basic_cartpole.ipynb

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  "metadata": {
    "colab": {
      "name": "basic-cartpole.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPdGPEZ3ge2fcaymEQPtZUm",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ruperty/colab/blob/master/basic_cartpole.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g_hgxxphPvr-",
        "colab_type": "text"
      },
      "source": [
        "# Cartpole with PCT\n",
        "\n",
        "A demonstration of Perceptual Control Theory applied to the Inverted Pendulum problem using the simulated environment provided by OpenAI gym. \n",
        "\n",
        "![alt text](http://www.perceptualrobots.com/wp-content/uploads/2020/05/poster-2.jpg)\n",
        "\n",
        "[OpenAI](https://openai.com/) is a program for testing the Reinforcement Learning approach to learning.\n",
        "\n",
        "However, RL is a very convoluted way of addressing this particular problem. RL, and convential AI, seem to see any problem as one of trying to map problem states to actions, which is a fundamental misunderstanding of the nature of the behaviour of living systems. \n",
        "\n",
        "PCT provides a very parsimonious and effective approach which avoids any need to map states and actions. Instead action values are varied dynamically in order to control the perceived inputs.\n",
        "\n",
        "For more information on PCT see http://www.pctweb.org/ and http://perceptualrobots.com/."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IJCy0L7qBD7r",
        "colab_type": "text"
      },
      "source": [
        "# Colab Notebook\n",
        "This page is a \"**notebook**\" which allows users to run code in cells online and see the results, without having to set up a programming environment. \n",
        "\n",
        "You can even add your own code and run that. Though the file is read-only so if you want to keep it you will have to save it as a copy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CthL4lyAB3xS",
        "colab_type": "text"
      },
      "source": [
        "The first few cells are to set up the environment, install and import modules. To run each cell do **shift+enter** or run mutiple cells with the above menu item, **Runtime**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tbTCJ3x_BvXj",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z5wbo9VyPh_d",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#remove \" > /dev/null 2>&1\" to see what is going on under the hood\n",
        "!pip install gym pyvirtualdisplay > /dev/null 2>&1\n",
        "!apt-get install -y xvfb python-opengl ffmpeg > /dev/null 2>&1\n",
        "!apt-get install x11-utils  > /dev/null 2>&1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4B_K-un7Pydl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# imports gym module from OpenAI\n",
        "import gym\n",
        "\n",
        "# some other required modules\n",
        "import numpy as np\n",
        "import glob\n",
        "import io\n",
        "import base64\n",
        "from IPython.display import HTML\n",
        "from IPython import display as ipythondisplay\n",
        "from gym.wrappers import Monitor\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vTQqkc0RPurX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Utility functions to enable video recording of gym environment and displaying it\n",
        "# To enable video, just do \"env = wrap_env(env)\"\"\n",
        "\n",
        "def show_video():\n",
        "  mp4list = glob.glob('video/*.mp4')\n",
        "  if len(mp4list) > 0:\n",
        "    mp4 = mp4list[0]\n",
        "    video = io.open(mp4, 'r+b').read()\n",
        "    encoded = base64.b64encode(video)\n",
        "    ipythondisplay.display(HTML(data='''<video alt=\"test\" autoplay                 \n",
        "                 controls style=\"height: 400px;\">\n",
        "                <source src=\"data:video/mp4;base64,{0}\" type=\"video/mp4\" />\n",
        "             </video>'''.format(encoded.decode('ascii'))))\n",
        "  else: \n",
        "    print(\"Could not find video\")\n",
        "    \n",
        "def wrap_env(env):\n",
        "  env = Monitor(env, './video', force=True)\n",
        "  return env"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kEpluzk3VIP0",
        "colab_type": "code",
        "outputId": "16d4df09-8631-4672-9c01-0777cd777086",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "from pyvirtualdisplay import Display\n",
        "display = Display(visible=0, size=(1400, 900))\n",
        "display.start() "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pyvirtualdisplay.display.Display at 0x7f86b82fe5c0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hrw-DOfwV_k7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# a function to help with plotting the data\n",
        "def add_plot_data(ctr, state, action, plot_data):\n",
