Quadcopter_Project.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#################################### INNER ##########################################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project: Train a Quadcopter How to Fly\n",
    "\n",
    "Design an agent to fly a quadcopter, and then train it using a reinforcement learning algorithm of your choice! \n",
    "\n",
    "Try to apply the techniques you have learnt, but also feel free to come up with innovative ideas and test them."
   ]
  },
  {
   "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.\n",
    "- `physics_sim.py`: This file contains the simulator for the quadcopter.  **DO NOT MODIFY THIS FILE**.\n",
    "\n",
    "For this project, you will define your own task in `task.py`.  Although we have provided a example task to get you started, you are encouraged to change it.  Later in this notebook, you will learn more about how to amend this file.\n",
    "\n",
    "You will also design a reinforcement learning agent in `agent.py` to complete your chosen task.  \n",
    "\n",
    "You are welcome to create any additional files to help you to organize your code.  For instance, you may find it useful to define a `model.py` file defining any needed neural network architectures.\n",
    "\n",
    "## Controlling the Quadcopter\n",
    "\n",
    "We provide a sample agent in the code cell below to show you how to use the sim to control the quadcopter.  This agent is even simpler than the sample agent that you'll examine (in `agents/policy_search.py`) later in this notebook!\n",
    "\n",
    "The agent controls the quadcopter by setting the revolutions per second on each of its four rotors.  The provided agent in the `Basic_Agent` class below always selects a random action for each of the four rotors.  These four speeds are returned by the `act` method as a list of four floating-point numbers.  \n",
    "\n",
    "For this project, the agent that you will implement in `agents/agent.py` will have a far more intelligent method for selecting actions!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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 quadcopter.  \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 quadcopter.\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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import csv\n",
    "import numpy as np\n",
    "from 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 quadcopter evolved during the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b2d6260b8>"
      ]
     },
     "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 quadcopter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b0ba42a90>"
      ]
     },
     "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 quadcopter over the $x$-, $y$-, and $z$-axes),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b0b987518>"
      ]
     },
     "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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b0b9afa58>"
      ]
     },
     "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b0b9015f8>"
      ]
     },
     "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 quadcopter in ($x,y,z$) dimensions and the Euler angles),\n",
    "- `task.sim.v` (the velocity of the quadcopter 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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-10.01134058   7.1778992   28.76713621   0.34880739   0.14165406   0.        ]\n",
      "[-4.99241764  5.52643069  4.97855226]\n",
      "[ 0.09422102  0.05445362  0.        ]\n"
     ]
    }
   ],
   "source": [
    "# the pose, velocity, and angular velocity of the quadcopter 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": [
    "In the sample task in `task.py`, we use the 6-dimensional pose of the quadcopter to construct the state of the environment at each timestep.  However, when amending the task for your purposes, you are welcome to expand the size of the state vector by including the velocity information.  You can use any combination of the pose, velocity, and angular velocity - feel free to tinker here, and construct the state to suit your task.\n",
    "\n",
    "## The Task\n",
    "\n",
    "A sample task has been provided for you in `task.py`.  Open this file in a new window now. \n",
    "\n",
    "The `__init__()` method is used to initialize several variables that are needed to specify the task.  \n",
    "- The simulator is initialized as an instance of the `PhysicsSim` class (from `physics_sim.py`).  \n",
    "- Inspired by the methodology in the original DDPG paper, we make use of action repeats.  For each timestep of the agent, we step the simulation `action_repeats` timesteps.  If you are not familiar with action repeats, please read the **Results** section in [the DDPG paper](https://arxiv.org/abs/1509.02971).\n",
    "- We set the number of elements in the state vector.  For the sample task, we only work with the 6-dimensional pose information.  To set the size of the state (`state_size`), we must take action repeats into account.  \n",
    "- The environment will always have a 4-dimensional action space, with one entry for each rotor (`action_size=4`). You can set the minimum (`action_low`) and maximum (`action_high`) values of each entry here.\n",
    "- The sample task in this provided file is for the agent to reach a target position.  We specify that target position as a variable.\n",
    "\n",
    "The `reset()` method resets the simulator.  The agent should call this method every time the episode ends.  You can see an example of this in the code cell below.\n",
    "\n",
    "The `step()` method is perhaps the most important.  It accepts the agent's choice of action `rotor_speeds`, which is used to prepare the next state to pass on to the agent.  Then, the reward is computed from `get_reward()`.  The episode is considered done if the time limit has been exceeded, or the quadcopter has travelled outside of the bounds of the simulation.\n",
    "\n",
    "In the next section, you will learn how to test the performance of an agent on this task."
