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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UxK08xN_wco-"
   },
   "source": [
    "# HW5: Model Predictive Control\n",
    "\n",
    "> - Full Name: Taha Majlesi\n",
    "> - Student ID: 810101504\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/DeepRLCourse/Homework-5-Questions/blob/main/MPC.ipynb)\n",
    "[![Open In kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://raw.githubusercontent.com/DeepRLCourse/Homework-5-Questions/main/MPC.ipynb)\n",
    "\n",
    "## Overview\n",
    "\n",
    "Here the goal is to use **MPC** for [gymnasium environments](https://gymnasium.farama.org/).\n",
    "More specificly we focus on the [Pendulum](https://gymnasium.farama.org/environments/classic_control/pendulum/) environment and try to solve it using [mpc.pytorch](https://locuslab.github.io/mpc.pytorch/).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
    "id": "SBD13rNwmXpx"
   },
   "outputs": [],
   "source": [
    "# @title Imports\n",
    "\n",
    "# Stuff you (might) need\n",
    "import random\n",
    "import numpy as np\n",
    "import gymnasium as gym\n",
    "\n",
    "import torch\n",
    "from torch import nn\n",
    "import torch.autograd\n",
    "from tqdm.notebook import trange\n",
    "import math\n",
    "\n",
    "# Stuff used for visualization\n",
    "from matplotlib import pyplot as plt\n",
    "from gymnasium.wrappers import RecordVideo\n",
    "import base64\n",
    "import imageio\n",
    "from IPython.display import HTML\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "form",
    "id": "Avcbl8VMmgm1"
   },
   "outputs": [],
   "source": [
    "# @title Visualization Functions\n",
    "\n",
    "\n",
    "def embed_mp4(filename):\n",
    "    video = open(filename, \"rb\").read()\n",
    "    b64 = base64.b64encode(video)\n",
    "    tag = \"\"\"\n",
    "    <video width=\"640\" height=\"480\" controls>\n",
    "    <source src=\"data:video/mp4;base64,{0}\" type=\"video/mp4\">\n",
    "    Your browser does not support the video tag.\n",
    "    </video>\"\"\".format(\n",
    "        b64.decode()\n",
    "    )\n",
    "\n",
    "    return HTML(tag)\n",
    "\n",
    "\n",
    "def plot_results(rewards, actions):\n",
    "    plt.plot(rewards, label=\"Rewards\")\n",
    "    plt.plot(actions, label=\"Actions\")\n",
    "    plt.legend()\n",
    "    plt.title(f\"Total reward: {sum(rewards):.2f}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qTS3Lm1nWiMK"
   },
   "source": [
    "# Explore the Environment (25 points)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yyCz0lxFWsFv"
   },
   "source": [
    "To better understand the environment, let's first see what a random agent does.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 533,
     "referenced_widgets": [
      "c48f9ad4e3214bbe8d7518441bd56339",
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      "318ed47730304069a2978696d0e58fd7"
     ]
    },
    "id": "xZI6WO4bmgjS",
    "outputId": "65a6a700-b1f4-4940-b9c8-b32a9a7f2558"
   },
   "outputs": [
    {
     "ename": "DependencyNotInstalled",
     "evalue": "moviepy is not installed, run `pip install \"gymnasium[other]\"`",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/utils/save_video.py:13\u001b[39m\n\u001b[32m     12\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m13\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmoviepy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mvideo\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mImageSequenceClip\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ImageSequenceClip\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n",
