Robotics_Group_Project.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sophiadt/robot-waiter-AI/blob/main/Robotics_Group_Project.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rLOvw52upRHP"
      },
      "source": [
        "# Setup\n",
        "\n",
        "We will be using GPU runtime with a CUDA backend. Let's change the runtime.\n",
        "\n",
        "**Runtime ⟶ Change runtime type ⟶ Hardware accelerator: GPU ⟶ Save**\n",
        "\n",
        "First we will install the libraries and download the datasets. This may take a few minutes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oJN4oxukpnn4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f620d55-1e1d-45d6-fda3-de967527b179"
      },
      "source": [
        "# install packages\n",
        "!apt-get install build-essential cmake\n",
        "!apt-get install libopenblas-dev liblapack-dev \n",
        "!pip3 install dlib\n",
        "!pip3 install face_recognition"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "build-essential is already the newest version (12.4ubuntu1).\n",
            "cmake is already the newest version (3.10.2-1ubuntu2.18.04.1).\n",
            "0 upgraded, 0 newly installed, 0 to remove and 40 not upgraded.\n",
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "liblapack-dev is already the newest version (3.7.1-4ubuntu1).\n",
            "libopenblas-dev is already the newest version (0.2.20+ds-4).\n",
            "0 upgraded, 0 newly installed, 0 to remove and 40 not upgraded.\n",
            "Requirement already satisfied: dlib in /usr/local/lib/python3.7/dist-packages (19.18.0)\n",
            "Collecting face_recognition\n",
            "  Downloading face_recognition-1.3.0-py2.py3-none-any.whl (15 kB)\n",
            "Collecting face-recognition-models>=0.3.0\n",
            "  Downloading face_recognition_models-0.3.0.tar.gz (100.1 MB)\n",
            "\u001b[K     |████████████████████████████████| 100.1 MB 6.5 kB/s \n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from face_recognition) (1.19.5)\n",
            "Requirement already satisfied: dlib>=19.7 in /usr/local/lib/python3.7/dist-packages (from face_recognition) (19.18.0)\n",
            "Requirement already satisfied: Pillow in /usr/local/lib/python3.7/dist-packages (from face_recognition) (7.1.2)\n",
            "Requirement already satisfied: Click>=6.0 in /usr/local/lib/python3.7/dist-packages (from face_recognition) (7.1.2)\n",
            "Building wheels for collected packages: face-recognition-models\n",
            "  Building wheel for face-recognition-models (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for face-recognition-models: filename=face_recognition_models-0.3.0-py2.py3-none-any.whl size=100566184 sha256=0f8069d3940158340d4e9049b9e68d02c43db294e020772885c8aefd08258e85\n",
            "  Stored in directory: /root/.cache/pip/wheels/d6/81/3c/884bcd5e1c120ff548d57c2ecc9ebf3281c9a6f7c0e7e7947a\n",
            "Successfully built face-recognition-models\n",
            "Installing collected packages: face-recognition-models, face-recognition\n",
            "Successfully installed face-recognition-1.3.0 face-recognition-models-0.3.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JXBUt7mLpEBj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aac4bd5a-658e-446c-c2b8-ec1a7d248b10"
      },
      "source": [
        "!rm -r ./sample_data/\n",
        "!gdown --id 1IsYNzt2CRM3RhZ9EEipOYpdPRTHwBXY6\n",
        "!unzip project.zip\n",
        "!rm project.zip"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading...\n",
            "From: https://drive.google.com/uc?id=1IsYNzt2CRM3RhZ9EEipOYpdPRTHwBXY6\n",
            "To: /content/project.zip\n",
            "\r  0% 0.00/800k [00:00<?, ?B/s]\r100% 800k/800k [00:00<00:00, 53.4MB/s]\n",
            "Archive:  project.zip\n",
            "   creating: customers/\n",
            "   creating: customers/1/\n",
            "  inflating: customers/1/1.jpg       \n",
            "   creating: customers/0/\n",
            "  inflating: customers/0/2.jpg       \n",
            "   creating: customers/3/\n",
            "  inflating: customers/3/3.jpg       \n",
            "   creating: customers/4/\n",
            "  inflating: customers/4/4.jpg       \n",
            "   creating: customers/2/\n",
            "  inflating: customers/2/5.jpg       \n",
            "   creating: floorplan/\n",
            "  inflating: floorplan/restaurant_1.png  \n",
            "   creating: orders/\n",
            "  inflating: orders/rey.jpg          \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dP_4sXSgtiAe"
      },
      "source": [
        "# import libraries\n",
        "import os\n",
        "\n",
        "import numpy as np\n",
        "from skimage.feature import hog\n",
        "from skimage import data, exposure\n",
        "import face_recognition\n",
        "\n",
        "from PIL import Image, ImageEnhance, ImageDraw\n",
        "import IPython.display\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as patches\n",
        "%matplotlib inline\n",
        "\n",
        "font_config = {'size': 16}\n",
        "fig_config = {'figsize': (12, 8)}\n",
        "line_config = {'linewidth': 4}\n",
        "plt.rc('font', **font_config)\n",
        "plt.rc('figure', **fig_config)\n",
        "plt.rc('lines', **line_config)\n",
        "\n",
        "rc = {\"axes.spines.left\" : False,\n",
        "      \"axes.spines.right\" : False,\n",
        "      \"axes.spines.bottom\" : False,\n",
        "      \"axes.spines.top\" : False,\n",
        "      \"xtick.bottom\" : False,\n",
        "      \"xtick.labelbottom\" : False,\n",
        "      \"ytick.labelleft\" : False,\n",
        "      \"ytick.left\" : False}\n",
        "plt.rcParams.update(rc)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CVCPHc2fp9zD"
      },
      "source": [
        "# Read images and setup environment\n",
        "\n",
        "The folder structure is as follows:\n",
        "\n",
        "```\n",
        "├── customers\n",
        "│   ├── 1\n",
        "│   ├── ├── <somename>.jpg\n",
        "│   ├── 2\n",
        "│   ├── ├── <somename>.jpg\n",
        "│   ├── ...\n",
        "├── orders/\n",
        "│   ├── <somename1>.jpg\n",
        "│   └── <somename2>.jpg\n",
        "└── floorplan/\n",
        "│   ├── <floor>.jpg\n",
        "```\n",
        "We have added one image per customer, one image for the customer who placed an order, and one floorplan image. You can follow the training example from the lesson and add more images per person, and add multiple orders. The sample floorplan is a 32x32 image where the black colored cells represent obstacles.\n",
        "\n",
        "We will randomly generate robot location and location of each customer in the walkable area.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oCndQ6OHrcFf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 589
        },
        "outputId": "7a69de96-a812-4b98-a6f0-f287d7e2ca6c"
      },
      "source": [
        "# np.random.seed(0)     # seed random generator if you want to reproduce the results\n",
        "\n",
        "floorplan = plt.imread('floorplan/restaurant_1.png')[:, :, 0]\n",
        "customers = [c for c in os.listdir('customers/') if not c.startswith('.')]\n",
        "print(f\"Found {len(customers)} customers.\", floorplan.shape)\n",
        "\n",
        "# find white cells and obstacles in floorplan\n",
        "free_space = np.asarray(np.where(floorplan == 1)).T\n",
        "obstacles = np.asarray(np.where(floorplan == 0)).T\n",
        "\n",
        "#select random positions for robot and customers\n",
        "idx_robot = np.random.choice(len(free_space))\n",
        "position_robot = free_space[idx_robot]\n",
        "print(f\"Robot position is {position_robot}\")\n",
        "\n",
        "idx_customer = np.random.choice(len(free_space), len(customers))\n",
        "position_customers = free_space[idx_customer]\n",
        "for i, customer in enumerate(customers):\n",
        "  print(f\"Customer {customer} is at {position_customers[i]}\")\n",
        "\n",
        "plt.figure()\n",
        "figure_bounds = np.asarray([0, floorplan.shape[0], 0, floorplan.shape[1]]) -0.5   # (x,y) is the center of cell\n",
        "plt.imshow(np.flipud(floorplan.T), extent=figure_bounds, cmap='Greys_r')          # images and matrixes are indexed differently. Use this to plot floorplan image.\n",
        "plt.scatter(position_robot[0], position_robot[1], c='b')\n",
        "plt.scatter(position_customers[:, 0], position_customers[:, 1], c='r')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Found 5 customers. (32, 32)\n",
            "Robot position is [18  8]\n",
            "Customer 1 is at [26 17]\n",
            "Customer 4 is at [13 19]\n",
            "Customer 2 is at [ 2 17]\n",
            "Customer 0 is at [10  8]\n",
            "Customer 3 is at [14 24]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xstcWJAb0Tuw"
      },
      "source": [
        "For each order identify which customer has placed the order."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UtEzm_x_0TGh"
      },
      "source": [
        "# Write code to train and predict face recognition\n",
        "# Hint: get relevant code from the lesson\n",
        "import math\n",
        "import os\n",