   ]
  },
  {
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode = 1000, score =   6.841 (best =   6.842), noise_scale = 3.25"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import pandas as pd\n",
    "from agents.policy_search import PolicySearch_Agent\n",
    "from task import Task\n",
    "\n",
    "num_episodes = 1000\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 quadcopter 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": 98,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The reward after episode 1 is 69.96895697122554\n",
      "The reward after episode 2 is 69.95700221605976\n",
      "The reward after episode 3 is 69.9813194232695\n",
      "The reward after episode 4 is 67.46519194217144\n",
      "The reward after episode 5 is 75.72128603671446\n",
      "The reward after episode 6 is 64.32825976957169\n",
      "The reward after episode 7 is 55.941703344294595\n",
      "The reward after episode 8 is 69.92809289637646\n",
      "The reward after episode 9 is 69.67783466116215\n",
      "The reward after episode 10 is 72.99737496132417\n",
      "The reward after episode 11 is 73.09626772302494\n",
      "The reward after episode 12 is 75.79390968298209\n",
      "The reward after episode 13 is 78.78299597178167\n",
      "The reward after episode 14 is 77.6761308099427\n",
      "The reward after episode 15 is 75.38332222614792\n",
      "The reward after episode 16 is 96.37392772193598\n",
      "The reward after episode 17 is 72.36764254854023\n",
      "The reward after episode 18 is 72.45151266873711\n",
      "The reward after episode 19 is 64.06137953924194\n",
      "The reward after episode 20 is 77.85576720711528\n",
      "The reward after episode 21 is 66.52988318400945\n",
      "The reward after episode 22 is 71.60886877094721\n",
      "The reward after episode 23 is 71.96880845295242\n",
      "The reward after episode 24 is 82.633680331245\n",
      "The reward after episode 25 is 103.69688886229598\n",
      "The reward after episode 26 is 86.79866094211184\n",
      "The reward after episode 27 is 80.30504236411643\n",
      "The reward after episode 28 is 84.07832539215997\n",
      "The reward after episode 29 is 78.35457262668645\n",
      "The reward after episode 30 is 72.69854258308186\n",
      "The reward after episode 31 is 81.02549304509552\n",
      "The reward after episode 32 is 81.47147229766314\n",
      "The reward after episode 33 is 75.42330359350868\n",
      "The reward after episode 34 is 81.06203269325381\n",
      "The reward after episode 35 is 80.95814318767827\n",
      "The reward after episode 36 is 75.71614359710136\n",
      "The reward after episode 37 is 77.7676775015751\n",
      "The reward after episode 38 is 63.99815098197411\n",
      "The reward after episode 39 is 80.73242917044232\n",
      "The reward after episode 40 is 81.59451229080932\n",
      "The reward after episode 41 is 84.07810603051344\n",
      "The reward after episode 42 is 75.1704475853767\n",
      "The reward after episode 43 is 75.64777518634034\n",
      "The reward after episode 44 is 80.31811390182743\n",
      "The reward after episode 45 is 74.65857618066612\n",
      "The reward after episode 46 is 78.6642776685408\n",
      "The reward after episode 47 is 83.50097666635814\n",
      "The reward after episode 48 is 77.08583195719766\n",
      "The reward after episode 49 is 75.12421233415687\n",
      "The reward after episode 50 is 77.6211836750431\n",
      "The reward after episode 51 is 80.61289341567831\n",
      "The reward after episode 52 is 84.16614309853884\n",
      "The reward after episode 53 is 77.26826647298651\n",
      "The reward after episode 54 is 75.3010355846752\n",
      "The reward after episode 55 is 81.74439081435065\n",
      "The reward after episode 56 is 230.14376493704376\n",
      "The reward after episode 57 is 73.09649264061441\n",
      "The reward after episode 58 is 73.35734964098594\n",
      "The reward after episode 59 is 87.30016513630966\n",
      "The reward after episode 60 is 69.8466015751203\n",
      "The reward after episode 61 is 134.16793563061003\n",
      "The reward after episode 62 is 80.67673198251441\n",
      "The reward after episode 63 is 78.44654413348147\n",
      "The reward after episode 64 is 46.86084092098986\n",