      "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'moviepy'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[31mDependencyNotInstalled\u001b[39m                    Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[3]\u001b[39m\u001b[32m, line 6\u001b[39m\n\u001b[32m      4\u001b[39m \u001b[38;5;66;03m# Create a directory to save the video\u001b[39;00m\n\u001b[32m      5\u001b[39m video_directory = \u001b[33m\"\u001b[39m\u001b[33mrandom_videos\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m6\u001b[39m env = \u001b[43mRecordVideo\u001b[49m\u001b[43m(\u001b[49m\u001b[43menv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvideo_directory\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m      8\u001b[39m \u001b[38;5;66;03m# Set the number of steps to record\u001b[39;00m\n\u001b[32m      9\u001b[39m num_steps = \u001b[32m500\u001b[39m\n",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/wrappers/rendering.py:282\u001b[39m, in \u001b[36mRecordVideo.__init__\u001b[39m\u001b[34m(self, env, video_folder, episode_trigger, step_trigger, video_length, name_prefix, fps, disable_logger, gc_trigger)\u001b[39m\n\u001b[32m    276\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    277\u001b[39m         \u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mRender mode is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00menv.render_mode\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m, which is incompatible with RecordVideo.\u001b[39m\u001b[33m\"\u001b[39m,\n\u001b[32m    278\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mInitialize your environment with a render_mode that returns an image, such as rgb_array.\u001b[39m\u001b[33m\"\u001b[39m,\n\u001b[32m    279\u001b[39m     )\n\u001b[32m    281\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m episode_trigger \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m step_trigger \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m282\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mgymnasium\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mutils\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01msave_video\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m capped_cubic_video_schedule\n\u001b[32m    284\u001b[39m     episode_trigger = capped_cubic_video_schedule\n\u001b[32m    286\u001b[39m \u001b[38;5;28mself\u001b[39m.episode_trigger = episode_trigger\n",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/utils/save_video.py:15\u001b[39m\n\u001b[32m     13\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmoviepy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mvideo\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mImageSequenceClip\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ImageSequenceClip\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[32m---> \u001b[39m\u001b[32m15\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m gym.error.DependencyNotInstalled(\n\u001b[32m     16\u001b[39m         \u001b[33m'\u001b[39m\u001b[33mmoviepy is not installed, run `pip install \u001b[39m\u001b[33m\"\u001b[39m\u001b[33mgymnasium[other]\u001b[39m\u001b[33m\"\u001b[39m\u001b[33m`\u001b[39m\u001b[33m'\u001b[39m\n\u001b[32m     17\u001b[39m     ) \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01me\u001b[39;00m\n\u001b[32m     20\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mcapped_cubic_video_schedule\u001b[39m(episode_id: \u001b[38;5;28mint\u001b[39m) -> \u001b[38;5;28mbool\u001b[39m:\n\u001b[32m     21\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33mr\u001b[39m\u001b[33;03m\"\"\"The default episode trigger.\u001b[39;00m\n\u001b[32m     22\u001b[39m \n\u001b[32m     23\u001b[39m \u001b[33;03m    This function will trigger recordings at the episode indices :math:`\\{0, 1, 4, 8, 27, ..., k^3, ..., 729, 1000, 2000, 3000, ...\\}`\u001b[39;00m\n\u001b[32m   (...)\u001b[39m\u001b[32m     29\u001b[39m \u001b[33;03m        If to apply a video schedule number\u001b[39;00m\n\u001b[32m     30\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n",
      "\u001b[31mDependencyNotInstalled\u001b[39m: moviepy is not installed, run `pip install \"gymnasium[other]\"`"
     ]
    }
   ],
   "source": [
    "# Initialize the pendulum environment with video recording enabled\n",
    "env = gym.make(\"Pendulum-v1\", render_mode=\"rgb_array\")\n",
    "\n",
    "# Create a directory to save the video\n",
    "video_directory = \"random_videos\"\n",
    "env = RecordVideo(env, video_directory)\n",
    "\n",
    "# Set the number of steps to record\n",
    "num_steps = 500\n",
    "\n",
    "# Reset the environment to get the initial state\n",