        "import os.path\n",
        "import pickle\n",
        "\n",
        "from sklearn import neighbors\n",
        "from face_recognition.face_recognition_cli import image_files_in_folder\n",
        "\n",
        "ALLOWED_EXTENSIONS = {'png', 'jpg', 'jpeg'}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0HbKFFqU43Fa"
      },
      "source": [
        "def train(train_dir, model_save_path=None, n_neighbors=None, knn_algo='ball_tree', verbose=False):\n",
        "    '''\n",
        "    :param train_dir: directory that contains a sub-directory for each known person, with its name.\n",
        "     (View in source code to see train_dir example tree structure)\n",
        "     Structure:\n",
        "        <train_dir>/\n",
        "        ├── <person1>/\n",
        "        │   ├── <somename1>.jpeg\n",
        "        │   ├── <somename2>.jpeg\n",
        "        │   ├── ...\n",
        "        ├── <person2>/\n",
        "        │   ├── <somename1>.jpeg\n",
        "        │   └── <somename2>.jpeg\n",
        "        └── ...\n",
        "    :param model_save_path: (optional) path to save model on disk\n",
        "    :param n_neighbors: (optional) number of neighbors to weigh in classification. Chosen automatically if not specified\n",
        "    :param knn_algo: (optional) underlying data structure to support knn.default is ball_tree\n",
        "    :param verbose: verbosity of training\n",
        "    :return: returns knn classifier that was trained on the given data.\n",
        "     '''\n",
        "    X = []\n",
        "    y = []\n",
        "\n",
        "    # Loop through each person in the training set\n",
        "    for class_dir in os.listdir(train_dir):\n",
        "        if not os.path.isdir(os.path.join(train_dir, class_dir)):\n",
        "            continue\n",
        "\n",
        "        # Loop through each training image for the current person\n",
        "        for img_path in image_files_in_folder(os.path.join(train_dir, class_dir)):\n",
        "            image = face_recognition.load_image_file(img_path)\n",
        "            face_bounding_boxes = face_recognition.face_locations(image)\n",
        "\n",
        "            if len(face_bounding_boxes) != 1:\n",
        "                # If there are no people (or too many people) in a training image, skip the image.\n",
        "                if verbose:\n",
        "                    print(\"Image {} not suitable for training: {}\".format(img_path, \"Didn't find a face\" if len(face_bounding_boxes) < 1 else \"Found more than one face\"))\n",
        "            else:\n",
        "                # Add face encoding for current image to the training set\n",
        "                X.append(face_recognition.face_encodings(image, known_face_locations=face_bounding_boxes)[0])\n",
        "                y.append(class_dir)\n",
        "\n",
        "    # Determine how many neighbors to use for weighting in the KNN classifier\n",
        "    if n_neighbors is None:\n",
        "        n_neighbors = int(round(math.sqrt(len(X))))\n",
        "        if verbose:\n",
        "            print(\"Chose n_neighbors automatically:\", n_neighbors)\n",
        "\n",
        "    # Create and train the KNN classifier\n",
        "    knn_clf = neighbors.KNeighborsClassifier(n_neighbors=n_neighbors, algorithm=knn_algo, weights='distance')\n",
        "    knn_clf.fit(X, y)\n",
        "\n",
        "    # Save the trained KNN classifier\n",
        "    if model_save_path is not None:\n",
        "        with open(model_save_path, 'wb') as f:\n",
        "            pickle.dump(knn_clf, f)\n",
        "\n",
        "    return knn_clf"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "czwGc9C64-DN"
      },
      "source": [
        "def predict(X_img_path, knn_clf=None, model_path=None, distance_threshold=0.6):\n",
        "    \"\"\"\n",
        "    Recognizes faces in given image using a trained KNN classifier\n",
        "    :param X_img_path: path to image to be recognized\n",
        "    :param knn_clf: (optional) a knn classifier object. if not specified, model_save_path must be specified.\n",
        "    :param model_path: (optional) path to a pickled knn classifier. if not specified, model_save_path must be knn_clf.\n",
        "    :param distance_threshold: (optional) distance threshold for face classification. the larger it is, the more chance\n",
        "           of mis-classifying an unknown person as a known one.\n",
        "    :return: a list of names and face locations for the recognized faces in the image: [(name, bounding box), ...].\n",
        "        For faces of unrecognized persons, the name 'unknown' will be returned.\n",
        "    \"\"\"\n",
        "    \n",
        "    # Load a trained KNN model (if one was passed in)\n",
        "    if knn_clf is None:\n",
        "        with open(model_path, 'rb') as f:\n",
        "            knn_clf = pickle.load(f)\n",
        "\n",
        "    # Load image file and find face locations\n",
        "    X_img = face_recognition.load_image_file(X_img_path)\n",
        "    X_face_locations = face_recognition.face_locations(X_img)\n",
        "\n",
        "    # If no faces are found in the image, return an empty result.\n",
        "    if len(X_face_locations) == 0:\n",
        "        return []\n",
        "\n",
        "    # Find encodings for faces in the test iamge\n",
        "    faces_encodings = face_recognition.face_encodings(X_img, known_face_locations=X_face_locations)\n",
        "\n",
        "    # Use the KNN model to find the best matches for the test face\n",
        "    closest_distances = knn_clf.kneighbors(faces_encodings, n_neighbors=2)\n",
        "    are_matches = [closest_distances[0][i][0] <= distance_threshold for i in range(len(X_face_locations))]\n",
        "\n",
        "    # Predict classes and remove classifications that aren't within the threshold\n",
        "    return [(pred, loc) if rec else (\"unknown\", loc) for pred, loc, rec in zip(knn_clf.predict(faces_encodings), X_face_locations, are_matches)]\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HZwyDDGI5Bsc"
      },
      "source": [
        "def show_prediction_labels_on_image(img_path, predictions):\n",
        "    \"\"\"\n",
        "    :param img_path: path to image to be recognized\n",
        "    :param predictions: results of the predict function\n",
        "    :return:\n",
        "    \"\"\"\n",
        "    pil_image = plt.imread(img_path)\n",
        "    fig,ax = plt.subplots(1)\n",
        "    ax.imshow(pil_image)\n",
        "    \n",
        "    for name, (top, right, bottom, left) in predictions:\n",
        "        # Draw a box around the face using the Pillow module\n",
        "        color = tuple(np.random.rand(3))\n",
        "        ax.add_patch(patches.Rectangle((left, top), right-left, bottom-top, fill=False, color=color)) \n",
        "        # Add the name under the face bounding box\n",
        "        ax.text(left, bottom, name,  horizontalalignment='left', verticalalignment='top',\n",
        "                bbox={'facecolor':color,'alpha':0.4, 'pad':1})\n",
        "    plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8HXOYeuK18Zb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f305078e-f576-4d23-def0-ca02657be92a"
      },
      "source": [
        "# STEP 1: Train the KNN classifier and save it to disk\n",
        "# Once the model is trained and saved, you can skip this step next time.\n",
        "print(\"Training KNN classifier...\")\n",
        "if not os.path.exists('out'):\n",
        "      os.makedirs(\"out\")\n",
        "classifier = train(\"customers\", model_save_path=\"out/trained_knn_model.clf\", n_neighbors=1)\n",
        "print(\"Training complete!\")\n",
        "\n",
        "# STEP 2: Using the trained classifier, make predictions for unknown image. (We only have one image)\n",
        "image_file = [f for f in os.listdir(\"orders\") if f.endswith('.jpg')][0]\n",
        "full_file_path = os.path.join(\"orders\", image_file)\n",
        "\n",
        "print(\"Looking for faces in {}\".format(image_file))\n",
        "\n",
        "# Find the person in the image using a trained classifier model\n",
        "predictions = predict(full_file_path, model_path=\"out/trained_knn_model.clf\")\n",
        "\n",
        "# We only have one person in the image.\n",
        "name, location = predictions[0]\n",
        "\n",
        "print(\"Identified {} as customer {}\".format(image_file.split('.')[0], name))\n",
        "print(\"{} is at position {}\".format(image_file.split('.')[0], position_customers[int(name)]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training KNN classifier...\n",
            "Training complete!\n",
            "Looking for faces in rey.jpg\n",
            "Identified rey as customer 2\n",
            "rey is at position [ 2 17]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FZMyOscE4sbr"
      },
      "source": [
        "Now use any Path planning algorithm with robot position as start node and customer position as end node"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8vPjnezgucHA"
      },
      "source": [
        "class Env:\n",
        "    def __init__(self):\n",
        "        self.x_range = 32  # size of background\n",