        "  if ctr<0:\n",
        "    plot_data = [[0],[state[0]],[state[1]],[state[2]],[state[3]], [0]]\n",
        "  else:\n",
        "   plot_data[0].append(ctr+1)\n",
        "   plot_data[1].append(state[0])\n",
        "   plot_data[2].append(state[1])\n",
        "   plot_data[3].append(state[2])\n",
        "   plot_data[4].append(state[3])\n",
        "   if action : dir=1 \n",
        "   else: dir=-1\n",
        "   plot_data[5].append(dir)\n",
        "  return plot_data\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oNkuup3AVWJn",
        "colab_type": "text"
      },
      "source": [
        "# Cartpole Environment\n",
        "\n",
        "The next cell creates the Cartpole environment and runs some random actions in a loop.\n",
        "\n",
        "The environment provides the values for the Cart Position, Cart Velocity,\tPole Angle and Pole Velocity At Tip, and takes an action of 0 or 1, to move the cart to the left and right, respectively.\n",
        "\n",
        "The loop will run until there is a failure such as pole angle exceeding 12 degrees. A \"reward\" of 1 is awarded for each iteration that the cartpole stays up.\n",
        "\n",
        "A video will be generated showing the cartpole being run. It will be very short as the system will fail quickly as the actions are random."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yc9R70abQESu",
        "colab_type": "code",
        "outputId": "414248ce-2c78-414d-ce9e-82e1b5700dba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        }
      },
      "source": [
        "env = wrap_env(gym.make(\"CartPole-v1\"))\n",
        "state = env.reset()\n",
        "loops = 100\n",
        "plot_data = add_plot_data(-1, state, None, None)\n",
        "reward = 0\n",
        "\n",
        "for i in range(loops):\n",
        "   env.render()\n",
        "   action = env.action_space.sample() # take a random action\n",
        "   observation =env.step(action) \n",
        "   plot_data = add_plot_data(i, observation[0], action, plot_data)\n",
        "   done = observation[2]\n",
        "   reward+=observation[1]\n",
        "   if done: \n",
        "        if i < loops :\n",
        "          print(\"Failed after %d loops with a pole angle of %2.2f degrees\" %( i+1, np.rad2deg(observation[0][2])))\n",
        "        else:\n",
        "          print(\"Finished after \", i, \" loops\")\n",
        "        env.reset()\n",
        "        break\n",
        "\n",
        "print(\"Reward \", reward, \" from \", i+1, \" loops\")\n",
        "env.close()\n",
        "show_video()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Failed after 16 loops with a pole angle of -13.19 degrees\n",
            "Reward  16.0  from  16  loops\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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          "metadata": {
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    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kNCuTFp_ZCKM",
        "colab_type": "text"
      },
      "source": [
        "If the video showed very little you can run the above cell again to see if you get a better result.\n",
        "\n",
        "Ok, let's plot the observed values of the cartpole over the loop.\n",
        "\n",
        "Here are some from the above run:\n",
        "\n",
        "\n",
        "*   The angle of the pole.\n",
        "*   The other values.\n",
        "*   The actions taken, where -1 is left and 1 is right.\n",
        "\n",
        "The pole angle quickly exceeds 12 degrees.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kAAwcrUcE958",
        "colab_type": "code",
        "outputId": "8273ca10-c89a-4125-acfe-aafdf55b0422",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "import plotly.graph_objects as go\n",
        "\n",
        "anglefig = go.Figure()\n",
        "anglefig.add_trace(go.Scatter(mode='markers+lines',x=plot_data[0], y=np.rad2deg(plot_data[3]), name=\"poleAng\"))\n",
        "anglefig.update_layout(title=\"Pole Angle\", xaxis_title=\"Time\", yaxis_title=\"Angle (degrees)\")\n",
        "anglefig.show()\n",
        "\n",
        "fig = go.Figure()\n",
        "fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[1], name=\"cartPos\"))\n",
        "fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[2], name=\"cartVel\"))\n",
        "fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[4], name=\"poleVel\"))\n",
        "fig.update_layout(title=\"Other values\", xaxis_title=\"Time\", yaxis_title=\"Angle/Pos\")\n",
        "fig.show()\n",
        "\n",
        "actionfig = go.Figure()\n",
        "actionfig.add_trace(go.Scatter(mode='markers+lines',line=dict(color='firebrick'),x=plot_data[0], y=plot_data[5], name=\"direction\"))\n",
        "actionfig.update_layout(title=\"Action\", xaxis_title=\"Time\", yaxis_title=\"Direction\")\n",