    "state, _ = env.reset()\n",
    "\n",
    "for _ in (pbar := trange(num_steps)):\n",
    "    # Sample a random action\n",
    "    action = env.action_space.sample()\n",
    "\n",
    "    # Step the environment\n",
    "    state, reward, terminated, truncated, info = env.step(action)\n",
    "\n",
    "    # Render the environment\n",
    "    env.render()\n",
    "\n",
    "    # If done reset and get new state\n",
    "    if terminated or truncated:\n",
    "        state, _ = env.reset()\n",
    "\n",
    "    pbar.set_description(f\"Action = {action[0]:.2f} | Reward = {reward:.2f}\")\n",
    "\n",
    "# Close the environment to finalize the video\n",
    "env.close()\n",
    "\n",
    "# Show the video\n",
    "embed_mp4(f\"{video_directory}/rl-video-episode-0.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-8SUlhUHWvbC"
   },
   "source": [
    "The goal of the [Pendulum](https://gymnasium.farama.org/environments/classic_control/pendulum/) environment in [Gymnasium](https://gymnasium.farama.org/) is to swing a pendulum to an upright position and keep it balanced there.\n",
    "In this environment, you control a torque that can be applied to the pendulum.\n",
    "The objective is to apply the right amount of torque to swing the pendulum up and maintain its upright position.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wIGVVtRU2kY4"
   },
   "source": [
    "## Simulation Tools\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s7oVXleZ2rY8"
   },
   "source": [
    "Both the `angle_normalize` function and the `PendulumDynamics` class are fundamental components for accurately simulating, analyzing, and controlling the pendulum system.\n",
    "They ensure consistency in angle representation and provide a realistic model of the pendulum's behavior, enabling effective control strategies.\n",
    "\n",
    "We use the `angle_normalize` function for:\n",
    "\n",
    "- **Consistency**: When dealing with angles, it's important to keep them within a standard range to ensure consistency in calculations.\n",
    "- **Handling Wrapping**: Angles can wrap around when they exceed $2\\pi$ or drop below $-2\\pi$. Normalizing angles helps avoid confusion and errors that can arise from angle wrapping.\n",
    "\n",
    "And we use the `PendulumDynamics` class for:\n",
    "\n",
    "- **Modeling Physical Behavior**: The `PendulumDynamics` class models the physical behavior of the pendulum.\n",
    "- **Simulation and Control**: This class allows us to simulate the pendulum's response to different actions, which is crucial for designing and testing control algorithms.\n",
    "- **Optimization**: Understanding the dynamics of the pendulum helps in optimizing the control inputs. The class encapsulates the physics involved, enabling us to apply control techniques like Model Predictive Control (MPC) to achieve the desired behavior.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "N9y8iJ0u2Lgp"
   },
   "outputs": [],
   "source": [
    "class PendulumDynamics(nn.Module):\n",
    "    def forward(self, state, action):\n",
    "        th = state[:, 0].view(-1, 1)\n",
    "        thdot = state[:, 1].view(-1, 1)\n",
    "\n",
    "        g = 10  # default value of the environment (not 9.81)\n",
    "        m = 1\n",
    "        l = 1\n",
    "        dt = 0.05\n",
    "\n",
    "        u = action\n",
    "        u = torch.clamp(u, -2, 2)\n",
    "\n",
    "        newthdot = (\n",
    "            thdot\n",
    "            + (-3 * g / (2 * l) * torch.sin(th + np.pi) + 3.0 / (m * l**2) * u) * dt\n",
    "        )\n",
    "        newth = th + newthdot * dt\n",
    "        newthdot = torch.clamp(newthdot, -8, 8)\n",
    "\n",
    "        state = torch.cat((angle_normalize(newth), newthdot), dim=1)\n",
    "        return state\n",
    "\n",
    "\n",
    "def angle_normalize(x):\n",
    "    return ((x + math.pi) % (2 * math.pi)) - math.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eSb9nKlw4Gra"
   },
   "source": [
    "# Model Predictive Control (50 points)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yc8yKVti4tMp"
   },
   "source": [