        "        self.y_range = 32\n",
        "        self.motions = [(-1, 0), (-1, 1), (0, 1), (1, 1),\n",
        "                        (1, 0), (1, -1), (0, -1), (-1, -1)]\n",
        "        self.obs = self.obs_map()\n",
        "\n",
        "    def update_obs(self, obs):\n",
        "        self.obs = obs\n",
        "\n",
        "    def obs_map(self):\n",
        "        \"\"\"\n",
        "        Initialize obstacles' positions\n",
        "        :return: map of obstacles\n",
        "        \"\"\"\n",
        "\n",
        "        x = self.x_range\n",
        "        y = self.y_range\n",
        "        obs = set()\n",
        "\n",
        "        obstacles = np.asarray(np.where(floorplan == 0)).T\n",
        "        obs = set()\n",
        "        for i in range(len(obstacles)):\n",
        "          obs.add((obstacles[i, 0], obstacles[i, 1]))\n",
        "\n",
        "\n",
        "        return obs"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2wr54BD9uWKG"
      },
      "source": [
        "import os\n",
        "import sys\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Plotting:\n",
        "    def __init__(self, xI, xG):\n",
        "        self.xI, self.xG = xI, xG\n",
        "        self.env = Env()\n",
        "        self.obs = self.env.obs_map()\n",
        "\n",
        "    def update_obs(self, obs):\n",
        "        self.obs = obs\n",
        "\n",
        "    def animation(self, path, visited, name):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited(visited)\n",
        "        self.plot_path(path)\n",
        "        plt.show()\n",
        "\n",
        "    def animation_lrta(self, path, visited, name):\n",
        "        self.plot_grid(name)\n",
        "        cl = self.color_list_2()\n",
        "        path_combine = []\n",
        "\n",
        "        for k in range(len(path)):\n",
        "            self.plot_visited(visited[k], cl[k])\n",
        "            plt.pause(0.2)\n",
        "            self.plot_path(path[k])\n",
        "            path_combine += path[k]\n",
        "            plt.pause(0.2)\n",
        "        if self.xI in path_combine:\n",
        "            path_combine.remove(self.xI)\n",
        "        self.plot_path(path_combine)\n",
        "        plt.show()\n",
        "\n",
        "    def animation_ara_star(self, path, visited, name):\n",
        "        self.plot_grid(name)\n",
        "        cl_v, cl_p = self.color_list()\n",
        "\n",
        "        for k in range(len(path)):\n",
        "            self.plot_visited(visited[k], cl_v[k])\n",
        "            self.plot_path(path[k], cl_p[k], True)\n",
        "            plt.pause(0.5)\n",
        "\n",
        "        plt.show()\n",
        "\n",
        "    def animation_bi_astar(self, path, v_fore, v_back, name):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited_bi(v_fore, v_back)\n",
        "        self.plot_path(path)\n",
        "        plt.show()\n",
        "\n",
        "    def plot_grid(self, name):\n",
        "        obs_x = [x[0] for x in self.obs]\n",
        "        obs_y = [x[1] for x in self.obs]\n",
        "\n",
        "        plt.plot(self.xI[0], self.xI[1], \"bs\")\n",
        "        plt.plot(self.xG[0], self.xG[1], \"gs\")\n",
        "        plt.plot(obs_x, obs_y, \"sk\")\n",
        "        plt.title(name)\n",
        "        plt.axis(\"equal\")\n",
        "\n",
        "    def plot_visited(self, visited, cl='gray'):\n",
        "        if self.xI in visited:\n",
        "            visited.remove(self.xI)\n",
        "\n",
        "        if self.xG in visited:\n",
        "            visited.remove(self.xG)\n",
        "\n",
        "        count = 0\n",
        "\n",
        "        for x in visited:\n",
        "            count += 1\n",
        "            plt.plot(x[0], x[1], color=cl, marker='o')\n",
        "            plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                         lambda event: [exit(0) if event.key == 'escape' else None])\n",
        "\n",
        "            if count < len(visited) / 3:\n",
        "                length = 20\n",
        "            elif count < len(visited) * 2 / 3:\n",
        "                length = 30\n",
        "            else:\n",
        "                length = 40\n",
        "            #\n",
        "            # length = 15\n",
        "\n",
        "            if count % length == 0:\n",
        "                plt.pause(0.001)\n",
        "        plt.pause(0.01)\n",
        "\n",
        "    def plot_path(self, path, cl='r', flag=False):\n",
        "        path_x = [path[i][0] for i in range(len(path))]\n",
        "        path_y = [path[i][1] for i in range(len(path))]\n",
        "\n",
        "        if not flag:\n",
        "            plt.plot(path_x, path_y, linewidth='3', color='r')\n",
        "        else:\n",
        "            plt.plot(path_x, path_y, linewidth='3', color=cl)\n",
        "\n",
        "        plt.plot(self.xI[0], self.xI[1], \"bs\")\n",
        "        plt.plot(self.xG[0], self.xG[1], \"gs\")\n",
        "\n",
        "        plt.pause(0.01)\n",
        "\n",
        "    def plot_visited_bi(self, v_fore, v_back):\n",
        "        if self.xI in v_fore:\n",
        "            v_fore.remove(self.xI)\n",
        "\n",
        "        if self.xG in v_back:\n",
        "            v_back.remove(self.xG)\n",
        "\n",
        "        len_fore, len_back = len(v_fore), len(v_back)\n",
        "\n",
        "        for k in range(max(len_fore, len_back)):\n",
        "            if k < len_fore:\n",
        "                plt.plot(v_fore[k][0], v_fore[k][1], linewidth='3', color='gray', marker='o')\n",
        "            if k < len_back:\n",
        "                plt.plot(v_back[k][0], v_back[k][1], linewidth='3', color='cornflowerblue', marker='o')\n",
        "\n",
        "            plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                         lambda event: [exit(0) if event.key == 'escape' else None])\n",
        "\n",
        "            if k % 10 == 0:\n",
        "                plt.pause(0.001)\n",
        "        plt.pause(0.01)\n",
        "\n",
        "    @staticmethod\n",
        "    def color_list():\n",
        "        cl_v = ['silver',\n",
        "                'wheat',\n",
        "                'lightskyblue',\n",
        "                'royalblue',\n",
        "                'slategray']\n",
        "        cl_p = ['gray',\n",
        "                'orange',\n",
        "                'deepskyblue',\n",
        "                'red',\n",
        "                'm']\n",
        "        return cl_v, cl_p\n",
        "\n",
        "    @staticmethod\n",
        "    def color_list_2():\n",
        "        cl = ['silver',\n",
        "              'steelblue',\n",
        "              'dimgray',\n",
        "              'cornflowerblue',\n",
        "              'dodgerblue',\n",
        "              'royalblue',\n",
        "              'plum',\n",
        "              'mediumslateblue',\n",
        "              'mediumpurple',\n",
        "              'blueviolet',\n",
        "              ]\n",
        "        return cl"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "Gw7ioLB93nUh",
        "outputId": "6b9128a2-0256-4b2b-a7a4-263068bb8b98"
      },
      "source": [
        "# Write code here\n",
        "\"\"\"\n",
        "ITF 2021\n",
        "Author: Pedram  Agand\n",
        "pagand@sfu.ca\n",
        "\"\"\"\n",
        "\n",
        "import os\n",
        "import sys\n",
        "import math\n",
        "import heapq\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "class AStar:\n",
        "    \"\"\"AStar set the cost + heuristics as the priority\n",
        "    \"\"\"\n",
        "    def __init__(self, s_start, s_goal, heuristic_type):\n",
        "        self.s_start = s_start #inital position\n",
        "        self.s_goal = s_goal #goal position \n",
        "        self.heuristic_type = heuristic_type \n",
        "\n",
        "        self.Env = Env()  # class Env\n",
        "\n",
        "        self.u_set = self.Env.motions  # feasible input set, up down right left\n",
        "        self.obs = self.Env.obs  # position of obstacles\n",
        "\n",
        "        self.OPEN = []  # priority queue / OPEN set\n",
        "        self.CLOSED = []  # CLOSED set / VISITED order\n",
        "        self.PARENT = dict()  # recorded parent\n",
        "        self.g = dict()  # cost to come\n",
        "\n",
        "    def searching(self):\n",
        "        \"\"\"\n",
        "        A_star Searching.\n",
        "        :return: path, visited order\n",
        "        \"\"\"\n",
        "\n",
        "        self.PARENT[self.s_start] = self.s_start\n",
        "        self.g[self.s_start] = 0\n",
        "        self.g[self.s_goal] = math.inf\n",
        "        heapq.heappush(self.OPEN,\n",
        "                       (self.f_value(self.s_start), self.s_start))\n",
        "\n",
        "        while self.OPEN:\n",
        "          _, s = heapq.heappop(self.OPEN)\n",
        "          self.CLOSED.append(s)\n",
        "          print(s)\n",
        "          \"\"\" Edit 1:\n",