      "The reward after episode 65 is 64.40909387961824\n",
      "The reward after episode 66 is 101.31171116189768\n",
      "The reward after episode 67 is 91.68342094351328\n",
      "The reward after episode 68 is 152.27747084078075\n",
      "The reward after episode 69 is 157.22617846231373\n",
      "The reward after episode 70 is 78.6106595729662\n",
      "The reward after episode 71 is 66.78354563380992\n",
      "The reward after episode 72 is 66.7390987329216\n",
      "The reward after episode 73 is 80.97647950164183\n",
      "The reward after episode 74 is 120.97047669025861\n",
      "The reward after episode 75 is 55.623412416130364\n",
      "The reward after episode 76 is 147.93056677806078\n",
      "The reward after episode 77 is 254.2656601680329\n",
      "The reward after episode 78 is 61.597109678768504\n",
      "The reward after episode 79 is 62.51879588261281\n",
      "The reward after episode 80 is 251.11480832493535\n",
      "The reward after episode 81 is 133.85157792883206\n",
      "The reward after episode 82 is 460.1698507983811\n",
      "The reward after episode 83 is 67.40692809965766\n",
      "The reward after episode 84 is 41.33642554961531\n",
      "The reward after episode 85 is 52.17382956866629\n",
      "The reward after episode 86 is 70.68456133932749\n",
      "The reward after episode 87 is 142.99916856055972\n",
      "The reward after episode 88 is 143.01343661685155\n",
      "The reward after episode 89 is 143.01077281077184\n",
      "The reward after episode 90 is 143.01276090893126\n",
      "The reward after episode 91 is 143.00758026762165\n",
      "The reward after episode 92 is 143.00988543440798\n",
      "The reward after episode 93 is 143.01058995518164\n",
      "The reward after episode 94 is 143.01316179269978\n",
      "The reward after episode 95 is 143.00880999172136\n",
      "The reward after episode 96 is 143.01209300005297\n",
      "The reward after episode 97 is 143.0108381066019\n",
      "The reward after episode 98 is 143.00780789569512\n",
      "The reward after episode 99 is 143.0103388284691\n",
      "The reward after episode 100 is 143.00843742304602\n",
      "The reward after episode 101 is 143.01405015418\n",
      "The reward after episode 102 is 143.01205520581019\n",
      "The reward after episode 103 is 143.00972408352436\n",
      "The reward after episode 104 is 143.01121018425908\n",
      "The reward after episode 105 is 143.0108587957593\n",
      "The reward after episode 106 is 143.0133760551708\n",
      "The reward after episode 107 is 143.01049463321536\n",
      "The reward after episode 108 is 143.00821667001364\n",
      "The reward after episode 109 is 143.0096128129086\n",
      "The reward after episode 110 is 143.01310768236516\n",
      "The reward after episode 111 is 143.01297193016293\n",
      "The reward after episode 112 is 143.01137633481946\n",
      "The reward after episode 113 is 143.01413989582414\n",
      "The reward after episode 114 is 143.0111498914996\n",
      "The reward after episode 115 is 143.0128487947984\n",
      "The reward after episode 116 is 143.00857648597477\n",
      "The reward after episode 117 is 143.0079512390193\n",
      "The reward after episode 118 is 143.0123543401091\n",
      "The reward after episode 119 is 143.01264582580234\n",
      "The reward after episode 120 is 143.01223480363814\n",
      "The reward after episode 121 is 143.0140521134933\n",
      "The reward after episode 122 is 143.01304175516913\n",
      "The reward after episode 123 is 143.0110521737159\n",
      "The reward after episode 124 is 143.01060896799424\n",
      "The reward after episode 125 is 143.0077302670514\n",
      "The reward after episode 126 is 143.01245445802982\n",
      "The reward after episode 127 is 143.01339438752237\n",
      "The reward after episode 128 is 143.00862166228276\n",
      "The reward after episode 129 is 143.01023491474047\n",
      "The reward after episode 130 is 143.00997127358812\n",
      "The reward after episode 131 is 143.01189366750543\n",
      "The reward after episode 132 is 143.01130245632615\n",
      "The reward after episode 133 is 143.0091605273662\n",
      "The reward after episode 134 is 143.0099793254174\n",
      "The reward after episode 135 is 143.01221878569933\n",
