Quadcopter_Project.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ERnzSfFRwiM9"
   },
   "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": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 122
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 24511,
     "status": "ok",
     "timestamp": 1559929123585,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "BrUYuaKjwiM_",
    "outputId": "e11112d3-3ee8-4ee5-8652-e8afce213e24"
   },
   "outputs": [],
   "source": [
    "# Run this cell to mount Google Drive for Colab\n",
    "from google.colab import drive\n",
    "drive.mount('/content/drive/')\n",
    "# !ls \"/content/drive/My Drive/\"http://localhost:8888/notebooks/Quadcopter_Project.ipynb#\n",
    "\n",
    "import os\n",
    "os.chdir('/content/drive/My Drive/Colab Notebooks/RL-Quadcopter-2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 17
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3693,
     "status": "ok",
     "timestamp": 1559929130398,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "i4r8SCbJwiND",
    "outputId": "a7553de1-3f3b-4e24-e509-a69c2bec5174"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import visuals\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RRts6qeKwiNO"
   },
   "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": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MyfPLH00wiNP"
   },
   "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": {
    "colab_type": "text",
    "id": "jcNzhKdCwiNR"
   },
   "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": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "QEZ1DyL5wiNS",
    "outputId": "562b50c2-4965-4a7d-ca1e-49b5892f876b"
   },
   "outputs": [
    {
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       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
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       "        require(['plotly'], function(Plotly) {\n",
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       "        "
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     "output_type": "display_data"
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   ],
   "source": [
    "import csv\n",
    "import numpy as np\n",
    "from tasks.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 = 'BasicAgent_History.csv'           # 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', newline='') 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": {
    "colab_type": "text",
    "id": "ksVIU32RwiNW"
   },
   "source": [
    "Run the code cell below to visualize how the **position** and **velocity** of the quadcopter evolved during the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0GkmmfZDBJ-0",
    "outputId": "ab1213eb-8c86-4ff3-e600-dc6d65ed0a39"
   },
   "outputs": [
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       "            paths: {\n",
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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visuals.plot_position(file_output, size=(10, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-soqpxTQwiNj"
   },
   "source": [
    "Next, you can plot the Euler angles (the rotation of the quadcopter over the $x$-, $y$-, and $z$-axes) and the velocities (in radians per second) corresponding to each of the Euler angles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "u53faKT3wiNj",
    "outputId": "132c3c26-050f-460b-e879-8ae2d4fc8861"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visuals.plot_euler_angle(file_output, size=(10, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5XVUHCy-wiNt"
   },
   "source": [
    "Finally, you can use the code cell below to print the agent's choice of actions.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "B51ouMxSBJ_M",
    "outputId": "d0d481d6-de37-4cfa-b340-4606fc2b9a23"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "        <script type=\"text/javascript\">\n",
       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
       "            }\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
       "        }\n",
       "        </script>\n",
       "        "
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visuals.plot_rotor_speed(file_output, size=(10, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "32eA2T7iwiN4"