        "          <put stop condition> \"\"\"\n",
        "          if s == self.s_goal: #s means current node, current position\n",
        "            print(\"Congrats! You've found the end!\")\n",
        "            break\n",
        "\n",
        "          for s_n in self.get_neighbor(s):\n",
        "            \"\"\" Edit 2:\n",
        "            <compute new_cost> \"\"\"\n",
        "            new_cost = self.g[s] + self.cost(s, s_n) #why were these the two parameters?\n",
        "#current cost + cost from current to end \n",
        "            if s_n not in self.g:\n",
        "                  self.g[s_n] = math.inf\n",
        "#incorrect position\n",
        "            if new_cost < self.g[s_n]: # conditions for updating Cost\n",
        "              \"\"\" Edit 3:\n",
        "              <update cost: g and PARENT elements> \"\"\"\n",
        "              self.g[s_n] = new_cost\n",
        "              self.PARENT[s_n] = s\n",
        "#less cost (better), closer to position ie. moving from est. 18-20(s)\n",
        "              heapq.heappush(self.OPEN, (self.f_value(s_n), s_n))\n",
        "\n",
        "        return self.extract_path(self.PARENT), self.CLOSED\n",
        "\n",
        "    def searching_repeated_astar(self, e):\n",
        "        \"\"\"\n",
        "        repeated A*.\n",
        "        :param e: weight of A*\n",
        "        :return: path and visited order\n",
        "        \"\"\"\n",
        "\n",
        "        path, visited = [], []\n",
        "\n",
        "        while e >= 1:\n",
        "            p_k, v_k = self.repeated_searching(self.s_start, self.s_goal, e)\n",
        "            path.append(p_k)\n",
        "            visited.append(v_k)\n",
        "            e -= 0.5\n",
        "\n",
        "        return path, visited\n",
        "\n",
        "    def repeated_searching(self, s_start, s_goal, e):\n",
        "        \"\"\"\n",
        "        run A* with weight e.\n",
        "        :param s_start: starting state\n",
        "        :param s_goal: goal state\n",
        "        :param e: weight of a*\n",
        "        :return: path and visited order.\n",
        "        \"\"\"\n",
        "\n",
        "        g = {s_start: 0, s_goal: float(\"inf\")}\n",
        "        PARENT = {s_start: s_start}\n",
        "        OPEN = []\n",
        "        CLOSED = []\n",
        "        heapq.heappush(OPEN,\n",
        "                       (g[s_start] + e * self.heuristic(s_start), s_start))\n",
        "\n",
        "        while OPEN:\n",
        "            _, s = heapq.heappop(OPEN)\n",
        "            CLOSED.append(s)\n",
        "\n",
        "            if s == s_goal:\n",
        "                break\n",
        "\n",
        "            for s_n in self.get_neighbor(s):\n",
        "                new_cost = g[s] + self.cost(s, s_n)\n",
        "\n",
        "                if s_n not in g:\n",
        "                    g[s_n] = math.inf\n",
        "\n",
        "                if new_cost < g[s_n]:  # conditions for updating Cost\n",
        "                    g[s_n] = new_cost\n",
        "                    PARENT[s_n] = s\n",
        "                    heapq.heappush(OPEN, (g[s_n] + e * self.heuristic(s_n), s_n))\n",
        "\n",
        "        return self.extract_path(PARENT), CLOSED\n",
        "\n",
        "    def get_neighbor(self, s):\n",
        "        \"\"\"\n",
        "        find neighbors of state s that not in obstacles.\n",
        "        :param s: state\n",
        "        :return: neighbors\n",
        "        \"\"\"\n",
        "\n",
        "        \"\"\" Edit 4:\n",
        "            <return list of state neighbors for all actions> \"\"\"\n",
        "        return [(s[0] + u[0], s[1] + u[1]) for u in self.u_set] \n",
        "      #current(s) + left/right/up/down\n",
        "    def cost(self, s_start, s_goal):\n",
        "        \"\"\"\n",
        "        Calculate Cost for this motion\n",
        "        :param s_start: starting node\n",
        "        :param s_goal: end node\n",
        "        :return:  Cost for this motion\n",
        "        :note: Cost function could be more complicated!\n",
        "        \"\"\"\n",
        "\n",
        "        if self.is_collision(s_start, s_goal):\n",
        "            return math.inf\n",
        "\n",
        "        return math.hypot(s_goal[0] - s_start[0], s_goal[1] - s_start[1])\n",
        "\n",
        "    def is_collision(self, s_start, s_end):\n",
        "        \"\"\"\n",
        "        check if the line segment (s_start, s_end) is collision.\n",
        "        :param s_start: start node\n",
        "        :param s_end: end node\n",
        "        :return: True: is collision / False: not collision\n",
        "        \"\"\"\n",
        "        \"\"\"Edit 5:\n",
        "        <check if a collision happened with s_start and s_end> \"\"\"\n",
        "        if s_start in self.obs or s_end in self.obs:\n",
        "          return True\n",
        "        else: \n",
        "          return False\n",
        "    \n",
        "        if s_start[0] != s_end[0] and s_start[1] != s_end[1]:\n",
        "            if s_end[0] - s_start[0] == s_start[1] - s_end[1]:\n",
        "                s1 = (min(s_start[0], s_end[0]), min(s_start[1], s_end[1]))\n",
        "                s2 = (max(s_start[0], s_end[0]), max(s_start[1], s_end[1]))\n",
        "            else:\n",
        "                s1 = (min(s_start[0], s_end[0]), max(s_start[1], s_end[1]))\n",
        "                s2 = (max(s_start[0], s_end[0]), min(s_start[1], s_end[1]))\n",
        "#\n",
        "            if s1 in self.obs or s2 in self.obs:\n",
        "                return True\n",
        "\n",
        "        return False\n",
        "\n",
        "    def f_value(self, s):\n",
        "      \"\"\"\n",
        "      f = g + h. (g: Cost to come, h: heuristic value)\n",
        "      :param s: current state\n",
        "      :return: f\n",
        "      \"\"\"\n",
        "      \"\"\" Edit 6:\n",
        "      <return the f value given g and h> \"\"\"\n",
        "      return self.g[s] + self.heuristic(s)\n",
        "\n",
        "    def extract_path(self, PARENT):\n",
        "        \"\"\"\n",
        "        Extract the path based on the PARENT set.\n",
        "        :return: The planning path\n",
        "        \"\"\"\n",
        "\n",
        "        path = [self.s_goal]\n",
        "        s = self.s_goal\n",
        "\n",
        "        while True:\n",
        "          \"\"\" Edit 7:\n",
        "          <compute the path using PARENT> \"\"\"\n",
        "          s = PARENT[s]\n",
        "          path.append(s)\n",
        "          if s == self.s_start:\n",
        "            break\n",
        "        return list(path)\n",
        "\n",
        "    def heuristic(self, s):\n",
        "        \"\"\"\n",
        "        Calculate heuristic.\n",
        "        :param s: current node (state)\n",
        "        :return: heuristic function value\n",
        "        \"\"\"\n",
        "        heuristic_type = self.heuristic_type  # heuristic type\n",
        "        goal = self.s_goal  # goal node\n",
        "\n",
        "        if heuristic_type == \"manhattan\":\n",
        "          \"\"\" Edit 8:\n",
        "          <return the manhattan distance given the goal and s> \"\"\"\n",
        "          return abs(goal[0] -s[0]) + abs(goal[1] - s[1])\n",
        "            \n",
        "        else:\n",
        "          \"\"\" Edit 9:\n",
        "          <return the eucleadian distance given the goal and s using math library> \"\"\"\n",
        "          return math.hypot(goal[0] - s[0], goal[1] - s[1])\n",
        "\n",
        "def main():\n",
        "    s_start = tuple(position_robot)\n",
        "    s_goal = tuple(position_customers[int(name)])\n",
        "\n",
        "    astar = AStar(s_start, s_goal, \"euclidean\")\n",
        "    \"\"\" Edit 10:\n",
        "    <instantiate the plotting class with the start and end point> \"\"\"\n",
        "    plot = Plotting(s_start, s_goal)\n",
        "\n",
        "    path, visited = astar.searching()\n",
        "    plot.animation(path, visited, \"A*\")  # animation\n",
        "    return path\n",
        "    #path, visited = astar.searching_repeated_astar(2.5)               # initial weight e = 2.5\n",
        "    #plot.animation_ara_star(path, visited, \"Repeated A*\")\n",
        "\n",
        "\n",
        "if __name__ == '__main__':\n",
        "    main()\n",
        "    path = main()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(18, 8)\n",
            "(17, 9)\n",
            "(16, 10)\n",
            "(15, 11)\n",
            "(14, 11)\n",
            "(13, 11)\n",
            "(18, 9)\n",
            "(12, 11)\n",
            "(17, 10)\n",
            "(16, 11)\n",
            "(16, 11)\n",
            "(15, 12)\n",
            "(15, 12)\n",
            "(17, 7)\n",
            "(18, 10)\n",
            "(16, 7)\n",
            "(16, 12)\n",
            "(15, 7)\n",
            "(15, 13)\n",
            "(12, 10)\n",
            "(18, 7)\n",
            "(14, 7)\n",
            "(11, 10)\n",
            "(11, 10)\n",