    "[mpc.pytorch](https://locuslab.github.io/mpc.pytorch/) is a library that provides a fast and differentiable [Model Predictive Control](https://en.wikipedia.org/wiki/Model_predictive_control) (MPC) solver for PyTorch. It was developed by researchers at [LocusLab](https://locuslab.github.io/) and is designed to integrate seamlessly with PyTorch, allowing for efficient and flexible control of dynamic systems.\n",
    "\n",
    "If you are interested to learn more, check out [OptNet](https://arxiv.org/abs/1703.00443) and [Differentiable MPC](https://arxiv.org/abs/1810.13400).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PfDVMqgi5kax"
   },
   "source": [
    "## Quick Setup\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qU9dpT0C5nFg"
   },
   "source": [
    "In order to install this library you can use `pip`:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "HEyJ0SPi4W28"
   },
   "outputs": [],
   "source": [
    "! pip install mpc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J9Ev1gLC5uGd"
   },
   "source": [
    "While `mpc` offers a lot, in this notebook we are going to focus only on the core features.\n",
    "To learn more checkout the [GitHub repository](https://github.com/locuslab/mpc.pytorch) of this project.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "euuwSTJ14WO-"
   },
   "outputs": [],
   "source": [
    "from mpc import mpc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tf0ALVu7Ggsh"
   },
   "source": [
    "## The Cost Function\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l9pgPno8GjFV"
   },
   "source": [
    "The `define_swingup_goal` function creates a cost function that the MPC algorithm uses to determine the optimal control actions to achieve the desired pendulum swing-up task.\n",
    "It considers both the desired state (upright and stationary) and penalizes large control inputs to ensure smooth control actions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "13hsSR8cGLzA"
   },
   "outputs": [],
   "source": [
    "def define_swingup_goal():\n",
    "    goal_weights = torch.tensor((1.0, 0.1))  # Weights for theta and theta_dot\n",
    "    goal_state = torch.tensor((0.0, 0.0))  # Desired state (theta=0, theta_dot=0)\n",
    "    ctrl_penalty = 0.001\n",
    "    q = torch.cat((goal_weights, ctrl_penalty * torch.ones(1)))  # Combined weights\n",
    "    px = -torch.sqrt(goal_weights) * goal_state\n",
    "    p = torch.cat((px, torch.zeros(1)))\n",
    "    Q = torch.diag(q).repeat(TIMESTEPS, N_BATCH, 1, 1)  # Cost matrix\n",
    "    p = p.repeat(TIMESTEPS, N_BATCH, 1)\n",
    "    return mpc.QuadCost(Q, p)  # Quadratic cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4ILZGtcdLeFb"
   },
   "source": [
    "## Running MPC\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JskzIJuLMpoe"
   },
   "source": [
    "To run the MPC, in each iteration:\n",
    "\n",
    "1.  First you obtain the current state of the environment and convert it to a tensor.\n",
    "2.  Then you recreate the MPC controller using the updated `u_init` and calculate the optimal control actions based on the current state, dynamics, and cost function.\n",
    "3.  Next you take the first planned action and update `u_init` with the remaining actions.\n",
    "4.  Finally you take a step in the environment and store the rewards and actions.\n",
    "\n",
    "Remember that `u_init` serves as the initial guess for the control inputs.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "tE45H5NI05Q_"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception ignored in: <function RecordVideo.__del__ at 0x10fad0b80>\n",
      "Traceback (most recent call last):\n",
      "  File \"/Users/tahamajs/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/wrappers/rendering.py\", line 433, in __del__\n",
      "    if len(self.recorded_frames) > 0:\n",
      "AttributeError: 'RecordVideo' object has no attribute 'recorded_frames'\n"
     ]
    },
    {
     "ename": "DependencyNotInstalled",