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   "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": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YOs-IcmewiN7",
    "outputId": "86643af0-958c-4c33-e578-5914e9ce3189"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-6.9994045   2.66047426 28.34535746  0.03419123  0.40229795  0.        ]\n",
      "[-5.52156787  2.0542151   4.98641309]\n",
      "[-0.05555936  0.20116559  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": {
    "colab_type": "text",
    "id": "piJP8bfrwiOC"
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   "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": {
    "colab_type": "text",
    "id": "avr6uB1TwiOE"
   },
   "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": 0,
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    "colab": {},
    "colab_type": "code",
    "id": "urzkiV73wiOE",
    "outputId": "d3a43321-21f9-4a8d-b443-527ca2626884"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode = 1000, score =  -3.028 (best =   0.469), noise_scale = 3.25"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from agents.policy_search import PolicySearch_Agent\n",
    "from tasks.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()"
   ]
  },
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   "execution_count": 0,
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    "id": "G4H_ic8pwiOT",
    "outputId": "d0e584df-be18-4b38-d447-77b6de4fad3f"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score =  -3.028, noise_scale = 3.2\n"
     ]
    }
   ],
   "source": [
    "import csv\n",
    "\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",
    "          'reward']\n",
    "\n",
    "file_history = 'PolicySearch_Agent_History.csv'\n",
    "\n",
    "# Run the simulation, and save the results.\n",
    "state = agent.reset_episode()\n",
    "with open(file_history, 'w', newline='') as csvfile:\n",
    "    writer = csv.writer(csvfile)\n",
    "    writer.writerow(labels)\n",
    "    writer.writerow([task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(action) + [reward])\n",
    "    while True:\n",
    "        action = agent.act(state) \n",
    "        next_state, reward, done = task.step(action)\n",
    "        writer.writerow([task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(action) + [reward])\n",
    "        state = next_state\n",
    "        if done:\n",
    "            print(\"score = {:7.3f}, noise_scale = {}\".format(agent.score, agent.noise_scale))\n",
    "            break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xCAIyaAjBJ_n"
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   "source": [
    "### 3D Trajectory for Policy Search Agent\n",
    "\n",
    "* <font color='blue'>Blue mark</font> represnets the start point\n",
    "* <font color='red'>Red mark</font> represnets the end point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"imgs/PolicySearch_Agent_History.png\" target=\"_blank\"><img src=\"imgs/PolicySearch_Agent_History.png\" alt=\"PolicySearch 3D Trajectory\" title=\"PolicySearch 3D Trajectory\"></a>"
   ]
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    "visuals.plot_trajectory_3d('PolicySearch_Agent_History.csv', 'PolicySearch Trajectory', filename='PolicySearch Trajectory',\n",
    "                           width=700, height=700, axis_ranges=([-5,5], [-5,5], [0,11]))"
   ]
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   "cell_type": "markdown",
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   "source": [
    "This agent should perform very poorly on this task.  And that's where you come in!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "SfPxA6AiwiOn"
   },
   "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": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zaiQxBUjBKAD"
   },
   "source": [
    "## Vertical Takeoff Task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
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   "source": [
    "## TODO: Train your agent here.\n",
    "import sys\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from agents.ddpg import DDPG\n",
    "from tasks.vtakeoff_task import VerticalTakeoffTask\n",
    "\n",
    "runtime = 5.                                     # time limit of the episode\n",
    "init_pos = np.array([2., 3., 0., 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",