      "The reward after episode 136 is 143.01205315565426\n",
      "The reward after episode 137 is 143.01287577728715\n",
      "The reward after episode 138 is 143.0118209108016\n",
      "The reward after episode 139 is 143.01128185331626\n",
      "The reward after episode 140 is 143.0115675646154\n",
      "The reward after episode 141 is 143.00988851878185\n",
      "The reward after episode 142 is 143.01240827483088\n",
      "The reward after episode 143 is 143.01129308084452\n",
      "The reward after episode 144 is 143.01305451663177\n",
      "The reward after episode 145 is 143.0091886315685\n",
      "The reward after episode 146 is 143.006248189902\n",
      "The reward after episode 147 is 143.01051690321992\n",
      "The reward after episode 148 is 143.009652298224\n",
      "The reward after episode 149 is 143.01182575420899\n",
      "The reward after episode 150 is 143.0119675871207\n",
      "The reward after episode 151 is 143.00960943862984\n",
      "The reward after episode 152 is 143.00975481670685\n",
      "The reward after episode 153 is 143.00977667078075\n",
      "The reward after episode 154 is 143.009656899531\n",
      "The reward after episode 155 is 143.00921566920647\n",
      "The reward after episode 156 is 143.0110103993219\n",
      "The reward after episode 157 is 143.01242535882483\n",
      "The reward after episode 158 is 143.00979259865844\n",
      "The reward after episode 159 is 143.01115119743014\n",
      "The reward after episode 160 is 143.0104400516493\n",
      "The reward after episode 161 is 143.01068822577227\n",
      "The reward after episode 162 is 143.0115227413082\n",
      "The reward after episode 163 is 143.01134924116434\n",
      "The reward after episode 164 is 143.01383081439315\n",
      "The reward after episode 165 is 143.01150541334977\n",
      "The reward after episode 166 is 143.0097152819678\n",
      "The reward after episode 167 is 143.01020827188836\n",
      "The reward after episode 168 is 143.01086322749546\n",
      "The reward after episode 169 is 143.01129214466928\n",
      "The reward after episode 170 is 143.01332600037532\n",
      "The reward after episode 171 is 143.009757323749\n",
      "The reward after episode 172 is 143.010726843059\n",
      "The reward after episode 173 is 143.01180453890527\n",
      "The reward after episode 174 is 143.01182668887765\n",
      "The reward after episode 175 is 143.01223956110667\n",
      "The reward after episode 176 is 143.00727515482674\n",
      "The reward after episode 177 is 143.0124399974604\n",
      "The reward after episode 178 is 143.0129277056084\n",
      "The reward after episode 179 is 143.01191232953735\n",
      "The reward after episode 180 is 143.01273723121204\n",
      "The reward after episode 181 is 143.00718721516122\n",
      "The reward after episode 182 is 143.0138613900367\n",
      "The reward after episode 183 is 143.01048832581017\n",
      "The reward after episode 184 is 143.0117858835863\n",
      "The reward after episode 185 is 143.0128043188214\n",
      "The reward after episode 186 is 143.01033709230552\n",
      "The reward after episode 187 is 143.0105782788803\n",
      "The reward after episode 188 is 143.00878155081082\n",
      "The reward after episode 189 is 143.0127336740077\n",
      "The reward after episode 190 is 143.01369224856242\n",
      "The reward after episode 191 is 143.0068738628444\n",
      "The reward after episode 192 is 143.01224970379124\n",
      "The reward after episode 193 is 143.01356945369525\n",
      "The reward after episode 194 is 143.01256964052246\n",
      "The reward after episode 195 is 143.01046108638403\n",
      "The reward after episode 196 is 143.01257309992963\n",
      "The reward after episode 197 is 143.01331288984088\n",
      "The reward after episode 198 is 143.0111901018429\n",
      "The reward after episode 199 is 143.01465141995726\n",
      "The reward after episode 200 is 143.0083109590007\n"
     ]
    }
   ],
   "source": [
    "## TODO: Train your agent here.\n",
    "import sys\n",
    "import pandas as pd\n",
    "from agents.ddpg import DDPG_agent\n",
    "from task import Task\n",
    "\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",
    "\n",
    "num_episodes = 200\n",
    "target_pos = np.array([0., 0., 20.])\n",
