based on the average reward obtained in each episode (`score`), it keeps track of the best set of parameters found so far, how the score is changing, and accordingly tweaks a scaling factor to widen or tighten the noise.\n",
    "\n",
    "Run the code cell below to see how the agent performs on the sample task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode =   34, score =  -6.000 (best =  -6.000), noise_scale = 3.25"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\hp\\Desktop\\Quadrotor\\test55\\quadcopter-project\\physics_sim.py:114: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  J = V / n * D\n",
      "C:\\Users\\hp\\Desktop\\Quadrotor\\test55\\quadcopter-project\\physics_sim.py:114: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  J = V / n * D\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode =   50, score =  -6.000 (best =  -6.000), noise_scale = 3.2"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import pandas as pd\n",
    "from agents.policy_search import PolicySearch_Agent\n",
    "from tasks.base_task import Task\n",
    "\n",
    "num_episodes = 50\n",
    "target_pos = np.array([0., 0., 10.])\n",
    "task = Task(target_pos=target_pos)\n",
    "agent = PolicySearch_Agent(task) \n",
    "\n",
    "for i_episode in range(1, num_episodes+1):\n",
    "    state = agent.reset_episode() # start a new episode\n",
    "    while True:\n",
    "        action = agent.act(state) \n",
    "        next_state, reward, done = task.step(action)\n",
    "        agent.step(reward, done)\n",
    "        state = next_state\n",
    "        if done:\n",
    "            print(\"\\rEpisode = {:4d}, score = {:7.3f} (best = {:7.3f}), noise_scale = {}\".format(\n",
    "                i_episode, agent.score, agent.best_score, agent.noise_scale), end=\"\")  # [debug]\n",
    "            break\n",
    "    sys.stdout.flush()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This agent should perform very poorly on this task.  And that's where you come in!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Define the Task, Design the Agent, and Train Your Agent!\n",
    "\n",
    "Amend `task.py` to specify a task of your choosing.  If you're unsure what kind of task to specify, you may like to teach your drone to takeoff, hover in place, land softly, or reach a target pose.  \n",
    "\n",
    "After specifying your task, use the sample agent in `agents/policy_search.py` as a template to define your own agent in `agents/agent.py`.  You can borrow whatever you need from the sample agent, including ideas on how you might modularize your code (using helper methods like `act()`, `learn()`, `reset_episode()`, etc.).\n",
    "\n",
    "Note that it is **highly unlikely** that the first agent and task that you specify will learn well.  You will likely have to tweak various hyperparameters and the reward function for your task until you arrive at reasonably good behavior.\n",
    "\n",
    "As you develop your agent, it's important to keep an eye on how it's performing. Use the code above as inspiration to build in a mechanism to log/save the total rewards obtained in each episode to file.  If the episode rewards are gradually increasing, this is an indication that your agent is learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode =  726, score =  21.271, low score =   1.664, high score =  90.058"
     ]
    }
   ],
   "source": [
    "## TODO: Train your agent here\n",
    "import os\n",
    "import pickle\n",
    "from agents.agent import DDPG_Agent\n",
    "from tasks.task import Task\n",
    "#from tasks.task import Task\n",
    "\n",
    "exportPath = './data/'\n",
    "if not os.path.exists(exportPath):\n",
    "    os.makedirs(exportPath)\n",
    "\n",
    "# z axis is up\n",
    "init_pose = np.array([0.0, 0.0, 1.0, 0.0, 0.0, 0.0]) \n",
    "target_pos = np.array([0.0, 0.0, 10.0])\n",
    "task = Task(init_pose=init_pose, target_pos=target_pos, runtime=5.0)\n",
    "#agent = PolicySearch_Agent(task) \n",