    "task = VerticalTakeoffTask(init_pos, init_velocities, init_angle_velocities, runtime)\n",
    "agent = DDPG(task, batch_size=64)\n",
    "best_total_reward = -np.inf\n",
    "rewards_list = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 123,
     "status": "ok",
     "timestamp": 1559934064553,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "52YHRbfdwiOv",
    "outputId": "94f9b4f5-df50-497f-be2b-dc62f410e608"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode=1000, TotalReward=250.333 (Best=250.333), x=-0.889, y=-1.522, z=127.465, time=5.02"
     ]
    }
   ],
   "source": [
    "num_episodes = 1000\n",
    "episode_num_start = 1\n",
    "\n",
    "for i_episode in range(episode_num_start, episode_num_start+num_episodes):\n",
    "    total_reward = 0\n",
    "    state = agent.reset_episode() # start a new episode\n",
    "    while True:\n",
    "        action = agent.act(state)\n",
    "        # Take action, get new state and reward\n",
    "        next_state, reward, done = task.step(action)\n",
    "        total_reward += reward\n",
    "        agent.step(action, reward, next_state, done)\n",
    "        state = next_state\n",
    "        if done:\n",
    "            rewards_list.append((i_episode, total_reward))\n",
    "            \n",
    "            if total_reward > best_total_reward:\n",
    "                best_total_reward = total_reward\n",
    "            \n",
    "            print(\"\\rEpisode={:4d}, TotalReward={:7.3f} (Best={:7.3f}), x={:5.3f}, y={:5.3f}, z={:5.3f}, time={:4.2f}\".format(\n",
    "                i_episode, total_reward, best_total_reward, task.sim.pose[0], task.sim.pose[1], task.sim.pose[2], task.sim.time), end='')\n",
    "            sys.stdout.flush()\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kBQFZHE3Ghmc"
   },
   "outputs": [],
   "source": [
    "# Save reward per episode to file\n",
    "import csv\n",
    "\n",
    "with open('VTakeoff_Training_Rewards.csv', 'w', newline='') as csvfile:\n",
    "    writer = csv.writer(csvfile)\n",
    "    writer.writerow(['Episode', 'Total Reward'])\n",
    "    writer.writerows(rewards_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "Vz4UeCkpwiO0"
   },
   "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": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 392
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1923,
     "status": "ok",
     "timestamp": 1559934134756,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "OuYix9ClwiO4",
    "outputId": "da2ef2a2-151e-4ac3-fdb7-261b08dd14e1"
   },
   "outputs": [
    {
     "data": {
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df/31Xq4GAAAAzQEhu4lqQja3VAcAAEANQnYTEbIBAABwOUK2SQjZAAAAqEHI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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visuals.plot_rewards(rewards_list, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HM0yr-FjwiPE"
   },
   "source": [
    "## Run Vertical Takeoff Simulations from Different Initial Positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3889,
     "status": "ok",
     "timestamp": 1559934285041,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "ehg2hj7mwiPE",
    "outputId": "f6f8c89d-ddd7-4b89-e981-3cd8e89c4197"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Reward=250.333, x=5.000, y=1.000, z=127.463\n",
      "Total Reward=250.333, x=10.000, y=10.000, z=127.463\n",
      "Total Reward=250.333, x=11.000, y=7.000, z=127.463\n"
     ]
    }
   ],
   "source": [
    "import csv\n",
    "\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",
    "          'reward']\n",
    "\n",
    "init_pos_list = [np.array([5., 1., 0., 0., 0., 0.]),\n",
    "                 np.array([10., 10., 0., 0., 0., 0.]),\n",
    "                 np.array([11., 7., 0., 0., 0., 0.])]\n",
    "\n",
    "for i in range(len(init_pos_list)):\n",
    "    task.sim.init_pose = init_pos_list[i]\n",
    "    file_history = \"DDPG_VTakeoff_History_{}.csv\".format(i)\n",
    "\n",
    "    # Run the simulation, and save the results.\n",
    "    state = agent.reset_episode()\n",
    "    with open(file_history, 'w', newline='') as csvfile:\n",
    "        writer = csv.writer(csvfile)\n",
    "        writer.writerow(labels)\n",
    "        writer.writerow([task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(action) + [reward])\n",