     "evalue": "moviepy is not installed, run `pip install \"gymnasium[other]\"`",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/utils/save_video.py:13\u001b[39m\n\u001b[32m     12\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m13\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmoviepy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mvideo\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mImageSequenceClip\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ImageSequenceClip\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n",
      "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'moviepy'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[31mDependencyNotInstalled\u001b[39m                    Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[6]\u001b[39m\u001b[32m, line 11\u001b[39m\n\u001b[32m      9\u001b[39m env = gym.make(\u001b[33m\"\u001b[39m\u001b[33mPendulum-v1\u001b[39m\u001b[33m\"\u001b[39m, render_mode=\u001b[33m\"\u001b[39m\u001b[33mrgb_array\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m     10\u001b[39m video_directory = \u001b[33m\"\u001b[39m\u001b[33mmpc_videoss\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m---> \u001b[39m\u001b[32m11\u001b[39m env = \u001b[43mRecordVideo\u001b[49m\u001b[43m(\u001b[49m\u001b[43menv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvideo_directory\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m     12\u001b[39m env.reset()  \u001b[38;5;66;03m# Reset the underlying environment\u001b[39;00m\n\u001b[32m     13\u001b[39m env.unwrapped.state = [np.pi, \u001b[32m1\u001b[39m]  \u001b[38;5;66;03m# Environment must start in downward position\u001b[39;00m\n",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/wrappers/rendering.py:282\u001b[39m, in \u001b[36mRecordVideo.__init__\u001b[39m\u001b[34m(self, env, video_folder, episode_trigger, step_trigger, video_length, name_prefix, fps, disable_logger, gc_trigger)\u001b[39m\n\u001b[32m    276\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m    277\u001b[39m         \u001b[33mf\u001b[39m\u001b[33m\"\u001b[39m\u001b[33mRender mode is \u001b[39m\u001b[38;5;132;01m{\u001b[39;00menv.render_mode\u001b[38;5;132;01m}\u001b[39;00m\u001b[33m, which is incompatible with RecordVideo.\u001b[39m\u001b[33m\"\u001b[39m,\n\u001b[32m    278\u001b[39m         \u001b[33m\"\u001b[39m\u001b[33mInitialize your environment with a render_mode that returns an image, such as rgb_array.\u001b[39m\u001b[33m\"\u001b[39m,\n\u001b[32m    279\u001b[39m     )\n\u001b[32m    281\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m episode_trigger \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m step_trigger \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m282\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mgymnasium\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mutils\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01msave_video\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m capped_cubic_video_schedule\n\u001b[32m    284\u001b[39m     episode_trigger = capped_cubic_video_schedule\n\u001b[32m    286\u001b[39m \u001b[38;5;28mself\u001b[39m.episode_trigger = episode_trigger\n",
      "\u001b[36mFile \u001b[39m\u001b[32m~/Documents/uni/DRL/.venv/lib/python3.13/site-packages/gymnasium/utils/save_video.py:15\u001b[39m\n\u001b[32m     13\u001b[39m     \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmoviepy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mvideo\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mImageSequenceClip\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m ImageSequenceClip\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[32m---> \u001b[39m\u001b[32m15\u001b[39m     \u001b[38;5;28;01mraise\u001b[39;00m gym.error.DependencyNotInstalled(\n\u001b[32m     16\u001b[39m         \u001b[33m'\u001b[39m\u001b[33mmoviepy is not installed, run `pip install \u001b[39m\u001b[33m\"\u001b[39m\u001b[33mgymnasium[other]\u001b[39m\u001b[33m\"\u001b[39m\u001b[33m`\u001b[39m\u001b[33m'\u001b[39m\n\u001b[32m     17\u001b[39m     ) \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01me\u001b[39;00m\n\u001b[32m     20\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mcapped_cubic_video_schedule\u001b[39m(episode_id: \u001b[38;5;28mint\u001b[39m) -> \u001b[38;5;28mbool\u001b[39m:\n\u001b[32m     21\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33mr\u001b[39m\u001b[33;03m\"\"\"The default episode trigger.\u001b[39;00m\n\u001b[32m     22\u001b[39m \n\u001b[32m     23\u001b[39m \u001b[33;03m    This function will trigger recordings at the episode indices :math:`\\{0, 1, 4, 8, 27, ..., k^3, ..., 729, 1000, 2000, 3000, ...\\}`\u001b[39;00m\n\u001b[32m   (...)\u001b[39m\u001b[32m     29\u001b[39m \u001b[33;03m        If to apply a video schedule number\u001b[39;00m\n\u001b[32m     30\u001b[39m \u001b[33;03m    \"\"\"\u001b[39;00m\n",