    "#agent = Basic_Agent(task) \n",
    "agent = DDPG_Agent(task)\n",
    "\n",
    "# before training\n",
    "resultsAll = []\n",
    "high_score = -1000000.0\n",
    "low_score = 1000000.0\n",
    "\n",
    "# number of episodes to train\n",
    "num_episodes = 750\n",
    "\n",
    "training_results = {\n",
    "    'score': [],\n",
    "    }\n",
    "\n",
    "for i_episode in range(1, num_episodes+1):\n",
    "    # start a new episode\n",
    "    state = agent.reset_episode() \n",
    "    score = 0\n",
    "\n",
    "    episode_results = {\n",
    "        'time': [],\n",
    "        'x': [],\n",
    "        'y': [],\n",
    "        'z': [],\n",
    "        'phi': [],\n",
    "        'theta': [],\n",
    "        'psi': [],\n",
    "        'vx': [],\n",
    "        'vy': [],\n",
    "        'vz': [],\n",
    "        'reward': [],\n",
    "        }\n",
    "\n",
    "    while True:\n",
    "        action = agent.act(state)  \n",
    "        next_state, reward, done = task.step(action)\n",
    "\n",
    "        agent.step(action, reward, next_state, done)\n",
    "        state = next_state\n",
    "        score += reward\n",
    "        high_score = max(high_score, score)\n",
    "        low_score = min(low_score, score)\n",
    "\n",
    "        # track the results for offline analysis\n",
    "        episode_results['time'].append(task.sim.time)\n",
    "        episode_results['x'].append(state[0])\n",
    "        episode_results['y'].append(state[1])\n",
    "        episode_results['z'].append(state[2])\n",
    "        episode_results['phi'].append(state[3])\n",
    "        episode_results['theta'].append(state[4])\n",
    "        episode_results['psi'].append(state[5])\n",
    "        episode_results['vx'].append(state[6])\n",
    "        episode_results['vy'].append(state[7])\n",
    "        episode_results['vz'].append(state[8])\n",
    "        episode_results['reward'].append(reward)\n",
    "        \n",
    "        if done:\n",
    "            print(\"\\rEpisode = {:4d}, score = {:7.3f}, low score = {:7.3f}, high score = {:7.3f}\".format(i_episode, score, low_score, high_score), end=\"\")\n",
    "            training_results['score'].append(score)\n",
    "            break\n",
    "\n",
    "    resultsAll.append(episode_results)\n",
    "\n",
    "    sys.stdout.flush()\n",
    "\n",
    "# save results for later analysis\n",
    "with open(\"{}results0.bin\".format(exportPath), 'wb') as pickleFile:\n",
    "    pickle.dump(resultsAll, pickleFile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Plot the Rewards\n",
    "\n",
    "Once you are satisfied with your performance, plot the episode rewards, either from a single run, or averaged over multiple runs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## plot rewards over all episodes\n",
    "import pandas as pd\n",
    "\n",
    "plt.plot(training_results['score'], label='reward')\n",
    "plt.legend()\n",
    "_ = plt.ylim()\n",
    "\n",
    "df = pd.DataFrame(training_results['score'])\n",
    "p1 = df.rolling(window=25).mean().plot(legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Render top result\n",
    "with open('data/results0.bin', 'rb') as pickleFile:\n",
    "    results = pickle.load(pickleFile)\n",
    "\n",
    "# Sort wrt episode reward\n",
    "episodeRewards = [np.sum(r['reward']) for r in results]\n",
    "resultIndices = np.argsort(episodeRewards)\n",
    "\n",
    "# Get top results\n",
    "resultIndices = list(reversed(resultIndices))[0:1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot reward for top result\n",
    "for iE, e in enumerate(resultIndices):\n",
    "    res = results[e]\n",
    "    \n",
    "    # plot reward\n",
    "    plt.plot(res['time'], res['reward'], label='reward')\n",
    "    plt.legend()\n",
    "    _ = plt.ylim()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot position for top result\n",
    "for iE, e in enumerate(resultIndices):\n",