    "task = Task(init_pose, init_velocities, init_angle_velocities, runtime, target_pos)\n",
    "agent = DDPG_agent(task)\n",
    "\n",
    "scores = [] # keeps final score of each episode\n",
    "for i_episode in range(1, num_episodes+1):\n",
    "    state = agent.reset_episode() # start a new episode\n",
    "    score = 0 # initialize episode score to 0\n",
    "    while True:\n",
    "        action = agent.act(state) \n",
    "        next_state, reward, done = task.step(action)\n",
    "        agent.step(action, reward, next_state, done)\n",
    "        state = next_state\n",
    "        score += reward # accumulate reward\n",
    "        if done:\n",
    "            print(\"The reward after episode {} is {}\".format(i_episode, score))\n",
    "            scores.append(score) # append final episode score\n",
    "            break;\n",
    "    sys.stdout.flush()"
   ]
  },
  {
   "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": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9ac8621898>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9ac859e0f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## TODO: Plot the rewards.\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(list(zip(1+np.arange(len(scores)), scores)), columns=['i_episode', 'score'])\n",
    "ax = df.plot.scatter(x='i_episode', y='score', label='Reward/Episode')\n",
    "rolling = df['score'].rolling(10).mean()\n",
    "rolling.plot(color=[\"r\",\"b\"], ax=ax, label='Rolling mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check Performance\n",
    "\n",
    "Monitor change in position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The final reward is 143.00687509380532\n"
     ]
    }
   ],
   "source": [
    "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",
    "file_output = 'testdata.txt'\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",
    "    state = agent.reset_episode() # start a new episode\n",
    "    score = 0 # initialize episode score to 0\n",
    "    while True:\n",
    "        action = agent.act(state) # rotor speeds\n",
    "        next_state, reward, done = task.step(action)\n",
    "        to_write = [task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(action)\n",
    "        for ii in range(len(labels)):\n",
    "            results[labels[ii]].append(to_write[ii])\n",
    "        writer.writerow(to_write)\n",
    "        agent.step(action, reward, next_state, done)\n",
    "        state = next_state\n",
    "        score += reward # accumulate reward\n",
    "        if done:\n",
    "            print(\"The final reward is {}\".format(score))\n",
    "            scores.append(score) # append final episode score\n",
    "            break;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9acb9ee978>"
      ]
     },
     "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 agent learns to reach the target height of 20 pretty fast (a little bit after the 0.8 time mark)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9acad1a1d0>"
      ]
     },
     "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": {
    "collapsed": true
   },
   "source": [
    "## Reflections\n",
    "\n",
    "**Question 1**: Describe the task that you specified in `task.py`.  How did you design the reward function?\n",
    "\n",
    "**Answer**: The task I specified is the takeoff task. The agent is required to take off from its initial height of 10 and reach a height of 20.\n",
    "\n",
    "I tried many reward functions. All of them penalize the agent for being away from the target position and reward it for flying. The reward function trials are summarized below:\n",
    "1. I used the Euclidean distance measure in the penalty, scaled by a factor in the interval [0.2, 1]. I tried scaling it by a factor of 0.2, but it slowed down the learning process, so I increased this factor in order to increase the penalty and drive the agent to learn faster. I also tried adding a constant reward of 10 to reward not crashing. However, the unbounded reward caused learning to be slow and unexpected.\n",
    "2. I also tried using the suggested reward function, which does a similar thing of rewarding flying and penalizing being away from the target position.\n",
    "2. To improve performance, I tried adding a tanh function to limit the output to [-1, 1].\n",