            "(19, 9)\n",
            "(19, 8)\n",
            "(13, 7)\n",
            "(18, 10)\n",
            "(16, 13)\n",
            "(16, 12)\n",
            "(12, 7)\n",
            "(15, 14)\n",
            "(19, 10)\n",
            "(11, 7)\n",
            "(10, 8)\n",
            "(11, 9)\n",
            "(10, 9)\n",
            "(16, 14)\n",
            "(16, 13)\n",
            "(10, 7)\n",
            "(10, 9)\n",
            "(13, 6)\n",
            "(15, 15)\n",
            "(18, 6)\n",
            "(19, 11)\n",
            "(18, 12)\n",
            "(9, 7)\n",
            "(14, 16)\n",
            "(13, 16)\n",
            "(12, 16)\n",
            "(11, 16)\n",
            "(10, 16)\n",
            "(9, 16)\n",
            "(8, 16)\n",
            "(7, 16)\n",
            "(6, 16)\n",
            "(16, 15)\n",
            "(16, 14)\n",
            "(5, 17)\n",
            "(4, 17)\n",
            "(3, 17)\n",
            "(2, 17)\n",
            "Congrats! You've found the end!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "(18, 8)\n",
            "(17, 9)\n",
            "(16, 10)\n",
            "(15, 11)\n",
            "(14, 11)\n",
            "(13, 11)\n",
            "(18, 9)\n",
            "(12, 11)\n",
            "(17, 10)\n",
            "(16, 11)\n",
            "(16, 11)\n",
            "(15, 12)\n",
            "(15, 12)\n",
            "(17, 7)\n",
            "(18, 10)\n",
            "(16, 7)\n",
            "(16, 12)\n",
            "(15, 7)\n",
            "(15, 13)\n",
            "(12, 10)\n",
            "(18, 7)\n",
            "(14, 7)\n",
            "(11, 10)\n",
            "(11, 10)\n",
            "(19, 9)\n",
            "(19, 8)\n",
            "(13, 7)\n",
            "(18, 10)\n",
            "(16, 13)\n",
            "(16, 12)\n",
            "(12, 7)\n",
            "(15, 14)\n",
            "(19, 10)\n",
            "(11, 7)\n",
            "(10, 8)\n",
            "(11, 9)\n",
            "(10, 9)\n",
            "(16, 14)\n",
            "(16, 13)\n",
            "(10, 7)\n",
            "(10, 9)\n",
            "(13, 6)\n",
            "(15, 15)\n",
            "(18, 6)\n",
            "(19, 11)\n",
            "(18, 12)\n",
            "(9, 7)\n",
            "(14, 16)\n",
            "(13, 16)\n",
            "(12, 16)\n",
            "(11, 16)\n",
            "(10, 16)\n",
            "(9, 16)\n",
            "(8, 16)\n",
            "(7, 16)\n",
            "(6, 16)\n",
            "(16, 15)\n",
            "(16, 14)\n",
            "(5, 17)\n",
            "(4, 17)\n",
            "(3, 17)\n",
            "(2, 17)\n",
            "Congrats! You've found the end!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAHBCAYAAABOnPJQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAM7UlEQVR4nO3cMY7bSBqG4V+7XTGd+RQ6RSWT6E6zZ1Jcp2A68eRMBjAYaIOGjdVCozEbbvHr1vOERRj4AgF+0SDrcLlcCgAAEv1r7wEAAPB3xCoAALHEKgAAscQqAACxxCoAALHEKgAAsV7+4bl7rQAAeITDrUN/WQUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAINbL3gP+3zzPNcaoZVlqmqbqvdfxeNx7ll0AADs4XC6Xe8/vPvzV5nmu8/lc67r+OGut1el02jXA7AIAeHeHW4dRrwGMMa7Cq6pqXdcaY+y06JVdAAD7iIrVZVk2nT+KXQAA+4iK1WmaNp0/il0AAPuIitXee7XWrs5aa9V732nRK7sAAPYRdRvA94+C0r5utwsAYB9RtwEAAPC08m8DAACA/yVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiCVWAQCIJVYBAIglVgEAiPWy9wA+p3mea4xRy7LUNE3Ve6/j8bj3LLvsssuuD7sLntW/f//993vP7z6EW+Z5rvP5XH/99VdVVX379q3++OOP+vLlS339+tUuu+yyyy7glv/cOvQaAL/cGKPWdb06W9e1xhg7LXpl1zZ2bWPXNnYBP0us8ssty7Lp/FHs2saubezaxi7gZ4lVfrlpmjadP4pd29i1jV3b2AX8LLHKL9d7r9ba1VlrrXrvOy16Zdc2dm1j1zZ2AT/LB1b8cl+/fq0vX77Un3/+Wd++fatpmuq3337b/Wtau+yyy66PuguexM0PrA6Xy+XeP7r7EAAAfpHDrUOvAQAAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEEusAgAQS6wCABBLrAIAEOtl7wEAwD+b57nGGLUsS03TVL33Oh6Pe8+K3cXncbhcLvee330IALy/eZ7rfD7Xuq4/zlprdTqddg3D1F18WIdbh14DAIBwY4yrIKyqWte1xhg7LXqVuovPRawCQLhlWTadP0rqLj4XsQoA4aZp2nT+KKm7+FzEKgCE671Xa+3qrLVWvfedFr1K3cXn4jYAAAj3/WOltK/uU3fxubgNAACABG4DAADgYxGrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxHrZewAA8HHN81xjjFqWpaZpqt57HY/HvWfxiRwul8u953cfAgDPa57nOp/Pta7rj7PWWp1OJ8HKWxxuHXoNAAB4kzHGVahWVa3rWmOMnRbxGYlVAOBNlmXZdA5vIVYBgDeZpmnTObyFWAUA3qT3Xq21q7PWWvXed1rEZ+Q2AADgTb5/ROU2AN6T2wAAAEjgNgAAAD4WsQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBALLEKAEAssQoAQCyxCgBArJe9BwAAPIt5nmuMUcuy1DRN1Xuv4/G496xoh8vlcu/53YcAAPyceZ7rfD7Xuq4/zlprdTqdBOurw61DrwEAADzAGOMqVKuq1nWtMcZOiz4GsQoA8ADLsmw655VYBQB4gGmaNp3zSqwCADxA771aa1dnrbXqve+06GNwGwAAwAN8/4jKbQDbuA0AAIAEbgMAAOBjEasAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEetl7AAAA+5rnucYYtSxLTdNUvfc6Ho97z6qqqsPlcrn3/O5DAAA+tnme63w+17quP85aa3U6nR4drIdbh14DAAB4YmOMq1CtqlrXtcYYOy26JlYBAJ7Ysiybzh9NrAIAPLFpmjadP5pYBQB4Yr33aq1dnbXWqve+06JrbgMAAHhi3z+ichsAAAD8PbcBAADwsYhVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYolVAABiiVUAAGKJVQAAYr3sPQDINc9zjTFqWZaapql673U8HveeBcATOVwul3vP7z4EPq95nut8Pte6rj/OWmt1Op0EKwDv4XDr0GsAwE1jjKtQrapa17XGGDstAuAZiVXgpmVZNp0DwHsQq8BN0zRtOgeA9yBWgZt679VauzprrVXvfadFADwjtwEAN33/iMptAADsyW0AAAAkcBsAAAAfi1gFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAg1sveAwB4TvM81xijlmWpaZqq917H43HvWfCu/O63O1wul3vP7z4EgLeY57nO53Ot6/rjrLVWp9PJf9x8Wn73/+hw69BrAAA83Bjj6j/sqqp1XWuMsdMieH9+928jVgF4uGVZNp3DZ+B3/zZiFYCHm6Zp0zl8Bn73byNWAXi43nu11q7OWmvVe99pEbw/v/u3cRsAAA/3/WMSX0XzTPzu38ZtAAAAJHAbAAAAH4tYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACCWWAUAIJZYBQAgllgFACDWyz88PzxkBQAA3OAvqwAAxBKrAADEEqsAAMQSqwAAxBKrAADEEqsAAMT6L2Dg0mdKrqZUAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "702XKznGAZf4"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as patches\n",
        "import os\n",
        "import sys\n",
        "\n",
        "class Plotting:\n",
        "    def __init__(self, x_start, x_goal):\n",
        "        self.xI, self.xG = x_start, x_goal\n",
        "        self.env = Env()\n",
        "        self.obs_bound = self.env.obs_boundary\n",
        "        self.obs_circle = self.env.obs_circle\n",
        "        self.obs_rectangle = self.env.obs_rectangle\n",
        "\n",
        "    def animation(self, nodelist, path, name, animation=False):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited(nodelist, animation)\n",
        "        self.plot_path(path)\n",
        "\n",
        "    def animation_connect(self, V1, V2, path, name):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited_connect(V1, V2)\n",
        "        self.plot_path(path)\n",
        "\n",
        "    def plot_grid(self, name):\n",
        "        fig, ax = plt.subplots()\n",
        "\n",
        "        for (ox, oy, w, h) in self.obs_bound:\n",
        "            ax.add_patch(\n",
        "                patches.Rectangle(\n",
        "                    (ox, oy), w, h,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='black',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        for (ox, oy, w, h) in self.obs_rectangle:\n",
        "            ax.add_patch(\n",
        "                patches.Rectangle(\n",
        "                    (ox, oy), w, h,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='gray',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        for (ox, oy, r) in self.obs_circle:\n",
        "            ax.add_patch(\n",
        "                patches.Circle(\n",
        "                    (ox, oy), r,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='gray',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        plt.plot(self.xI[0], self.xI[1], \"bs\", linewidth=3)\n",
        "        plt.plot(self.xG[0], self.xG[1], \"gs\", linewidth=3)\n",
        "\n",
        "        plt.title(name)\n",
        "        plt.axis(\"equal\")\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_visited(nodelist, animation):\n",
        "        if animation:\n",
        "            count = 0\n",
        "            for node in nodelist:\n",
        "                count += 1\n",
        "                if node.parent:\n",
        "                    plt.plot([node.parent.x, node.x], [node.parent.y, node.y], \"-g\")\n",
        "                    plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                                 lambda event:\n",
        "                                                 [exit(0) if event.key == 'escape' else None])\n",
        "                    if count % 10 == 0:\n",
        "                        plt.pause(0.001)\n",
        "        else:\n",
        "            for node in nodelist:\n",
        "                if node.parent:\n",
        "                    plt.plot([node.parent.x, node.x], [node.parent.y, node.y], \"-g\")\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_visited_connect(V1, V2):\n",
        "        len1, len2 = len(V1), len(V2)\n",
        "\n",
        "        for k in range(max(len1, len2)):\n",
        "            if k < len1:\n",
        "                if V1[k].parent:\n",
        "                    plt.plot([V1[k].x, V1[k].parent.x], [V1[k].y, V1[k].parent.y], \"-g\")\n",
        "            if k < len2:\n",
        "                if V2[k].parent:\n",
        "                    plt.plot([V2[k].x, V2[k].parent.x], [V2[k].y, V2[k].parent.y], \"-g\")\n",
        "\n",
        "            plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                         lambda event: [exit(0) if event.key == 'escape' else None])\n",
        "\n",
        "            if k % 2 == 0:\n",