    "    res = results[e]   \n",
    "    \n",
    "    plt.plot(res['time'], res['x'], label='x')\n",
    "    plt.plot(res['time'], res['y'], label='y')\n",
    "    plt.plot(res['time'], res['z'], label='z')\n",
    "    plt.legend()\n",
    "    _ = plt.ylim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot angular velocity for top result\n",
    "for iE, e in enumerate(resultIndices):\n",
    "    res = results[e]   \n",
    "    \n",
    "    plt.plot(res['time'], res['phi'], label='phi')\n",
    "    plt.plot(res['time'], res['theta'], label='theta')\n",
    "    plt.plot(res['time'], res['psi'], label='psi')\n",
    "    plt.legend()\n",
    "    _ = plt.ylim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot velocity for top result\n",
    "for iE, e in enumerate(resultIndices):\n",
    "    res = results[e]   \n",
    "    \n",
    "    plt.plot(res['time'], res['vx'], label='vx')\n",
    "    plt.plot(res['time'], res['vy'], label='vy')\n",
    "    plt.plot(res['time'], res['vz'], label='vz')\n",
    "    plt.legend()\n",
    "    _ = plt.ylim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Generate visualisation\n",
    "from visualise import Quadrotor\n",
    "from IPython.display import Image\n",
    "import os\n",
    "import imageio\n",
    "\n",
    "exportPath = './video/'\n",
    "if not os.path.exists(exportPath):\n",
    "    os.makedirs(exportPath)\n",
    "        \n",
    "images = []\n",
    "\n",
    "for iE, e in enumerate(resultIndices):\n",
    "    res = results[e] \n",
    "   \n",
    "    filepath = \"{}frame{:10}_{:10}.png\".format(exportPath, iE, 0)\n",
    "    \n",
    "    q = Quadrotor(x=res['x'][0], \n",
    "            y=res['y'][0], \n",
    "            z=res['z'][0], \n",
    "            roll=res['phi'][0],\n",
    "            pitch=res['theta'][0], \n",
    "            yaw=res['psi'][0],\n",
    "            reward=res['reward'][0], \n",
    "            title=None,\n",
    "            filepath=filepath)\n",
    "    \n",
    "    q.set_target(0.0, 0.0, 10.0)\n",
    "    \n",
    "    # Render all frames in this episode\n",
    "    for i in range(1, len(res['x'])):\n",
    "        filepath = \"{}frame{:10}_{:10}.png\".format(exportPath, iE, i)\n",
    "        \n",
    "        q.update_pose(x=res['x'][i], \n",
    "        y=res['y'][i], \n",
    "        z=res['z'][i], \n",
    "        roll=res['phi'][i],\n",
    "        pitch=res['theta'][i], \n",
    "        yaw=res['psi'][i],\n",
    "        reward=res['reward'][i],\n",
    "        title=None,\n",
    "        filepath=filepath)\n",
    "        \n",
    "        images.append(imageio.imread(filepath))\n",
    "        \n",
    "    q.close()   \n",
    "    \n",
    "# Save all frames to animated gif\n",
    "imageio.mimsave(\"movie.gif\", images)\n",
    "\n",
    "# Render animated gif\n",
    "with open('./movie.gif','rb') as f:\n",
    "    display(Image(data=f.read(), format='png'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Task\n",
    "The task specified was to take off from (0, 0, 1) and fly to a point (0, 0, 10) and loiter. The reward function consisted of the following:\n",
    "\n",
    "- penalty based on distance$^2$ from target to encourage the quadcopter to fly toward target\n",
    "- penalty based on angular deviation to encourage the quadcopter to remain upright\n",
    "\n",
    "The following parameters were experimented with but not used in the final reward function:\n",
    "\n",
    "- reward for time to encourage quadcopter to remain in the air\n",
    "- penalty based on movement in the xy plane to encourage the quadcopter to fly vertically\n",
    "- penalty for high velocity to encourage quadcopter to fly slower\n",
    "- reward for quadcopter remaining close to target to encourage loitering\n",
    "\n",
    "The final reward function was equivalent to the following:\n",
    "``` python\n",
    "dist_from_target_squared = np.square(self.sim.pose[:3] - self.target_pos).sum()\n",