        "actionfig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
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      "source": [
        "# Perceptual Control\n",
        "\n",
        "Controlling the cartpole with PCT requires a small hierarchy of four levels:\n",
        "\n",
        "\n",
        "\n",
        "*   At the top, a unit that controls the pole angle by varying the pole velocity,\n",
        "*   then one that controls pole velocity by varying the cart position,\n",
        "*   then one that controls cart position by varying the cart velocity,\n",
        "*   then one that controls cart velocity by varying the direction of movement.\n",
        "\n",
        "For more details see [Richard Kennaway's description](http://www.livingcontrolsystems.com/demos/inverted_pendulum/inverted_pendulum.pdf). The control model on this page doesn't inlcude an integrator function as the intention is just to keep the cartpole upright in the central position. My next demo will show an integrator allows you to move the cartpole to different postions. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
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        "id": "5IatbmBpqmGl",
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      },
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        "# a function to help with plotting the data\n",
        "def add_control_plot_data(ctr, pole_angle_ref, pole_angle, pole_velocity_ref, pole_velocity, cart_position_ref, cart_position, cart_velocity_ref, cart_velocity, action, plot_data):\n",
        "  if ctr<0:\n",
        "    plot_data = [[0],[0],[pole_angle],[0],[pole_velocity],[0],[cart_position],[0],[cart_velocity], [0]]\n",
        "  else:\n",
        "   plot_data[0].append(ctr+1)\n",
        "   plot_data[1].append(pole_angle_ref)\n",
        "   plot_data[2].append(pole_angle)\n",
        "   plot_data[3].append(pole_velocity_ref)\n",
        "   plot_data[4].append(pole_velocity)\n",
        "   plot_data[5].append(cart_position_ref)\n",
        "   plot_data[6].append(cart_position)\n",
        "   plot_data[7].append(cart_velocity_ref)\n",
        "   plot_data[8].append(cart_velocity)\n",
        "   if action : dir=1 \n",
        "   else: dir=-1\n",
        "   plot_data[9].append(dir)\n",
        "  return plot_data"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hnGbMXHYQMYf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# the four-level control hierarchy\n",
        "def controller(ctr, pole_angle_ref, cart_position, cart_velocity, pole_angle, pole_velocity, plot_data):\n",
        "    pole_velocity_ref=proportional(pole_angle_ref, pole_angle, pole_angle_gain)\n",
        "    cart_position_ref=proportional(pole_velocity_ref, pole_velocity, pole_velocity_gain)\n",
        "    cart_velocity_ref=proportional(cart_position_ref, cart_position, cart_position_gain)\n",
        "    power=proportional(cart_velocity_ref, cart_velocity, cart_velocity_gain)\n",
        "    \n",
        "    action=1\n",
        "    if power>=0:\n",
        "        action = 0\n",
        "    \n",
        "    plot_data=add_control_plot_data(ctr, pole_angle_ref, pole_angle, pole_velocity_ref, pole_velocity, cart_position_ref, cart_position, cart_velocity_ref, cart_velocity, action, plot_data)\n",
        "      \n",
        "    return action, plot_data\n",
        "\n",
        "def proportional(r, p, g):\n",
        "    return (r-p)*g\n",
        "\n",
        "def get_states(state):\n",
        "    cart_position = state[0]\n",
        "    cart_velocity = state[1]\n",
        "    pole_angle = state[2]\n",
        "    pole_velocity = state[3]\n",
        "    return cart_position, cart_velocity, pole_angle, pole_velocity \n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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      "source": [
        "# some configuration settings\n",
        "pole_angle_ref = 0\n",
        "loops = 1000\n",
        "pole_angle_gain = 3\n",
        "pole_velocity_gain = 2\n",
        "cart_position_gain = 1\n",
        "cart_velocity_gain = 1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T6CslocZl9n0",
        "colab_type": "code",
        "outputId": "d49806ce-86d7-4db1-a1aa-33e008ffd133",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 438
        }
      },
      "source": [
        "genv = gym.make(\"CartPole-v1\")\n",
        "genv._max_episode_steps = 4000\n",
        "env = wrap_env(genv)\n",
        "reward = 0\n",
        "\n",
        "state = env.reset()\n",
        "cart_position, cart_velocity, pole_angle, pole_velocity = get_states(state)\n",
        "plot_data=add_control_plot_data(-1, 0, pole_angle, 0, pole_velocity, 0, cart_position, 0, cart_velocity, 0, None)\n",
        "\n",
        "for ctr in range(loops):\n",
        "    env.render()\n",
        "    action, plot_data = controller(ctr, pole_angle_ref, cart_position, cart_velocity, pole_angle, pole_velocity, plot_data)    \n",