    "        total_reward = 0\n",
    "        while True:\n",
    "            action = agent.act(state, False)\n",
    "            next_state, reward, done = task.step(action)\n",
    "            total_reward += reward\n",
    "            writer.writerow([task.sim.time] + list(task.sim.pose) + list(task.sim.v) + list(task.sim.angular_v) + list(action) + [reward])\n",
    "            state = next_state\n",
    "            if done:\n",
    "                print(\"Total Reward={:7.3f}, x={:5.3f}, y={:5.3f}, z={:5.3f}\".format(\n",
    "                    total_reward, task.sim.pose[0], task.sim.pose[1], task.sim.pose[2]))\n",
    "                break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1521
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3033,
     "status": "ok",
     "timestamp": 1559934300786,
     "user": {
      "displayName": "Hsin-Wei Wang",
      "photoUrl": "",
      "userId": "13772944166444182143"
     },
     "user_tz": -480
    },
    "id": "ohaUzm53BKA4",
    "outputId": "b3fe6284-8c41-430f-a8dd-6466d2266d2b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NQkICCQkJtGqlBwCLSP2x2q1sOLGBcRvH8eev/oyrsytv3PYGG8ZvYGyHsTg7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\nAAAADoRyBgAA4ED+D4FoEg0VSZtPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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L1aNHD3Xv3l2RkZGaPHmyuyPh/6uqqtJvfvMbJSQkuDsKJAUGBqpr166KioqS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\nMIoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GUdMbkpKSCAgIYPTo0QBkZGRw/vx5li1bZkqBnhAdHe1aTOEVpw/xf0Puw//m\nlgzMrHmYWURERKQmtc0tNW72C7BgwQJef/11V89YbGwsqamp11/hT4nhxE+b/YqIiIiJ3Ia4xo0b\n8+STT5KYmEj37t3NqMn3VA2nKsSJiIiISdzOiXv//fex2Wzcd999AOTl5fHAAw94vTCf4nRos18R\nERExldsQ99JLL5GTk0PLli0BsNlsHDx40OuF+RT1xImIiIjJ3Ia4Bg0a0KJFiyt+ZlGP05UubzFi\nsXj1FDMRERERF7epIyQkhKVLl+JwONi/fz+//e1vueuuu8yozXdUndignjgRERExidsQ99prr/HF\nF1/QqFEjHn74YVq0aMGrr75qRm2+Q3PiRERExGRuV6c2bdqUv/zlL7zwwgs0bdrUjJp8j4ZTRURE\nxGRuU8fmzZvp2bMnPXr0AGDnzp2MHz/e64X5FMOoPKxBw6kiIiJiErchbuLEifzf//0frVu3BiAi\nIoL169d7vTBfYjjsl1enqidOREREzFGr1HHbbbdd8dpqtXqlGF9lXB5OVU+ciIiImMXtnLjbbruN\nzZs3Y7FYqKioYPbs2QQHB5tRm89wOO34OVFPnIiIiJjGbep44403mDNnDsXFxdx6663k5eUxZ84c\nM2rzGYazAj8DLApxIiIiYhK3PXE333wzGRkZZtTis5yuLUYU4kRERMQcblPHgQMHGDx4MG3atKFt\n27YMGTKEAwcOmFGbz3Aa9surUxXiRERExBxuU8fDDz/MqFGjOHbsGEePHmXkyJEkJSWZUZvPcDoc\nGk4VERERU7lNHRcuXOBXv/oV/v7++Pv7M3r0aMrLy82ozWc4XatTFeJERETEHG7nxA0aNIgpU6bw\n0EMPYbFYWLFiBYmJiXzzzTcAtGrVyutF1neGYb98YoO2GBERERFzuA1xb731FgB///vfr/j58uXL\nsVgsmh/H5S1G1BMnIiIiJnIb4g4ePGhGHT6tanWqxU+bIIuIiIg5qu062rZtG19//bXr9eLFixky\nZAhPPfWUayhVKlUNp6onTkRERMxSber49a9/TcOGDQFYv349aWlpPProo7Ro0YKUlBTTCvQFTqez\n8sQGHUcmIiIiJql2ONXhcLgWLaxYsYKUlBSGDx/O8OHDsdlsphXoCxyOCvzQFiMiIiJinmpTh8Ph\nwG63A5CVlcWAAQNcv6v6uVRyOh2A5sSJiIiIeartiUtKSqJ///7cfPPNNGnShH79+gHw5Zdf0qJF\nC9MK9AVOx+VQq544ERERMUm1Ie6FF15g4MCBHDt2jISEBNceaE6nk9dee820An2B4agA1BMnIiIi\n5qlxi5E777zzqp9169bNa8WFli4MAAAbRklEQVT4KodTPXEiIiJiLqUODzAclXPi/LQ6VUREREyi\nEOcBVQsb0HCqiIiImKTGEOdwOIiLizOrFp9VtbBBc+JERETELDWGOKvVip+fH2fOnDGrHp/0XYhT\nx6aIiIiYw+3Zqc2aNSMsLIz4+HgCAgJcP09PT/dqYb7EcDqwABar249TRERExCPcpo5hw4YxbNgw\nM2rxWYbdfjnEaThVREREzOE2xCUnJ3Pp0iX27dsHQPfu3WnQoIHXC/MlTqe9clzaTz1xIiIiYg63\nqeOTTz4hOTmZzp07YxgGR44cYdGiRcTGxppRn09wOJ34o4UNIiIiYh63Ie6ZZ57hww8/pHv37gDs\n27ePpKQktm/f7vXifEXVPnEaThURERGzuA1xFRUVrgAHlSc2VFRUeLUoX2M4FeJERES+r6KigqKi\nIsrLy+u6lHqpcePGdOjQ4UdPU3Mb4qKjoxk3bhyjR48GICMjg+jo6B91s5+qqs1+NZwqIiLynaKi\nIpo3b07nzp1dZ7BLJcMwOHXqFEVFRXTp0uVHteF2Y7PXX3+dnj17kp6eTnp6Oj179uSNN974UTf7\nqfouxGmfOBERkSrl5eW0bt1aAe4aLBYLrVu3vq5eSrc9cW+88QZPP/00Tz/9tOtns2fPZsKECT/6\npj81htMJgJ964kRERK6gAFe96/1s3HYdLVq06KqfLVy48Lpu+lNjaDhVRESkXrJardhsNkJDQxk8\neDClpaU1vr+wsJClS5de930ff/xx2rZtS2ho6HW3VZ1qQ9yyZcsYPHgwBw8e5IEHHnD9ueeee2jV\nqlWtGp81axYhISGEhoaSlJREeXk52dnZ9OrVi9DQUJKTk7HbK4+sOn36NEOHDiU8PJyYmBjy8/Ov\n2aZhGLzwwgt069aN4ODgenFyhGs41arhVBERkfqkSZMm5OXlkZ+fT6tWrZgzZ06N7/8xIa4qy/y3\nMWPGsHbt2h/Uzg9V7XDqXXfdRVBQECdPnuSZZ55x/bx58+aEh4e7bbi4uJj09HR2795NkyZNGDVq\nFEuXLuXFF18kKyuLbt268cc//pFFixYxduxYJk+ejM1m491332XPnj385je/ISsr66p2Fy5cyJEj\nR9izZw9+fn6cOHHiRz6652g4VUREpP7r27cvu3btAio7hZ577jnWrFmDxWJh0qRJPPjgg6SlpVFQ\nUIDNZiM5OZnU1FRSU1PJzc3F39+fmTNnEhcXx8KFC8nMzOT8+fM4HA4+/fTTK+4VGxtLYWGhV5+n\n2hDXqVMnOnXqxJYtWzh+/Djbtm0DIDg4GH//2p1MYLfbKSsro0GDBly4cIGAgAAaNmxIt27dAIiP\nj+fll19m7Nix7N69m7S0NAB69OhBYWEhx48f55Zbbrmizddff52lS5fid3kRQdu2bX/4U3uYs2Vn\nYCdoixEREZFreulfX7D76FmPttnz1kBeHBxSq/c6HA6ysrIYO3YsAJmZmeTl5bFz505OnjxJ7969\niY2NZcqUKUyfPp3Vq1cDMGPGDCwWC59//jl79uwhISHBdYrVjh072LVrV61HKD3N7fjf22+/TUxM\nDG+//TZvvfUWffr04Z133nHbcPv27Xn22Wfp2LEjQUFBtGjRglGjRmG328nNzQXgnXfe4ciRIwBE\nRESQmZkJQE5ODocOHaKoqOiqdr/66itWrFhBdHQ0gwYNYv/+/de8/9y5c4mOjiY6OpqSkhK39V4P\no23lf0B+FoU4ERGR+qSsrAybzUa7du04fvw48fHxAGzcuJGkpCSsViu33HIL/fv3d3VY/beNGze6\ntlnr0aMHnTp1coW4+Pj4OgtwUIvVqX/+85/Ztm2bq8erpKSEn//854wYMaLG606fPs2qVas4ePAg\nLVu2ZOTIkWRkZLB8+XImTpzIxYsXSUhIwHq59yotLY0JEyZgs9kICwsjMjLS9bv/dvHiRRo3bkxu\nbi6ZmZk8/vjjbNiw4ar3paSkkJKSAuD1fe0MbTEiIiJSo9r2mHla1Zy4CxcucO+99zJnzhyeeuop\nj7QdEBDgkXZ+LLepw+l0XjFk2bp1a5yX54DV5OOPP6ZLly60adOGBg0aMGzYMDZv3kzfvn3ZsGED\nOTk5xMbGuoZWAwMDWbBgAXl5eSxevJiSkhK6du16VbsdOnRg2LBhAAwdOtQ1tl2XnDp2S0REpF5r\n2rQp6enpzJgxA7vdTr9+/VixYgUOh4OSkhLWr19PTEwMzZs359y5c67r+vXrR0ZGBlB59Ojhw4ev\nOMmqLrkNcffddx/33nsvCxcuZOHChfziF79g0KBBbhvu2LEjW7du5cKFCxiGQVZWFsHBwa6FCBcv\nXmTq1Kk8+eSTAJSWlnLp0iUA5s2bR2xsLIGBgVe1+8tf/pJ169YB8Omnn7pCYF0yjMoQp4UNIiIi\n9VdkZCTh4eEsW7bMtSNGREQEAwYM4JVXXqFdu3aEh4djtVqJiIhg1qxZjB8/HqfTSVhYGA8++CAL\nFy6kUaNGbu+VlJRE37592bt3Lx06dGD+/Pkefx6LYRiGuzdlZmayceNGoDKRDh06tFaNv/jii6xY\nsQJ/f38iIyOZN28ekyZNYvXq1TidTlJTU/nd734HwJYtW0hOTsZisRASEsL8+fO56aabAEhMTGTe\nvHnceuutlJaW8sgjj3D48GGaNWvGG2+8QURERI11REdHu+bheUPW2je49Xez8Z/5J+5IfNBr9xER\nEfElBQUFBAcH13UZ9dq1PqPa5pZahbj/5nQ6WbZsGY888sgPq7IOeTvEffTBHDo8/Vcavvr/8T/3\n1TxXUERE5EahEOfe9YS4aodTz549y8svv8z//u//8uGHH2IYBn/961/p2rUrb7311vVX/VPi0D5x\nIiIiYq5qV6f+6le/4qabbqJv377MmzePyZMnYxgG7733Hjabzcwa672qhR46dktERETMUm2IO3Dg\nAJ9//jkA48aNIygoiMOHD9O4cWPTivMVVVuM+Gl1qoiIiJik2uHUBg0auP5utVrp0KGDAlw1jKot\nRtQTJyIiIiaptidu586dri0+DMOgrKyMwMBADMPAYrFw9qxnj87wZa4tRtQTJyIiIiapNsQ5Lvcu\nSS04Kxf4KsSJiIiIWXROlAe4jt3S2akiIiL1itVqxWazERoayuDBgyktLa3x/YWFhSxduvS67nnk\nyBHi4uLo2bMnISEhzJ49+7raq45CnAfo2C0REZH6qers1Pz8fFq1asWcOXNqfP+PCXF2u/2K1/7+\n/syYMYPdu3ezdetW5syZw+7du39w7e5UO5wqtWc4tU+ciIhIjdakwdefe7bNdmEwaEqt3963b1/X\nmeuGYfDcc8+xZs0aLBYLkyZN4sEHHyQtLY2CggJsNhvJycmkpqaSmppKbm4u/v7+zJw5k7i4OBYu\nXEhmZibnz5/H4XDw6aefuu4TFBREUFAQAM2bNyc4OJji4mJ69uzp0cdXiPMAV4hTT5yIiEi95HA4\nyMrKYuzYsUDlkaJ5eXns3LmTkydP0rt3b2JjY5kyZQrTp09n9erVAMyYMQOLxcLnn3/Onj17SEhI\nYN++fQDs2LGDXbt20apVq2rvW1hYyGeffUafPn08/kwKcZ5gqCdORESkRj+gx8yTysrKsNlsFBcX\nExwcTHx8PAAbN24kKSkJq9XKLbfcQv/+/dm2bZtrZ44qGzdu5Le//S0APXr0oFOnTq4QFx8fX2OA\nO3/+PMOHD+fVV1+9ql1P0Jw4D3AtbFCIExERqVeq5sQdOnQIwzDczon7IQICAqr9XUVFBcOHD+eR\nRx5h2LBhHrvnf1OI84Cq4VSrVR2bIiIi9VHTpk1JT09nxowZ2O12+vXrx4oVK3A4HJSUlLB+/Xpi\nYmJo3rw5586dc13Xr18/MjIyANi3bx+HDx+me/fuNd7LMAzGjh1LcHAwTz/9tNeeSanDA4zL+8Sp\nJ05ERKT+ioyMJDw8nGXLljF69Gi2bNlCREQEFouFV155hXbt2tG6dWusVisRERGMGTOG8ePHk5qa\nSlhYGP7+/ixcuJBGjRrVeJ9NmzaxZMkSwsLCXOfNT548mcTERI8+j8UwDMOjLdZD0dHR5Obmeq39\nlX+bSM/0tXT61yqa3tHNa/cRERHxJQUFBQQHB9d1GfXatT6j2uYWDad6wuWeOKu1gZs3ioiIiHiG\nQpwHGJdXp1qs+jhFRETEHEodnnB5dSp++jhFRETEHEodHlC1OhWLPk4RERExh1KHB1SFOIufpY4r\nERERkRuFQpwnXF7YoOFUERGR+sVqtWKz2QgNDWXw4MGUlpbW+P7CwkKWLl16XfcsLy8nJiaGiIgI\nQkJCePHFF6+rveoodXiAhlNFRETqp6oTG/Lz82nVqpXbExt+TIiz2+1XvG7UqBHZ2dns3LmTvLw8\n1q5dy9atW39w7e4odXiAYVQdu6XhVBERkfqqb9++FBcXA5WnKvz+978nNDSUsLAwVqxYAUBaWhob\nNmzAZrMxa9YsysvLeeyxxwgLCyMyMpJ169YBsHDhQh544AEGDBjAwIEDr7iPxWKhWbNmQOXxWxUV\nFVgsns8IOrHBA5r5Xz47TcOpIiIi1zQ1Zyp7vtnj0TZ7tOrBH2L+UKv3OhwOsrKyGDt2LACZmZnk\n5eWxc+dOTp48Se/evYmNjWXKlClMnz6d1atXAzBjxgwsFguff/45e/bsISEhgX379gGwY8cOdu3a\nRatWra55v6ioKL788kt+85vf0KdPHw899XeUOjzgrlvurPyLQpyIiEi9UlZWhs1mo127dhw/fpz4\n+HgANm7cSFJSElarlVtuuYX+/fuzbdu2q67fuHEjo0ePBqBHjx506tTJFeLi4+OvGeCgci5eXl4e\nRUVF5OTkkJ+f7/FnU0+cJ1Rt9qsQJyIick217THztKo5cRcuXODee+9lzpw5PPXUUx5pOyAgwO17\nWrZsSVxcHGvXriU0NNQj962i1OEBroUNCnEiIiL1UtOmTUlPT2fGjBnY7Xb69evHihUrcDgclJSU\nsH79emJiYmjevDnnzp1zXdevXz8yMjIA2LdvH4cPH6Z79+413qukpMS1CrasrIyPPvqIHj16ePyZ\n1BPnCVVbjGh1qoiISL0VGRlJeHg4y5YtY/To0WzZsoWIiAgsFguvvPIK7dq1o3Xr1litViIiIhgz\nZgzjx48nNTWVsLAw/P39WbhwIY0aNarxPseOHSM5ORmHw4HT6WTUqFHcf//9Hn8ei2EYhsdbrWei\no6PJzc31Wvun5s/nxLTpdN+xHb+mTb12HxEREV9SUFBAcHBwXZdRr13rM6ptblHXkQdoOFVERETM\nptThCTqxQUREREym1OEJVatTvbCRn4iIiMi1KMR5gIZTRURExGxKHZ6g4VQRERExmVKHJzg1nCoi\nIiLmUojzAMPpUC+ciIiImErJwxOcBlitdV2FiIiIfI/VasVmsxEaGsrgwYNdJylUp7CwkKVLl3rk\n3g6Hg8jISK9s9AsKcZ5hODWUKiIiUg9VnZ2an59Pq1atmDNnTo3v/zEhzm63X/Pns2fP9upmxzp2\nywMMp1PDqSIiIjX4evJkLhbs8WibjYJ70O7552v9/r59+7Jr1y4ADMPgueeeY82aNVgsFiZNmsSD\nDz5IWloaBQUF2Gw2kpOTSU1NJTU1ldzcXPz9/Zk5cyZxcXEsXLiQzMxMzp8/j8Ph4NNPP73iXkVF\nRfz73//mhRdeYObMmR597ioKcZ7gNBTiRERE6jGHw0FWVhZjx44FIDMzk7y8PHbu3MnJkyfp3bs3\nsbGxTJkyhenTp7N69WoAZsyYgcVi4fPPP2fPnj0kJCSwb98+AHbs2MGuXbto1arVVff73e9+xyuv\nvMK5c+e89kwKcZ7g1HCqiIhITX5Ij5knlZWVYbPZKC4uJjg4mPj4eAA2btxIUlISVquVW265hf79\n+7Nt2zYCAwOvuH7jxo389re/BaBHjx506tTJFeLi4+OvGeBWr15N27ZtiYqK4pNPPvHas3m1+2jW\nrFmEhIQQGhpKUlIS5eXlZGdn06tXL0JDQ0lOTnaNI58+fZqhQ4cSHh5OTEwM+fn512xzzJgxdOnS\nBZvNhs1mIy8vz5uPUCuGoeFUERGR+qhqTtyhQ4cwDMPtnLgfIiAg4Jo/37RpE++//z6dO3fmoYce\nIjs7m9GjR3vsvlW8ljyKi4tJT08nNzeX/Px8HA4HS5cuJTk5meXLl5Ofn0+nTp1YtGgRAJMnT8Zm\ns7Fr1y4WL17MhAkTqm172rRp5OXlkZeXh81m89Yj1Frrxx+n0+JFdV2GiIiIVKNp06akp6czY8YM\n7HY7/fr1Y8WKFTgcDkpKSli/fj0xMTE0b978iiHQfv36kZGRAcC+ffs4fPgw3bt3r/FeL7/8MkVF\nRRQWFrJ8+XIGDBjAP//5T48/k1e7j+x2O2VlZdjtdi5cuEBAQAANGzakW7duQGU35MqVKwHYvXs3\nAwYMACq7KwsLCzl+/Lg3y/OYBu3a0diLq09ERETk+kVGRhIeHs6yZctco38REREMGDCAV155hXbt\n2hEeHo7VaiUiIoJZs2Yxfvx4nE4nYWFhPPjggyxcuJBGjRrV9aMAYDEMw/BW47Nnz+aFF16gSZMm\nJCQk8M9//pPOnTuzcuVKoqOjmTBhAtnZ2Xz++ec8//zzlJWVMWvWLHJycrjrrrv4z3/+Q1RU1BVt\njhkzhi1bttCoUSMGDhzIlClTrvlhzp07l7lz5wJQUlLCoUOHvPWYIiIicg0FBQVe3WLjp+Ban1F0\ndDS5ublur/VaT9zp06dZtWoVBw8e5OjRo3z77bdkZGSwfPlyJk6c6OqytF7eJDctLY3S0lJsNhuv\nvfYakZGRrt/9t5dffpk9e/awbds2vvnmG6ZOnXrN+6ekpJCbm0tubi5t2rTx1mOKiIiI1AmvrU79\n+OOP6dKliytADRs2jM2bNzN69Gg2bNgAwIcffuha4REYGMiCBQuAyr1bunTpQteuXa9qNygoCIBG\njRrx2GOPMX36dG89goiIiEi95bWeuI4dO7J161YuXLiAYRhkZWURHBzMiRMnALh48SJTp07lySef\nBKC0tJRLly4BMG/ePGJjY69a5gtw7NgxoDLovffee4SGhnrrEUREROQ6eXHWls+73s/GayGuT58+\njBgxgl69ehEWFobT6SQlJYVp06YRHBxMeHg4gwcPdi1mKCgoIDQ0lO7du7NmzRpmz57taisxMZGj\nR48C8MgjjxAWFkZYWBgnT55k0qRJ3noEERERuQ6NGzfm1KlTCnLXYBgGp06donHjxj+6Da8ubKgv\najtBUERERDynoqKCoqIiysvL67qUeqlx48Z06NCBBg0aXPHz2uYWndggIiIiXtGgQQO6dOlS12X8\nZOmYAREREREfpBAnIiIi4oMU4kRERER80A2xsOHmm2+mc+fOXr1HSUmJNhWuZ/Sd1D/6TuoffSf1\nj76T+sfs76SwsJCTJ0+6fd8NEeLMoBWw9Y++k/pH30n9o++k/tF3Uv/U1+9Ew6kiIiIiPkghTkRE\nRMQHWf/0pz/9qa6L+KmIioqq6xLke/Sd1D/6TuoffSf1j76T+qc+fieaEyciIiLigzScKiIiIuKD\nFOJEREREfJBCnAesXbuW7t27c/vttzNlypS6LueG9/jjj9O2bVtCQ0PruhS57MiRI8TFxdGzZ09C\nQkKYPXt2XZd0wysvLycmJoaIiAhCQkJ48cUX67okuczhcBAZGcn9999f16UI0LlzZ8LCwrDZbERH\nR9d1OVfQnLjr5HA46NatGx999BEdOnSgd+/eLFu2jJ49e9Z1aTes9evX06xZMx599FHy8/PruhwB\njh07xrFjx+jVqxfnzp0jKiqK9957T/8/qUOGYfDtt9/SrFkzKioquPvuu5k9ezZ33nlnXZd2w5s5\ncya5ubmcPXuW1atX13U5N7zOnTuTm5vLzTffXNelXEU9cdcpJyeH22+/na5du9KwYUMeeughVq1a\nVddl3dBiY2Np1apVXZch/yUoKIhevXoB0Lx5c4KDgykuLq7jqm5sFouFZs2aAVBRUUFFRQUWi6WO\nq5KioiL+/e9/M27cuLouRXyAQtx1Ki4u5rbbbnO97tChg/5xEqlBYWEhn332GX369KnrUm54DocD\nm81G27ZtiY+P13dSD/zud7/jlVdewc9P/zzXFxaLhYSEBKKiopg7d25dl3MF/VciIqY5f/48w4cP\n59VXXyUwMLCuy7nhWa1W8vLyKCoqIicnR9MP6tjq1atp27ZtvdyP7Ea2ceNGduzYwZo1a5gzZw7r\n16+v65JcFOKuU/v27Tly5IjrdVFREe3bt6/DikTqp4qKCoYPH84jjzzCsGHD6roc+S8tW7YkLi6O\ntWvX1nUpN7RNmzbx/vvv07lzZx566CGys7MZPXp0XZd1w6v6N71t27YMHTqUnJycOq7oOwpx16l3\n797s37+fgwcPcunSJZYvX84DDzxQ12WJ1CuGYTB27FiCg4N5+umn67ocAUpKSigtLQWgrKyMjz76\niB49etRxVTe2l19+maKiIgoLC1m+fDkDBgzgn//8Z12XdUP79ttvOXfunOvvH374Yb3a+UAh7jr5\n+/vz17/+lXvvvZfg4GBGjRpFSEhIXZd1Q0tKSqJv377s3buXDh06MH/+/Lou6Ya3adMmlixZQnZ2\nNjabDZvNxgcffFDXZd3Qjh07RlxcHOHh4fTu3Zv4+HhtaSHyPcePH+fuu+8mIiKCmJgYfvGLX3Df\nfffVdVku2mJERERExAepJ05ERETEBynEiYiIiPgghTgRERERH6QQJyIiIuKDFOJEREREfJB/XRcg\nIlIfnDp1ioEDBwLw9ddfY7VaadOmDQBNmzZl8+bNdVmeiMhVtMWIiMj3/OlPf6JZs2Y8++yzdV2K\niEi1NJwqIuJGs2bNAPjkk0/o378/Q4YMoWvXrqSlpZGRkUFMTAxhYWF89dVXQOVpCMOHD6d37970\n7t2bTZs21WX5IvITpRAnIvID7Ny5kzfeeIOCggKWLFnCvn37yMnJYdy4cbz22msATJgwgYkTJ7Jt\n2zZWrlzJuHHj6rhqEfkp0pw4EZEfoHfv3gQFBQHwP//zPyQkJAAQFhbGunXrAPj444/ZvXu365qz\nZ89y/vx5V4+eiIgnKMSJiPwAjRo1cv3dz8/P9drPzw+73Q6A0+lk69atNG7cuE5qFJEbg4ZTRUQ8\nLCEhwTW0CpCXl1eH1YjIT5VCnIiIh6Wnp5Obm0t4eDg9e/bkjTfeqOuSROQnSFuMiIiIiPgg9cSJ\niIiI+CCFOBEREREfpBAnIiIi4oMU4kRERER8kEKciIiIiA9SiBMRERHxQQpxIiIiIj7o/wfry1be\nmyz2WAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualization for an initial position.\n",
    "file_ddpg_vtakeoff = 'DDPG_VTakeoff_History_0.csv'\n",
    "visuals.plot_position(file_ddpg_vtakeoff, size=(10, 10))\n",
    "visuals.plot_euler_angle(file_ddpg_vtakeoff, size=(10, 10))\n",
    "visuals.plot_rotor_speed(file_ddpg_vtakeoff, size=(10, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MLWRxwYZBKBB"
   },
   "source": [
    "### 3D Trajectory for DDPG Agent\n",
    "\n",
    "* <font color='blue'>Blue mark</font> represnets the start point\n",