    "angular_deviation = np.sqrt(np.square(self.sim.pose[3:]).sum())\n",
    "reward = 1.0 - (0.004 * dist_from_target_squared + 0.008 * angular_deviation)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The algorithm used for learning was Deep Deterministic Policy Gradients (DDPG) as described in the [Continuous control with deep reinforcement learning](https://arxiv.org/abs/1509.02971) paper. The choice was based on the requirement to support learning in a continuous action space.\n",
    "\n",
    "The implementation was based on source code provided in the project classroom but modified to use the neural network architecture defined in the original paper. The state space was also extended to include velocity in addition to pose. \n",
    "\n",
    "After many iterations of parameter tuning without any significant progress I switched from a tanh activation to a sigmoid activation in the final layer of the actor network which immediately boosted the networks ability to learn.\n",
    "\n",
    "In general the agent learned to take and fly to the target but become unstable when loitering for any length of time. Small changes to the weights used in the reward function would have large impacts on the agents ability to fly the task.\n",
    "\n",
    "### Hyperparameters*\n",
    "Initial hyperparameters based on the [Continuous control with deep reinforcement learning](https://arxiv.org/abs/1509.02971) paper. The primary difference was the use of a sigmoid activation in final layer of the actor network rather than tanh.\n",
    "\n",
    "- Actor learning rate = 0.0001 \n",
    "- Critic learning rate = 0.001 \n",
    "- Discount factor $\\gamma$ = 0.99\n",
    "- Soft targets $\\tau$ = 0.001\n",
    "- Minibatch size = 64\n",
    "- Replay buffer size = 1000000\n",
    "- Exploration Noise Process = Ornstein-Uhlenbeck ($\\theta$ = 0.15, $\\alpha$ = 0.2)\n",
    "\n",
    "### Actor Neural Network Architecture*\n",
    "\n",
    "The actor architecture used two hidden layers of 400 and 300 respectively both with weight regularization and relu activation. Batch normalisation was also used after each hidden layer.\n",
    "\n",
    "The final output layer used a sigmoid activation with weights initialised to Uniform $[-3e-3, 3e-3]$. The output was then scaled to the action dimension $[0-1]$\n",
    "\n",
    "### Critic Neural Network Architecture*\n",
    "\n",
    "The critic architecture used two hidden layers of 400 and 300 respectively both with l2 weight regularization and relu activation. Batch normalisation was also used after each hidden layer.\n",
    "\n",
    "The action tensor was combined in the 2nd hidden layer using a relu activation.\n",
    "\n",
    "The final output layer connected to one output representing Q values with weights initialised to Uniform $[-3e-3, 3e-3]$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Some of the attempts to improve the learning included:\n",
    "- Disbaling l2 weight regularization in both actor and critic networks\n",
    "- Disabling random weights initialization in actor final output layer\n",
    "- The use of sigmoid vs tanh activation functions\n",
    "- Increasing actor learnign rate by factor 10\n",
    "- Increasing critic learning rate by factor 10\n",
    "- Increasing number of episodes - 500, 1000, 1500, 2000\n",
    "- Increasing penalties by factor 10\n",
    "- Decreasing penalties by factor 10\n",
    "- Increased exploration noise volatility $\\sigma$ from 0.2 to 0.3\n",
    "- Clamping reward to $[-1,1]$\n",
    "- Clamping reward to $[-1,1]$ using tanh\n",
    "- Using a non-linear funciton for reward such as distance$^2$ and angular_deviation$^2$\n",
    "- Simplifying the reward function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"Mean rewards over the last 10 episodes: {}\".format(np.sum(training_results['score'][-10:])/10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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