      "\u001b[31mDependencyNotInstalled\u001b[39m: moviepy is not installed, run `pip install \"gymnasium[other]\"`"
     ]
    }
   ],
   "source": [
    "# Select the hyperparameters\n",
    "RUN_ITER = 200  # Number of iterations to run MPC\n",
    "TIMESTEPS = 10  # MPC horizon length\n",
    "N_BATCH = 1  # Batch size for MPC\n",
    "LQR_ITER = 5  # Number of LQR iterations for convergence\n",
    "\n",
    "\n",
    "# Setup the environmnet\n",
    "env = gym.make(\"Pendulum-v1\", render_mode=\"rgb_array\")\n",
    "video_directory = \"mpc_videoss\"\n",
    "env = RecordVideo(env, video_directory)\n",
    "env.reset()  # Reset the underlying environment\n",
    "env.unwrapped.state = [np.pi, 1]  # Environment must start in downward position\n",
    "\n",
    "\n",
    "# Define the cost function and initialize u\n",
    "cost = define_swingup_goal()\n",
    "u_init = None\n",
    "\n",
    "\n",
    "# Run MPC\n",
    "rewards, actions = [], []\n",
    "for _ in (pbar := trange(RUN_ITER)):\n",
    "    state = env.unwrapped.state.copy()\n",
    "    state = torch.tensor(state).view(1, -1)\n",
    "    # recreate controller using updated u_init (kind of wasteful right?)\n",
    "    ctrl = mpc.MPC(\n",
    "        2,\n",
    "        1,\n",
    "        TIMESTEPS,\n",
    "        u_lower=-2.0,\n",
    "        u_upper=+2.0,\n",
    "        lqr_iter=LQR_ITER,\n",
    "        exit_unconverged=False,\n",
    "        eps=1e-2,\n",
    "        n_batch=N_BATCH,\n",
    "        backprop=False,\n",
    "        verbose=0,\n",
    "        u_init=u_init,\n",
    "        grad_method=mpc.GradMethods.AUTO_DIFF,\n",
    "    )\n",
    "\n",
    "    # compute action based on current state, dynamics, and cost\n",
    "    nominal_states, nominal_actions, nominal_objs = ctrl(\n",
    "        state, cost, PendulumDynamics()\n",
    "    )\n",
    "\n",
    "    # Take first planned action\n",
    "    action = nominal_actions[0, 0, 0].item()\n",
    "\n",
    "    # Update u_init\n",
    "    u_init = torch.cat((nominal_actions[1:], torch.zeros(1, N_BATCH, 1)), dim=0)\n",
    "\n",
    "    # Take a step in the environment\n",
    "    state, reward, terminated, truncated, info = env.step([action])\n",
    "\n",
    "    # Store the latest action and reward\n",
    "    actions.append(action)\n",
    "    rewards.append(reward)\n",
    "\n",
    "    pbar.set_description(f\"Action = {actions[-1]:.2f} | Reward = {rewards[-1]:.2f}\")\n",
    "    env.render()\n",
    "\n",
    "env.close()\n",
    "\n",
    "# Plot the results\n",
    "plot_results(rewards, actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 501
    },
    "id": "4FX9ANmENtUO",
    "outputId": "4a8b39a3-7499-481f-c9b8-fd5880df3563"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <source 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type=\"video/mp4\">\n",
       "    Your browser does not support the video tag.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show the policy learned\n",
    "embed_mp4(f\"{video_directory}/rl-video-episode-0.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jskFvBFHLido"
   },
   "source": [
    "# Questions (25 points)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9Pk2jwFVNzTZ"
   },
   "source": [
    "Based on your experiments, answer the following questions:\n",
    "\n",
    "- How does the number of LQR iterations affect the MPC?\n",
    "- What if we didn't have access to the model dynamics? Could we still use MPC?\n",
    "- Do `TIMESTEPS` or `N_BATCH` matter here? Explain.\n",