    "* <font color='red'>Red mark</font> represnets the end point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"imgs/DDPG_VTakeoff_History_0.png\" target=\"_blank\"><img src=\"imgs/DDPG_VTakeoff_History_0.png\" alt=\"DDPG 3D Trajectory\" title=\"DDPG 3D Trajectory\"></a>"
   ]
  },
  {
   "cell_type": "code",
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    "id": "8sCDQ9-ywiPH",
    "outputId": "1c2e4ff3-fb77-4786-dc1e-b08d40ec6983"
   },
   "outputs": [
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       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
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   "source": [
    "visuals.plot_trajectory_3d('DDPG_VTakeoff_History_0.csv', 'DDPG Trajectory', filename='DDPG Trajectory',\n",
    "                           width=800, height=800, axis_ranges=([-10,10], [-10,10], [0,120]))"
   ]
  },
  {
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   "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**:\n",
    "\n",
    "The takeoff task is defined in `vtakeoff_task.py`.\n",
    "\n",
    "***Goal***\n",
    "\n",
    "The quadcopter can take off vertically as high as possible within a limited period of time (5s) from any initial position.\n",
    "\n",
    "***State / Observation***\n",
    "\n",
    "At first the state was represented by `task.sim.pose[:3]` (position), `task.sim.pose[3:]` (Euler angles), `task.sim.v` (velocities) and `task.sim.angular_v` (angular velocities). However, I found that the agent could not take off vertically after successful training if the initial position was different from the one used for training. I thought this problem was mainly caused by the position of the state, so I removed `task.sim.pose[:3]` (position) from the state then tried to train the agent again.\n",
    "\n",
    "***Action***\n",
    "\n",
    "The minimum (`action_low`) was changed from 0 to 1 to avoid the \"divide by zero\" error in the simulator.\n",
    "\n",
    "***Reward Function***\n",
    "\n",
    "The reward is defined as the **hyperbolic tangent of $R$**. The purpose of hyperbolic tangent is to scale rewards between -1 and 1 to avoid instability in training due to exploding gradients. $R$ is defnied as below:\n",
    "\n",
    "\\begin{equation*}\n",
    "R=\\begin{cases}\n",
    "-20 & \\text{No Takeoff}\\\\\n",
    "-5 & \\text{Crash}\\\\\n",
    "0.8v_{z} -0.2( |v_{x} |+|v_{y} |) -0.01( |a_{φ} |+|a_{θ} |+|a_{ψ} |) & \\text{Otherwise}\n",
    "\\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "where $v$ denotes velocities and  $a$ denotes angular velocities. $v$<sub>*z*</sub> has the highest coefficient since vertical takeoff is what we care about the most. The reward function was inspired by the Humanoid Reward defined in this paper<sup>1</sup>.\n",
    "\n",
    "- **0.8$v$<sub>*z*</sub>:** Return positive reward if the quadcopter flies straight up, otherwise it will return negative value for penalization.\n",
    "- **0.2(|$v$<sub>x</sub>| + |$v$<sub>y</sub>|):** Penalize any x- and y-direction velocities since the goal is to take off vertically.\n",
    "- **0.01(|$a$<sub>φ</sub>| + |$a$<sub>θ</sub>| + |$a$<sub>ψ</sub>|):** Penalize wasting energy on φ, θ and ψ angular velocities.\n",
    "\n",
    "***References***\n",
    "1. [Emergence of Locomotion Behaviours in Rich Environments](https://arxiv.org/abs/1707.02286)"
   ]
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    "**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",
    "***Learning Algorithm***\n",
    "\n",
    "I only tried the Deep Deterministic Policy Gradient (DDPG)<sup>1</sup> algorithm as it was already able to finish the task. The DDPG agent consists of `ddpg.py`, `replay_buffer.py` and `ou_noise.py`, and original implementation of these components are provied by the Udacity course.\n",
    "\n",
    "***Final Hyperparameters***\n",
    "\n",
    "Most hyperparameters refer to the original DDPG paper<sup>1</sup>.\n",
    "\n",
    "- **Discount factor of $\\gamma$:** 0.99\n",
    "- **Minibatch size:** 64\n",
    "- **Replay buffer size:** 100000\n",
    "- **Soft target update $\\tau$:** 0.1\n",
    "- Ornstein–Uhlenbeck process\n",
    " - **$\\mu$:** 0\n",
    " - **$\\theta$:** 0.15\n",
    " - **$\\sigma$:** 0.2\n",
    "\n",
    "***Neural Network Architecture***\n",
    "\n",