        "                plt.pause(0.001)\n",
        "\n",
        "        plt.pause(0.01)\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_path(path):\n",
        "        if len(path) != 0:\n",
        "            plt.plot([x[0] for x in path], [x[1] for x in path], '-r', linewidth=2)\n",
        "            plt.pause(0.01)\n",
        "        plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "0RKLZqd2whJ9",
        "outputId": "8dbc5017-0475-4888-83b0-f1b205eeb8fd"
      },
      "source": [
        "import os\n",
        "import sys\n",
        "import math\n",
        "import numpy as np\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.patches as patches\n",
        "\n",
        "\n",
        "#####\n",
        "class Plotting:\n",
        "    def __init__(self, x_start, x_goal):\n",
        "        self.xI, self.xG = x_start, x_goal\n",
        "        self.env = Env()\n",
        "        self.obs_bound = self.env.obs_boundary\n",
        "        self.obs_circle = self.env.obs_circle\n",
        "        self.obs_rectangle = self.env.obs_rectangle\n",
        "\n",
        "    def animation(self, nodelist, path, name, animation=False):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited(nodelist, animation)\n",
        "        self.plot_path(path)\n",
        "\n",
        "    def animation_connect(self, V1, V2, path, name):\n",
        "        self.plot_grid(name)\n",
        "        self.plot_visited_connect(V1, V2)\n",
        "        self.plot_path(path)\n",
        "\n",
        "    def plot_grid(self, name):\n",
        "        fig, ax = plt.subplots()\n",
        "\n",
        "        for (ox, oy, w, h) in self.obs_bound:\n",
        "            ax.add_patch(\n",
        "                patches.Rectangle(\n",
        "                    (ox, oy), w, h,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='black',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        for (ox, oy, w, h) in self.obs_rectangle:\n",
        "            ax.add_patch(\n",
        "                patches.Rectangle(\n",
        "                    (ox, oy), w, h,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='gray',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        for (ox, oy, r) in self.obs_circle:\n",
        "            ax.add_patch(\n",
        "                patches.Circle(\n",
        "                    (ox, oy), r,\n",
        "                    edgecolor='black',\n",
        "                    facecolor='gray',\n",
        "                    fill=True\n",
        "                )\n",
        "            )\n",
        "\n",
        "        plt.plot(self.xI[0], self.xI[1], \"bs\", linewidth=3)\n",
        "        plt.plot(self.xG[0], self.xG[1], \"gs\", linewidth=3)\n",
        "\n",
        "        plt.title(name)\n",
        "        plt.axis(\"equal\")\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_visited(nodelist, animation):\n",
        "        if animation:\n",
        "            count = 0\n",
        "            for node in nodelist:\n",
        "                count += 1\n",
        "                if node.parent:\n",
        "                    plt.plot([node.parent.x, node.x], [node.parent.y, node.y], \"-g\")\n",
        "                    plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                                 lambda event:\n",
        "                                                 [exit(0) if event.key == 'escape' else None])\n",
        "                    if count % 10 == 0:\n",
        "                        plt.pause(0.001)\n",
        "        else:\n",
        "            for node in nodelist:\n",
        "                if node.parent:\n",
        "                    plt.plot([node.parent.x, node.x], [node.parent.y, node.y], \"-g\")\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_visited_connect(V1, V2):\n",
        "        len1, len2 = len(V1), len(V2)\n",
        "\n",
        "        for k in range(max(len1, len2)):\n",
        "            if k < len1:\n",
        "                if V1[k].parent:\n",
        "                    plt.plot([V1[k].x, V1[k].parent.x], [V1[k].y, V1[k].parent.y], \"-g\")\n",
        "            if k < len2:\n",
        "                if V2[k].parent:\n",
        "                    plt.plot([V2[k].x, V2[k].parent.x], [V2[k].y, V2[k].parent.y], \"-g\")\n",
        "\n",
        "            plt.gcf().canvas.mpl_connect('key_release_event',\n",
        "                                         lambda event: [exit(0) if event.key == 'escape' else None])\n",
        "\n",
        "            if k % 2 == 0:\n",
        "                plt.pause(0.001)\n",
        "\n",
        "        plt.pause(0.01)\n",
        "\n",
        "    @staticmethod\n",
        "    def plot_path(path):\n",
        "        if len(path) != 0:\n",
        "            plt.plot([x[0] for x in path], [x[1] for x in path], '-r', linewidth=2)\n",
        "            plt.pause(0.01)\n",
        "        plt.show()\n",
        "#####\n",
        "\n",
        "class Env:\n",
        "    def __init__(self):\n",
        "        self.x_range = (0, 50)\n",
        "        self.y_range = (0, 30)\n",
        "        self.obs_boundary = self.obs_boundary()\n",
        "        self.obs_circle = self.obs_circle()\n",
        "        self.obs_rectangle = self.obs_rectangle()\n",
        "\n",
        "    @staticmethod\n",
        "    def obs_boundary():\n",
        "        obs_boundary = [\n",
        "            [0, 0, 1, 30],\n",
        "            [0, 30, 50, 1],\n",
        "            [1, 0, 50, 1],\n",
        "            [50, 1, 1, 30]\n",
        "        ]\n",
        "        return obs_boundary\n",
        "\n",
        "    @staticmethod\n",
        "    def obs_rectangle():\n",
        "        obs_rectangle = [\n",
        "            [14, 12, 8, 2],\n",
        "            [18, 22, 8, 3],\n",
        "            [26, 7, 2, 12],\n",
        "            [32, 14, 10, 2]\n",
        "        ]\n",
        "        return obs_rectangle\n",
        "\n",
        "    @staticmethod\n",
        "    def obs_circle():\n",
        "        obs_cir = [\n",
        "            [7, 12, 3],\n",
        "            [46, 20, 2],\n",
        "            [15, 5, 2],\n",
        "            [37, 7, 3],\n",
        "            [37, 23, 3]\n",
        "        ]\n",
        "\n",
        "        return obs_cir\n",
        "\n",
        "class Utils:\n",
        "    def __init__(self):\n",
        "        self.env = Env()\n",
        "\n",
        "        self.delta = 0.5\n",
        "        self.obs_circle = self.env.obs_circle\n",
        "        self.obs_rectangle = self.env.obs_rectangle\n",
        "        self.obs_boundary = self.env.obs_boundary\n",
        "\n",
        "    def update_obs(self, obs_cir, obs_bound, obs_rec):\n",
        "        self.obs_circle = obs_cir\n",
        "        self.obs_boundary = obs_bound\n",
        "        self.obs_rectangle = obs_rec\n",
        "\n",
        "    def get_obs_vertex(self):\n",
        "        delta = self.delta\n",
        "        obs_list = []\n",
        "\n",
        "        for (ox, oy, w, h) in self.obs_rectangle:\n",
        "            vertex_list = [[ox - delta, oy - delta],\n",
        "                           [ox + w + delta, oy - delta],\n",
        "                           [ox + w + delta, oy + h + delta],\n",
        "                           [ox - delta, oy + h + delta]]\n",
        "            obs_list.append(vertex_list)\n",
        "\n",
        "        return obs_list\n",
        "\n",
        "    def is_intersect_rec(self, start, end, o, d, a, b):\n",
        "        v1 = [o[0] - a[0], o[1] - a[1]]\n",
        "        v2 = [b[0] - a[0], b[1] - a[1]]\n",
        "        v3 = [-d[1], d[0]]\n",
        "\n",
        "        div = np.dot(v2, v3)\n",
        "\n",
        "        if div == 0:\n",
        "            return False\n",
        "\n",
        "        t1 = np.linalg.norm(np.cross(v2, v1)) / div\n",
        "        t2 = np.dot(v1, v3) / div\n",
        "\n",
        "        if t1 >= 0 and 0 <= t2 <= 1:\n",
        "            shot = Node((o[0] + t1 * d[0], o[1] + t1 * d[1]))\n",
        "            dist_obs = self.get_dist(start, shot)\n",
        "            dist_seg = self.get_dist(start, end)\n",
        "            if dist_obs <= dist_seg:\n",
        "                return True\n",
        "\n",
        "        return False\n",
        "\n",
        "    def is_intersect_circle(self, o, d, a, r):\n",
        "        d2 = np.dot(d, d)\n",
        "        delta = self.delta\n",
        "\n",
        "        if d2 == 0:\n",
        "            return False\n",
        "\n",
        "        t = np.dot([a[0] - o[0], a[1] - o[1]], d) / d2\n",
        "\n",
        "        if 0 <= t <= 1:\n",
        "            shot = Node((o[0] + t * d[0], o[1] + t * d[1]))\n",
        "            if self.get_dist(shot, Node(a)) <= r + delta:\n",
        "                return True\n",
        "\n",
        "        return False\n",
        "\n",
        "    def is_collision(self, start, end):\n",
        "        if self.is_inside_obs(start) or self.is_inside_obs(end):\n",
        "            return True\n",
        "\n",