        "    observation =env.step(action)    \n",
        "    done = observation[2]\n",
        "    reward+=observation[1]\n",
        "    cart_position, cart_velocity, pole_angle, pole_velocity = get_states(observation[0])\n",
        "    if done: \n",
        "        print(ctr, observation)\n",
        "        break\n",
        " \n",
        "print(\"Reward \", reward, \" from \", ctr+1, \" loops\")    \n",
        "\n",
        "env.close()\n",
        "show_video()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reward  1000.0  from  1000  loops\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<video alt=\"test\" autoplay                 \n",
              "                 controls style=\"height: 400px;\">\n",
              "                <source 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type=\"video/mp4\" />\n",
              "             </video>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yj1TfvO_Itw6",
        "colab_type": "text"
      },
      "source": [
        "# Results\n",
        "It might look, in the above video, that nothing is happening. Well, that is because the control is very good. The system moves the pole to being balanced in a few moves and it stays that way for the remainder of the run. \n",
        "\n",
        "As you will see from the plots below each of the perceived (observed) variables denothing the state of the cart are kept low, around zero, which corresponds to the pole being upright and the car in the centre of the track.\n",
        "\n",
        "The pole angle, particularly, is kept under 0.5 of a degree from vertical, well away from the failure value of 12 degrees."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j_qjCIYhmAfr",
        "colab_type": "code",
        "outputId": "1f899bb4-931d-4b12-8745-c10b0ad0ada2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "# the control plots\n",
        "pole_angle_fig = go.Figure()\n",
        "pole_angle_fig.add_trace(go.Scatter(x=plot_data[0], y=np.rad2deg(plot_data[1]), name=\"ref\"))\n",
        "pole_angle_fig.add_trace(go.Scatter(x=plot_data[0], y=np.rad2deg(plot_data[2]), name=\"perc\"))\n",
        "pole_angle_fig.update_layout(title=\"Pole Angle\", xaxis_title=\"Time\", yaxis_title=\"Angle (degrees)\")\n",
        "pole_angle_fig.show()\n",
        "\n",
        "pole_velocity_fig = go.Figure()\n",
        "pole_velocity_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[3], name=\"ref\"))\n",
        "pole_velocity_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[4], name=\"perc\"))\n",
        "pole_velocity_fig.update_layout(title=\"Pole Velocity\", xaxis_title=\"Time\", yaxis_title=\"Velocity\")\n",
        "pole_velocity_fig.show()\n",
        "\n",
        "cart_position_fig = go.Figure()\n",
        "cart_position_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[5], name=\"ref\"))\n",
        "cart_position_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[6], name=\"perc\"))\n",
        "cart_position_fig.update_layout(title=\"Cart Position\", xaxis_title=\"Time\", yaxis_title=\"Position\")\n",
        "cart_position_fig.show()\n",
        "\n",
        "cart_velocity_fig = go.Figure()\n",
        "cart_velocity_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[7], name=\"ref\"))\n",
        "cart_velocity_fig.add_trace(go.Scatter(x=plot_data[0], y=plot_data[8], name=\"perc\"))\n",
        "cart_velocity_fig.update_layout(title=\"Cart Velocity\", xaxis_title=\"Time\", yaxis_title=\"Velocity\")\n",
        "cart_velocity_fig.show()\n",
        "\n",
        "actionfig = go.Figure()\n",
        "actionfig.add_trace(go.Scatter(line=dict(color='firebrick'),x=plot_data[0], y=plot_data[9], name=\"direction\"))\n",
        "actionfig.update_layout(title=\"Action\", xaxis_title=\"Time\", yaxis_title=\"Direction\")\n",
        "actionfig.show()\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<html>\n",
              "<head><meta charset=\"utf-8\" /></head>\n",
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        "# What Next?\n",
        "\n",
        "That's it for now. So, what next?\n",
        "\n",
        "Well, this system controls well, balancing the pole, but it just stays in the same position. It has to do this because its aim is to keep all the goal values at zero. One of these is the cart position which is the centre of the environment. So, it can not move from this position.\n",
        "\n",
        "It would be great if the cart could move around, while keeping the pole balanced. That is the subject of the next demo, https://colab.research.google.com/github/ruperty/colab/blob/master/moving_cartpole.ipynb.\n",
        "\n",
        "\n",
        "\n",
        "After that perhaps one that optimises the gain values of the control units to see if the stability of the system can be increased."
      ]
    }
  ]
}