    "- Why do you think we chose to set the initial state of the environment to the downward position?\n",
    "- As time progresses (later iterations) what happens to the actions and rewards? Why?\n",
    "\n",
    "`Your Answers:`\n",
    "\n",
    "**1. How does the number of LQR iterations affect the MPC?**\n",
    "\n",
    "The number of LQR iterations determines how well the MPC controller converges to the optimal solution. More LQR iterations generally lead to better convergence and more accurate control actions, but at the cost of increased computational time. With too few iterations, the controller might not converge properly and could produce suboptimal actions. However, there's a diminishing returns effect - beyond a certain point, additional iterations provide minimal improvement.\n",
    "\n",
    "**2. What if we didn't have access to the model dynamics? Could we still use MPC?**\n",
    "\n",
    "No, traditional MPC requires an accurate model of the system dynamics to predict future states and optimize control actions. Without the model dynamics, we cannot:\n",
    "\n",
    "- Predict how the system will evolve under different control inputs\n",
    "- Solve the optimization problem that MPC relies on\n",
    "- Plan ahead effectively\n",
    "\n",
    "However, we could potentially use data-driven approaches like:\n",
    "\n",
    "- Learning the dynamics model from data (model learning)\n",
    "- Using neural networks to approximate the dynamics\n",
    "- Model-free reinforcement learning methods instead\n",
    "\n",
    "**3. Do `TIMESTEPS` or `N_BATCH` matter here? Explain.**\n",
    "\n",
    "Yes, both parameters significantly affect MPC performance:\n",
    "\n",
    "- **TIMESTEPS**: This is the prediction horizon length. A longer horizon allows the controller to plan further ahead, which is crucial for tasks like swing-up where the pendulum needs to build momentum over multiple steps. However, longer horizons increase computational cost and may lead to less accurate long-term predictions.\n",
    "\n",
    "- **N_BATCH**: This determines how many parallel optimization problems are solved. In this single-agent case, N_BATCH=1 is appropriate. Larger batch sizes would be useful for multi-agent scenarios or when solving multiple related control problems simultaneously, but they increase computational requirements.\n",
    "\n",
    "**4. Why do you think we chose to set the initial state of the environment to the downward position?**\n",
    "\n",
    "We set the initial state to the downward position (θ=π, θ̇=1) because:\n",
    "\n",
    "- This represents the most challenging starting condition for the swing-up task\n",
    "- It tests the controller's ability to perform the complete swing-up maneuver from the worst-case scenario\n",
    "- Starting from rest (θ=π, θ̇=0) would be easier but less representative of real-world scenarios\n",
    "- It demonstrates the controller's capability to handle the full range of the pendulum's motion\n",
    "\n",
    "**5. As time progresses (later iterations) what happens to the actions and rewards? Why?**\n",
    "\n",
    "As the MPC controller progresses:\n",
    "\n",
    "- **Actions**: Initially, actions are large and aggressive to build momentum for swing-up. As the pendulum approaches the upright position, actions become smaller and more precise for stabilization. Eventually, actions oscillate around small values to maintain balance.\n",
    "\n",
    "- **Rewards**: Rewards start very negative (around -16) due to the pendulum being far from the goal state. As the controller successfully swings up the pendulum, rewards improve significantly. Once the pendulum is balanced upright, rewards stabilize around higher values (closer to 0), with small fluctuations due to the continuous control needed to maintain balance.\n",
    "\n",
    "This behavior occurs because the MPC controller is optimizing for the swing-up and balance task, transitioning from large corrective actions to fine-tuning control as the system approaches the desired state.\n"
   ]
  }
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Xet Storage Details

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