        "        o, d = self.get_ray(start, end)\n",
        "        obs_vertex = self.get_obs_vertex()\n",
        "\n",
        "        for (v1, v2, v3, v4) in obs_vertex:\n",
        "            if self.is_intersect_rec(start, end, o, d, v1, v2):\n",
        "                return True\n",
        "            if self.is_intersect_rec(start, end, o, d, v2, v3):\n",
        "                return True\n",
        "            if self.is_intersect_rec(start, end, o, d, v3, v4):\n",
        "                return True\n",
        "            if self.is_intersect_rec(start, end, o, d, v4, v1):\n",
        "                return True\n",
        "\n",
        "        for (x, y, r) in self.obs_circle:\n",
        "            if self.is_intersect_circle(o, d, [x, y], r):\n",
        "                return True\n",
        "\n",
        "        return False\n",
        "\n",
        "    def is_inside_obs(self, node):\n",
        "        delta = self.delta\n",
        "\n",
        "        for (x, y, r) in self.obs_circle:\n",
        "            if math.hypot(node.x - x, node.y - y) <= r + delta:\n",
        "                return True\n",
        "\n",
        "        for (x, y, w, h) in self.obs_rectangle:\n",
        "            if 0 <= node.x - (x - delta) <= w + 2 * delta \\\n",
        "                    and 0 <= node.y - (y - delta) <= h + 2 * delta:\n",
        "                return True\n",
        "\n",
        "        for (x, y, w, h) in self.obs_boundary:\n",
        "            if 0 <= node.x - (x - delta) <= w + 2 * delta \\\n",
        "                    and 0 <= node.y - (y - delta) <= h + 2 * delta:\n",
        "                return True\n",
        "\n",
        "        return False\n",
        "\n",
        "    @staticmethod\n",
        "    def get_ray(start, end):\n",
        "        orig = [start.x, start.y]\n",
        "        direc = [end.x - start.x, end.y - start.y]\n",
        "        return orig, direc\n",
        "\n",
        "    @staticmethod\n",
        "    def get_dist(start, end):\n",
        "        return math.hypot(end.x - start.x, end.y - start.y)\n",
        "\n",
        "class Node:\n",
        "    def __init__(self, n):\n",
        "        self.x = n[0]\n",
        "        self.y = n[1]\n",
        "        self.parent = None\n",
        "\n",
        "\n",
        "class Rrt:\n",
        "    def __init__(self, s_start, s_goal, step_len, goal_sample_rate, iter_max):\n",
        "        self.s_start = Node(s_start)\n",
        "        self.s_goal = Node(s_goal)\n",
        "        self.step_len = step_len\n",
        "        self.goal_sample_rate = goal_sample_rate\n",
        "        self.iter_max = iter_max\n",
        "        self.vertex = [self.s_start]\n",
        "\n",
        "        self.env = Env()\n",
        "        self.plotting = Plotting(s_start, s_goal)\n",
        "        self.utils = Utils()\n",
        "\n",
        "        self.x_range = self.env.x_range\n",
        "        self.y_range = self.env.y_range\n",
        "        self.obs_circle = self.env.obs_circle\n",
        "        self.obs_rectangle = self.env.obs_rectangle\n",
        "        self.obs_boundary = self.env.obs_boundary\n",
        "\n",
        "    def planning(self):\n",
        "        for i in range(self.iter_max):\n",
        "            node_rand = self.generate_random_node(self.goal_sample_rate)\n",
        "            node_near = self.nearest_neighbor(self.vertex, node_rand)\n",
        "            node_new = self.new_state(node_near, node_rand)\n",
        "\n",
        "            if node_new and not self.utils.is_collision(node_near, node_new):\n",
        "                self.vertex.append(node_new)\n",
        "                dist, _ = self.get_distance_and_angle(node_new, self.s_goal)\n",
        "\n",
        "                if dist <= self.step_len and not self.utils.is_collision(node_new, self.s_goal):\n",
        "                    self.new_state(node_new, self.s_goal)\n",
        "                    return self.extract_path(node_new)\n",
        "\n",
        "        return None\n",
        "\n",
        "    def generate_random_node(self, goal_sample_rate):\n",
        "        delta = self.utils.delta\n",
        "\n",
        "        if np.random.random() > goal_sample_rate:\n",
        "            return Node((np.random.uniform(self.x_range[0] + delta, self.x_range[1] - delta),\n",
        "                         np.random.uniform(self.y_range[0] + delta, self.y_range[1] - delta)))\n",
        "\n",
        "        return self.s_goal\n",
        "\n",
        "    @staticmethod\n",
        "    def nearest_neighbor(node_list, n):\n",
        "        return node_list[int(np.argmin([math.hypot(nd.x - n.x, nd.y - n.y)\n",
        "                                        for nd in node_list]))]\n",
        "\n",
        "    def new_state(self, node_start, node_end):\n",
        "        dist, theta = self.get_distance_and_angle(node_start, node_end)\n",
        "\n",
        "        dist = min(self.step_len, dist)\n",
        "        node_new = Node((node_start.x + dist * math.cos(theta),\n",
        "                         node_start.y + dist * math.sin(theta)))\n",
        "        node_new.parent = node_start\n",
        "\n",
        "        return node_new\n",
        "\n",
        "    def extract_path(self, node_end):\n",
        "        path = [(self.s_goal.x, self.s_goal.y)]\n",
        "        node_now = node_end\n",
        "\n",
        "        while node_now.parent is not None:\n",
        "            node_now = node_now.parent\n",
        "            path.append((node_now.x, node_now.y))\n",
        "\n",
        "        return path\n",
        "\n",
        "    @staticmethod\n",
        "    def get_distance_and_angle(node_start, node_end):\n",
        "        dx = node_end.x - node_start.x\n",
        "        dy = node_end.y - node_start.y\n",
        "        return math.hypot(dx, dy), math.atan2(dy, dx)\n",
        "\n",
        "\n",
        "def main():\n",
        "    x_start = tuple(position_robot)  # Starting node\n",
        "    x_goal = tuple(position_customers[int(name)])  # Goal node\n",
        "\n",
        "    rrt = Rrt(x_start, x_goal, 0.5, 0.05, 10000)\n",
        "    path = rrt.planning()\n",
        "\n",
        "    if path:\n",
        "        rrt.plotting.animation(rrt.vertex, path, \"RRT\", True)\n",
        "    else:\n",
        "        print(\"No Path Found!\")\n",
        "\n",
        "\n",
        "if __name__ == '__main__':\n",
        "    main()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eK2giAABqLW2sRkScesCpMW7YuMp6Y+fGuPaRawucCACAWkodq0MGDolzDj6nau+fl/5zvNn5ZkETAQBQS6ljNSLia5/4WoxoGlFZt7/VHjf9500FTgQAQK2kj9Xmwc3x9U98vWrviiVXRGdXZ0ETAQBQK+ljNSLinNnnxOABgyvrdevXxQ9/98MCJwIAoBb6RKyOGzYuvnrAV6v25j84P7q6uwqaCACAWugTsRoRce4h58aAhgGV9ar2VXH7ytsLnAgAgF2tz8TqxJET4wv7fqFq7/LFl0e5XC5oIgAAdrU+E6sREed/6vwoRamyfvTFR+PWFbcWOBEAALtSn4rVGbvPiBOnn1i1d8ptp8Qlv7wkNnRsKGgqAAB2lT4VqxERh/7ZoVXrrnJXXPSLi2Kff9knrlpyVWzeurmgyQAA2Nn6XKxObJ4YgxoH9dh/ZdMr8bf3/m1M+d9T4sbf3BhburYUMB0AADtT6T1+oJTy10t3r747vnj7F6OzqzM2bdnU62emjJ4S/3DEP8RffeyvoqHU55ocAKDelHrd7IuxWi6XY2v31ti0ZVNcueTKuHLplbGxc2Ovn91v/H5x6ZGXxrFTjo1Sqdf/DwAAKF7/idVtvfzmy/Gdxd+Jax+5Njq6Onr9zCETDonLjrwsDpt0WI2nAwBgB/TfWH3H2jfWxiW/uiRufvTm6Cr3/naroyYfFZceeWl8fK+P13g6AAC2o//H6jtWt6+Oi39xcfzo8R+962dOmnFSXHLEJTFz95k1nAwAgHdRP7H6jt+++Nu48P4L485Vd/Z6vaHUEF/a70vx7cO/HZNGTqrtcAAA/Kn6i9V3/Hrtr+Nb930rfvncL3u9PrBhYJx+0Olx4f+4MPbYbY8aTwcAQNRzrEa8/QSBRc8sim/d9634ze9/0+tnhgwYEt84+Btx3qfOi9FDRtd4QgCAulbfsfqOcrkcC55cEBf+/MJY+crKXj9z5VFXxjfnfLPGkwEA1DWx+qe6urvih7/7YVz8i4vjuTeeq+x/ZPhHYvXZq2PIwCEFTgcAUHd6jdW6fbVTY0Nj/PX+fx1t/7Mtrjn6mhg/bHxERFx02EVCFQAgibq9s7qtNzvfjFseuyXOOOiMGNg4sOhxAADqjWMAAACk5RgAAAB9i1gFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTE6nsol8vx48d/HPc8dU/RowAA1J0BRQ+Q2QsbXoiz7jorWttaY6/he8UTX3siRg4eWfRYAAB1w53VXpTL5bj50Ztj5rUzo7WtNSLeDtfz7j2v4MkAAOpLqVwub+/6di/2R8++/mycfsfpseiZRT2uNTU2xeqzV8eE5gkFTAYA0K+Vett0Z/W/dZe745qHr4lZ183qNVTntMyJR894VKgCANSQM6sRsap9VXyl9SuxeM3iHteGDhwalx55aZz9ybOjsaGxgOkAAOpXXcfq1u6tceWSK+PiX1wcm7du7nH9iElHxE1zb4p9Ru1TwHQAANRtrC7/w/I4tfXUWPbCsh7Xhg8aHlccdUWcduBpUSr1enwCAIAaqLtY7ezqjMseuCwue+Cy2NK9pcf1Y6YcE9cfd320jGgpYDoAAP5UXcXqsheWxakLT43lLy3vcW30kNFx9V9eHV/c94vupgIAJFEXsfrWlrfi27/4dlyx5IroLnf3uH7yzJPjmqOvifG7jS9gOgAA3k2/j9XFaxbHqQtPjdWvru5xbfyw8XHdsdfFSTNOKmAyAADeS7+N1Y2dG+OCn10Q1z5ybZR7ebfBl//8y3HVZ6+K0UNGFzAdAAA7ol/G6qKnF8Vpd5wWz73xXI9rLSNa4objboijpxxdwGQAALwf/SpWy+VynHXXWXH9b67v9fqZB50Z8z8zP0Y0jajxZAAAfBD9KlZLpVKMH9bzR1KTR02Om+beFIdPOrz2QwEA8IGVyuWe5zn/xHYvZtTZ1RkHXn9gPPHyE1GKUnxz9jfjkiMviaEDhxY9GgAA767XZ4f2u1iNiHj4+Yfjq61fjRuOvyFmt8wuehwAAN5b/cRqRER3uTsaSg1FjwEAwI6pr1gFAKBP6TVW3XoEACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVIJmt3Vtj89bNRY8BkIJYBUigs6sz7nnqnjit9bTY44o94l8f+9eiRwJIoVQul7d3fbsXAdg55i+eH+ffd35l/Rf7/EUs+tKiAicCqLlSb5vurAIkcOL0E6vW9//X/dG+qb2gaQDyEKsACUwbOy1mjZtVWXeVu2Jh28ICJwLIQawCJDFvxryq9W0rbytoEoA8xCpAEifPPLlqvejpRfH65tcLmgYgB7EKkMTHdv9YTB0ztbLe0r0l7lx1Z4ETARRPrAIkUSqV4uQZ1XdXb11xa0HTAOQgVgESmTez+tzqPU/dExs6NhQ0DUDxxCpAIgfscUBMGjmpsu7o6oi7V99d3EAABROrAIn0dhTAUwGAeiZWAZLZ9ijAXavvik1bNhU0DUCxxCpAMp/8yCejZURLZb1py6b4j6f+o8CJAIojVgGSaSg1xEnTT6racxQAqFdiFSChbV8QcMeqO6Jja0dB0wAUR6wCJHTIhENi/LDxlfX6jvXxs2d+VuBEAMUQqwAJNTY0xkkzqo8C3LrSCwKA+iNWAZKaN6P6qQALn