    "The network architectures mostly follow the original DDPG paper<sup>1</sup> as shown in the below two images which were generated by [Netron](https://github.com/lutzroeder/netron). I also used Adam optimizer with a learning rate of 0.0001 and 0.001 for actor and critic respectively. In critic, an extra dense layer of 64 units was added prior to the final output layer, and all hidden layers incorporated L2-regularizer with weight decay of 0.01 for `kernel_regularizer`.\n",
    "\n",
    "****Actor****\n",
    "\n",
    "<a href=\"imgs/ddpg-actor.png\" target=\"_blank\"><img src=\"imgs/ddpg-actor.png\" alt=\"Actor Architecture\" title=\"Actor Architecture\" style=\"max-height:600px;\"></a>\n",
    "\n",
    "****Critic****\n",
    "\n",
    "<a href=\"imgs/ddpg-critic.png\" target=\"_blank\"><img src=\"imgs/ddpg-critic.png\" alt=\"Critic Architecture\" title=\"Critic Architecture\" style=\"max-height:600px;\"></a>\n",
    "\n",
    "**References**:\n",
    "\n",
    "1. [Continuous control with deep reinforcement learning](https://arxiv.org/abs/1509.02971)"
   ]
  },
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   "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",
    "\n",
    "- According to the [episode rewards plot](#Plot-the-Rewards), it seems an easy task to learn as the reward reaches a plateau in just a few episodes. However, this was not always the case. Sometimes the agent did not converge on a high reward. Based on a few repeated experiments, the agent could learn the task successfully once in two or three tries.\n",
    "- There was an aha moment because the reward suddenly changed from a small negative value to a high positive value and remained on a high level.\n",
    "- The performance of the agent was excellent. The rewards remain high and stable starting from the early episodes. I have performed three vertical takeoff simulations from different initial positions, and the quadcopter was able to fly straight up in all simulations. [Here](#3D-Trajectory-for-DDPG-Agent) shows the 3D trajectory generated by [plotly](https://plot.ly/) in a simulation."
   ]
  },
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   "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",
    "\n",
    "I think this is the most challenging project so far in the ML Engineer Nanodegree Program. I started with reading the origianl DDPG paper to understand more details about the algorithm. To get more sense about how the quadcopter actually flies, I tried to find a 3D simulator which can display the animation of the quadcopter. Unfortunately I didn't find one that is easy to use, so finally decided to utilize [plotly](https://plot.ly/) for plotting the 3D trajectory.\n",
    "\n",
    "Actually I tried to solve the \"reach target positon\" task in the beginning, but after several days of trial and error without seeing a promising solution, I decided to go for the easier task \"vertical takeoff\". Even this task is not easy for the DDPG agent to learn. I think the hardest part of the project is that there are infinite possible combinations of hyperparameters, network architectures and reward functions. Each combination requires a bunch of time to train. Furthermore, you are not sure if DDPG is powerful enough to learn the task or you should resort to other algorithm after a lot of frustrating results. All I can do is refer to the settings of previous literatures, gradually change the settings, and keep reviewing whether my reward function is reasonable.\n",
    "\n",
    "Most people would intuitively know that the best solution of the vertical takeoff task is to set the 4 rotors at max speed all the time, but it's not that easy for the agent to learn. The final agent demonstrated above learned the optimal solution, but in fact I have trained an agent which only set 2 rotors at max speed. The quadcopter can still fly straight up under this condition but slower.\n",
    "\n",
    "Besides keep polishing the reward function, there are two ideas might worth trying to improve the agent.\n",
    "- Use prioritized experience replay instead of only random sampling from memory\n",
    "- Exploration with parameter noise<sup>1</sup> instead of action space noise\n",
    "\n",
    "**References**:\n",
    "\n",
    "1. [Parameter Space Noise for Exploration](https://arxiv.org/abs/1706.01905)"
   ]
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