    "3. I also tried penalizing the agent when it crashes or runs out of time\n",
    "4. I tried addring a reward directly proportional to positive vertical speed in order to encourage the takeoff task.\n",
    "\n",
    "Some of those factors improved performance. The final reward function reached is as follows:\n",
    "1. The suggested reward function without normalization.\n",
    "2. Penalizing the agent if it runs out of time or crashes.\n",
    "3. Rewarding positive z velocity to encourage the takeoff task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2**: Discuss your agent briefly, using the following questions as a guide:\n",
    "\n",
    "- What learning algorithm(s) did you try? What worked best for you?\n",
    "- What was your final choice of hyperparameters (such as $\\alpha$, $\\gamma$, $\\epsilon$, etc.)?\n",
    "- What neural network architecture did you use (if any)? Specify layers, sizes, activation functions, etc.\n",
    "\n",
    "**Answer**:\n",
    "\n",
    "* I used the suggested DDPG.\n",
    "* $\\gamma$ = 0.99, $\\tau$ = 0.01, exploration $\\mu$ = 0.1, exploration $\\theta$ = 0.15, exploration $\\sigma$ = 0.2\n",
    "* I have made several attempts, summarized below:\n",
    "    1. I used the suggested NN architectures, which are as follows:\n",
    "        - Actor: 3 hidden layers with ReLU activation, output layer with sigmoid\n",
    "        - Critic: 2 ReLU-activated layers for each of the state and action pathways\n",
    "    2. I tried increasing the number of hidden nodes in each layer to be 300-400, but it only slowed the training process and did not improve performance.\n",
    "    3. As suggested in the project review, I tried several methods to tackle numerical instability. First, I tried using L2 regularization and tweaking its kernel parameter, but performance was still unpredictable.\n",
    "    4. It seemed that the model was sensitive to initialization as the performance would vary greatly each time I run it. To address this, I used batch normalization after every layer in order to reduce model sensitivity to initial weights.\n",
    "    \n",
    "    In the end, the architecture I reached was as follows:\n",
    "        - Actor: 3 hidden layers with ReLU activation, output layer with sigmoid\n",
    "        - Critic: 2 ReLU-activated layers for each of the state and action pathways\n",
    "        - Batch normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3**: Using the episode rewards plot, discuss how the agent learned over time.\n",
    "\n",
    "- Was it an easy task to learn or hard?\n",
    "- Was there a gradual learning curve, or an aha moment?\n",
    "- How good was the final performance of the agent? (e.g. mean rewards over the last 10 episodes)\n",
    "\n",
    "**Answer**:\n",
    "- Reaching those results was very hard, and it was quite difficult for the agent to learn to perform the task well. It took a lot of hours, trials, and tweaking to get the desired result.\n",
    "- There was a gradual learning curve over the episodes 50-100, after which the score pretty much saturated.\n",
    "- Mean rewards over the last 10 episodes = 143"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4**: Briefly summarize your experience working on this project. You can use the following prompts for ideas.\n",
    "\n",
    "- What was the hardest part of the project? (e.g. getting started, plotting, specifying the task, etc.)\n",
    "- Did you find anything interesting in how the quadcopter or your agent behaved?\n",
    "\n",
    "**Answer**:\n",
    "- There is no doubt that this project was the most challenging of all 5 projects I did for the DLND. The hardest part of it was getting started. There are many design options and decisions that were left open to experimentation, so I spent a lot of time trying out combinations of different things (tasks, reward functions, and learning algorithms). However, I feel that it all paid off in the end because the project tied together the dense and rich RL material that I have been studying over the past couple of weeks.\n",
    "- I find it very interesting that the agent learned to minimize its motion in the x and y dimensions without me explicitly penalizing it for that."
   ]
  }
 ],
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