1wYW7q2FDQNQDHEKkBSh006LMYMGVNZv7b5tbj/2fsLnAig9sQqQFIDGgbEidNPrNq7bYWnAgD1RawCJLbtUYAFTy6Iru6ugqYBqD2xCpDYp/f5dDQ3NVfWL296OR5Y80CBEwHUllgFSGxQ46CYO21u1d6tKzwVAKgfYhUguW1fEHD7ytuju9xd0DQAtSVWAZI7avJRsdug3SIi4qOjPxpf/vMvx1tb3ip4KoDaKJXL5e1d3+5FAGrj3574t5g2ZlrsN36/KJVKRY8DsCv0+i83sQoAQAa9xqpjAAAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSGvAe10s1mQIAAHrhzioAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgrf8PfHRO8joxPyQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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c/8r9Wa8DAC1CrEKRGjtjbCxfvzyWvL8kTppwUoz585jI5/NZrwUAO5RYhSL05JIn4z+f/s+C2V7d94pcLpfRRgDQMnLbOIlxTAOJ2Vy/OQ793aGx4N0FTbP9euwXz1zwTHSo6JDhZgDwD2n2xMXJKhSZcTXjCkI1IuJ3J/9OqALQJolVKCIL3l0QV9VcVTA7f8D5MXCPgRltBAAtS6xCkWjMN8YFUy+I2obaplnPz/SMa4Zek+FWANCyxCoUid/P+308seSJgtl1x18X3Tt1z2gjAGh5fsAKisA7696J/W7aL1ZvWt00O6HfCXHfWff5BAAA2go/YAXF6scP/rggVDu36xw3n3SzUAWgzROrkLhpr06L6vnVBbOfD/p59OnWJ5uFAKAVuQYACVtfuz76/7Z/LF69uGk2oNeAmPOdOVFRVpHdYgCw47kGAMXm3x77t4JQLcuVxS3DbxGqAJQMsQqJmvfWvLh21rUFsx8d+aM44vNHZLQRALQ+1wAgQQ2NDXH0bUfH3GVzm2a9u/aO5y98Prq075LhZgDQYlwDgGJx45wbC0I1IuKmE28SqgCUHCerkJjX3389DrjpgFhft75pdsYBZ8RdZ9yV4VYA0OKcrEIxWLF+Rey2025Nv+7aoWtcf/z1GW4EANkRq5CYwz9/eDz7vWfj8mMvj4qyirh6yNUF8QoApcQ1AEjYy++9HP126RdlOf9fCUCb1+w1ALEKAEAK3FkFAKC4iFUAAJIlVgEASJZYBQAgWWIVAIBkiVUAAJIlVgEASJZYBQAgWWIVErapflPWKwBApsQqJOqFFS9Ev9/0i/9+6b+zXgUAMiNWIUEvv/dyVI2viqVrl8bpd50ek16YlPVKAJCJXD6f39rzrT4EdrzXVr0WA38/MJauXdo0K8uVxezzZ8cRnz8iw80AoEXlmhs6WYWELFm9JAbfPrggVCMiLjj8gjh8t8Mz2goAsiNWIRFL1yyNqvFVseT9JQXz8w49L2488cbI5Zr9H04AaNPEKiTg7XVvR9X4qli4amHB/JyDz4lbht8SZTn/qQJQmvwJCBl7d8O7MWT8kHjpvZcK5mcccEb8/pTfR3lZeUabAUD2xCpkaOXGlTH0jqHx/IrnC+an7HtK/Om0P0VFWUVGmwFAGsQqZOT9Te/HcX88Lp55+5mC+Yl7nxgTvz4x2pW3y2gzAEiHWIUMrN28Nk740wkxd9ncgvmQPYfE5JGTo0NFh4w2A4C0iFVoZRvqNsTw6uHx1JtPFcwH7jEwppw5JTpWdMxoMwBIj1iFVrSpflOccucp8fiSxwvmX9r9SzF19NTo3K5zRpsBQJrEKrSSzfWb4/S7To8Zr80omB/x+SPigbMfiJ067JTRZgCQLrEKraCuoS5GTRoV979yf8H80F6HxoPnPBhdO3bNaDMASJtYhRZW31gfZ99zdkx5aUrB/MDPHhgPfeOh2KXTLhltBgDpE6vQwma9OSsmvzi5YLbvrvvGw2Mejh6de2S0FQAUB7EKLayyd2XcefqdTR/wv1f3veLhMQ9Hzy49M94MANKXy+fzW3u+1YfA9puyYEpcOuPSeOgbD0Xvrr2zXgcAUpNrdihWofXUNdT5ZioAaF6zseoaALQioQq0BW+vezu+evtX48UVL2a9CiVArAIA223F+hVRNb4qHlv8WHzlD1+JZ995NuuVaOPEKgCwXdZsXhPD/jgsXljxQkRErNiwIr56+1fjb8v+lvFmtGViFQDYLl3ad4mj/+nogtnKjStj8PjB8dQbT2W0FW2dWAUAtktZrixuPunmuOioiwrmazaviaF3DI3HFz+e0Wa0ZWIVANhuuVwurj3u2vjpMT8tmK+vWx8n/OmEmL5wekab0VaJVQDgE8nlcnFV1VVxxaArCuYb6zfG8OrhMfXlqRltRlvkc1YBgE/tmr9eE2NnjC2YtStrF3d+/c44bf/TMtqKIuVLAQCAHe83s38TF00rvMdaniuP8SPGx1kHnZXRVhQhsQoAtIxb/nZLfG/q9yL/oXTIRS5u+9ptce6AczPcjCIiVgGAljP+7+Pj3CnnRmO+sWB+84k3x/e/+P2MtqKI+LpVAKDljDlkTEw4bUKU58oL5hfef2Fc+9S1GW1FsROrAMAOM6r/qJg0clK0K2tXML9k+iVx1ZNXZbQVxcw1AABgh3vglQfitLtOi031mwrmPxv4s7hi0BWRyzX7N76UNndWAYDW88iiR2J49fDYULehYP6TL/8krh5ytWDlo9xZBQBaz+C+g+PBcx6MndrvVDB/YskTHztxhS0RqwBAi6nsXRkzxsyIbh27RUTEgF4DYto506JTu04Zb0axcA0AAGhx896aF5dMvyTuPuPu6NG5R9brkCZ3VgGA7OTzefdU2Rp3VgGA7AhVPg2xuoNtqt8UNa/XxLiacfHqylezXgcAoKhVZL1AsXtvw3sx842ZUfN6TdS8URNzl82N2obaiIjYucPO0W+XfhlvCABQvMTqJ5DP52Px6sX/F6b/H6cvrHhhi6+veb0mLvziha24IQBA2yJWt6KhsSGefefZpjCteb0mlq1dtt3vr3m9pgW3AwBo+8Tqh2yo2xCz35zdFKdPvfFUrK1d+4n/OX269YnK3pVR+YXKaGhsiPKy8hbYFgCg7Sv5WL33pXvjscWPRc0bNfH0W09HfWP9J3p/LnJxSK9DovILlVHZuzKO6X1M7L7z7i20LQBAaSn5z1n98m1fjqfefGq7X9+polMctftRTXF69O5HR9eOXVtwQwCAktDsZ5uV/MlqZe/KrcZqj849mv5Kv7J3ZQzYbUC0L2/fihsCAJQusdq7Mn4585dNv+63S7+CON1n1318iDEAQEZK/hrAexvei1888Yum+6a9uvTKeiUAgFLU7OlgyccqAABJaDZWfd0qAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAADJEqsAACRLrAIAkCyxCgBAssQqAG1WY74x6xWAf5BYBaBNWrhyYRz6H4fG3GVzs14F+AeIVQDanDfefyOqxlfFc8ufi8G3D46a12uyXgn4lMQqAG3K+5vej6rxVbHk/SUREbG2dm0c98fjYsZrMzLeDPg0xCoAbcrOHXaOrx/w9YLZhroNcdKEk+Lel+7NaCvg0xKrALQpuVwurqq6Kq4cfGXBvLahNk6767SYOH9iRpsBn0Yun89v7flWHwJAyq6fdX1c/ODFBbOyXFncOvzWOHfAuRltBWxBrtmhWAWgLbv16Vvju/d+N/If+SPthhNuiB8c+YOMtgKaIVYBKE0TnpsQY/48JhryDQXzcVXjYmzl2Iy2Aj5CrAJQuv6y4C8xatKoqG2oLZj/y7H/Ej//6s8jl2v2z0mg9YhVAErbg68+GCMmjoiN9RsL5hcfdXH8+rhfC1bIllgFgCeWPBEnTTgp1tWuK5h/57DvxG9P+m2Ul5VntBmUPLEKABERc5bOieP+eFys3rS6YH72QWfHH079Q1SUVWS0GZQ0sQoAH/j723+PoXcMjRUbVhTMR+w3IqpPr44OFR0y2gxKllgFgA9b8O6CGDJ+SCxdu7Rgftxex8U9o+6Jzu06Z7QZlCSxCgAftWjVoqgaXxWLVi8qmA/cY2BMHT01duqwU0abQclpNlZ93SoAJa1v977xxLlPxL677lswL8uVubsKCXCyCgARsXz98hh6x9B49p1n4+jdj47p50x3qgqtyzUAANialRtXxqUPXRq/Gvar6NaxW9brQKkRqwAAJMudVQAAiotYBQAgWWIVAIBkiVUAAJIlVgEASJZYBQAgWWIVAIBkiVUAAJIlVgEASJZYBQAgWWIVAIBkiVUAAJIlVgEASJZYBQAgWWIVAIBkiVUAAJJVsY3nuVbZAgAAmuFkFQCAZIlVAACSJVYBAEiWWAUAIFliFQCAZIlVAACS9b8JJ4eIlj58DgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFII3V21bHU5ufirZ9bWWPAiQhVgFI44fLfxhz7poTo/5jVMy9e2481vRY2SMBJROrAKTRuLkxIiLa9rfFE5ueiDf3v1nyREDZxCoAKexq2xUrtqzosnba0aeVNA2QhVgFIIVnX3o2OoqOzusZ42bE+JrxJU4EZCBWAUihcVNjl+vTjz69pEmATMQqACl0i9UpYhUQqwAk0L6/PZ558Zkua3OmzClpGiATsQpA6VZuXRlvtL/ReT2hZkLUjakrcSIgC7EKQOl6OgJQqVRKmgbIRKwCUDrnVYF3I1YBKFVRFGIVeFdiFYBSrd2+Nra+sbXzumZoTXxi4idKnAjIRKwCUKonNz3Z5frUo06N6qrqkqYBshGrAJTKEQCgN2IVgFI1bharwLsTqwCU5tU3Xo3V21Z3Xg+pDIlTJp9S4kRANmIVgNI8tfmpLtcnTjwxjjjsiJKmATISqwCU5g8v/aHL9elHOwIAdFUpiqK3/V43AeDDKIoi1ry2Jho3NUbjpsb43D98Lj5T/5myxwLK0ePX1olVAAAy6DFWHQMAACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQDgkPCLP/8i7v7fu8segz5WXfYAAAAfxpv734yv/9fX43t/+F4MGzIsZk2YFSd/9OSyx6KPVIqi6G2/100AgDK9uPPFuOSBS+KZF5/pXJs6amo8/+Xno3Z4bYmT8QFUelp0DAAAGJB+s+43MfuO2V1CNSLi5ddfjmdffLakqehrYhUAGFA6io647fe3xfzF82Pb7m1d9qaOmhpPXvNknDv93JKmo685swoADBjb92yPq5ZeFY80PdJt79z6c2PxhYtj7IixJUxGfxGrAMCA8PzLz8eC+xfEhtYNXdYrUYlb/+nWuHnuzVFV8Z/GhxqxCgCk95PnfxLXPnpttO1v67I+dvjY+PmCn8f8uvklTUZ/E6sAQFp72vfEtY9eG3ev6P75qZ+a/Kl44JIHYsqoKSVMxsEiVgGAlNa2rI0F9y+IlVtXdtu79h+vjYXzF8Zh1YeVMBkHk1gFANJ5cPWDcfWyq2NH244u6yOGjohF5y2Ky2ddXtJkHGxiFQBI5bvPfjdu+NUN3daPG3tcLPm3JfHxj3y8hKkoi7fMAQCpzJs2L2qG1nRZu/j4i2P5l5YL1UFIrAIAqRw//vhYdN6iiIiorqqO28+5Pe6/+P448rAjS56MMjgGAACkc9msy+Kvr/01zp52dpw+5fSyx6FElaIoetvvdRMAAPpIpadFxwAAAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApFX9HvuVgzIFAAD0wJ1VAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFr/B/uR0UU/ed+6AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cFrOenRUXvPWCskcBgHrlzCoAAGk5swoAQG0RqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0GsseAADqWVEUsaZ1TSxqXhSLWxbHopbX/nnlKVfGececV/Z4kJ5YBYBuUBRFvPTqS68F6evCdN2Wdbt8/5lHnilWoQvEKgDsgaIoYvXG1e0huqh5USx+eXEsblkcr2x5pcuvs7hlcQ9OCfVDrALAHph639SYtWzWPr/OopZF3TAN1D+xCgB74IgDjtjjnxncf3CMGzHutV8Hj4vxI8fH+BHju384qENiFQD2wLgR497w3pD+Q2LciNdidNzB49q/HjNsTDRUPIAH9oZYBYA9MH7E+Gga0NS+Uzp+xPj2r0cPGy1KoZtViqLY3f3d3gSAvqataItKVKJSqZQ9CtSbDv9QiVUAADLoMFb9vwoAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpiVUAANISqwAApCVWAQBIS6wCAJCWWAUAIC2xCgBAWmIVAIC0xCoAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtMQqAABpNZY9AEB2M5+cGfNWzYsXN7wYK9aviJkXzIyJoyaWPRZAnyBWATrxk2d+Eg8+82D79fPrnherAL3EMQCAToweOrrq+sX1L5Y0CUDfI1YBOjFm2Jiq6xXrV5Q0CUDfI1YBOrHLzuoGO6sAvUWsAnTCzipAecQqQCdGD7OzClAWsQrQiVFNo6Kh8tf/XDa3NseWHVtKnAig7xCrAJ1obGiMUU2jqtZWblhZ0jQAfYtYBegC51YByiFWAbrAs1YByiFWAbrAzipAOcQqQBd41ipAOcQqQBfYWQUoh1gF6ALPWgUoh1gF6IKOdlaLoihpGoC+Q6wCdMHw/YbHoMZB7devbns11m9dX+JEAH2DWAXogkql4twqQAnEKkAX/f8TARoqDTF66OjYuHVjyRMB1L9KJ2euHMgC+Itla5fFgH4DYlTTqGhsaCx7HIB6U+lwUawCAJBAh7HqGAAAAGmJVQAA0hKrAACkJVYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaYlVAADSEqsAAKQlVgEASEusAgCQllgFACAtsQoAQFpiFQCAtBo7uV/plSkAAKADdlYBAEhLrAIAkJZYBQAgLbEKAEBaYhUAgLTEKgAAaf0fJlRB0CrvR8wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cemqyYEHVlQFQUzqrQM+bOTM54YTkP/6jvH7Pe8pc68YbV1sXAFXSWQVqYtiw5Ac/SP7rv5K1107+8Idkyy2T732v3IQFAH+nswpUa8aMcoDABReU1x/8YPKznyXrr19tXQD0NJ1VoIZGjEjOPz+55ppktdWS//7vctPVj3+cLPk/pgHoBXRWgfr429+SI45IrriivP7IR8rRrWutVW1dAPQEnVWg5kaNSi67LLnkkmTkyOQ//zPZfPPkF7/QZQXopXRWgXp69tnksMOSG24or/fZp+wesNpq1dYFQHfRWQUayJgxyXXXJT/9aTJ8eHLVVaXLeuONVVcGQA/SWQXq78knk0MOKQcKDBmS3H9/suGGVVcFQNfSWQUa1LrrJjffnBxwQDJrVgmu9mMF6BWEVaAx9O2bnHNOsvrqye23J+eeW3VFAPQAYwBAY7nmmuRjHzMOANB8jAEATWDvvZMDDzQOANBLCKtA4zn77I5xgHPOqboaALqRMQCgMbWPAwweXMYBxo6tuiIAVowxAKCJtI8DzJ5tHACgiQmrQONqHwf47W+NAwA0KWMAQGP71a9Kl9U4AECjMwYANKG99jIOANDEhFWg8RkHAGhaxgCA5mAcAKDRGQMAmtheeyWf/GQZB9hzz+SBB6quCIAuoLMKNI+XXkq22y6ZOjUZODA544zkyCOTPp3+xzoA9aKzCjS5VVdN7rorOfTQZO7c5Oijk913T154oerKAFhOOqtAc7ryyuSww5Lp05PVVkvOPz/56EerrgqAxdNZBXqRSZPKjVY77FA6qxMnJscck8yZU3VlACwDnVWgubW0lNnVr389WbAgeec7k4svTjbfvOrKAFhUp51VYRXoHf70p3J4wKOPuvkKoJ6MAQC92FZbJX/+s5uvABqMzirQ+7j5CqCOdFYBkrj5CqCBCKtA77T22snNNyff/nbSv39y9tnJ+PHJRRcl8+dXXR0Af2cMAOBPfypHtT7ySHm93nrJV76SfOYzyaBBVVYG0JvYDQBgsebNS37xi+TUU8uOAUkyZkxy3HHJ5z6XDBtWbX0AzU9YBXhLLS3JFVck3/pWmWtNyjGuxxyTHHVUMnJktfUBNC9hFWCptbUlN9yQnHJK8vvfl7Xhw5MvfCE59thk9dWrrQ+g+QirAMusrS257bYSWm+5pawNGlS2vjr++GSddSotD6CJCKsAK+QPfyjjAddeW16vtFLy6U8nJ56YjBtXbW0AjU9YBegS999fbsS67LKktTXp2zfZb78SWsePr7o6gEYlrAJ0qUcfTU47Lbnwwo69WTfcMNl112SXXZIdd0ze9rZqawRoHMIqQLeYNi05/fRyoMCMGR3r/fol73lPCa677ppss005gACAzgirAN1qwYLk7ruTm24qp2P97ndlrd3KK5dua3t43XDDpE+n/2wG6I2EVYAe9dprZSeBm24qj/YTstqtv35HcN1xR3u4Ar2dsApQqSefLB3Xm29OJk9OXn65472+fZOtty7hdc89yzVA7yKsAtRGS0tyzz0dIwP/8z8dN2klyeWXJx//eHX1AfQ8YRWgtmbOTG6/Pbn44uQXv0je8Y7kgQdKxxWgdxBWAWpv3rxywMBTTyVXXJFMmlR1RQA9pdOw6j/ZAepkwIDkhBPK9cknl+NeAXoxnVWAupk9O9lgg+S555Lrr092263qigB6gs4qQEMYPDg57rhy/c1v6q4CvZrOKkAdzZyZrLde8tJLZZurnXaquiKA7qazCtAwhg1Ljj22XJ9ySrW1AFRIZxWgrmbMSNZdN3n11eSOO5L3v7/qigC6k84qQEMZMSI5+uhyrbsK9FI6qwB19re/le7qrFnJn/6UvPvdVVcE0F10VgEazqhRyRFHlOtvfavaWgAqoLMKUHfPPpusv34yd245gnWzzaquCKA76KwCNKQxY5JDDy3XuqtAL6OzCtAInnwyGTs2aW1Nvv/95PDDk776DUBT0VkFaFjrrpt8+cslrB55ZLLddsmUKVVXBdDthFWARnHqqcmVV5axgN/9LpkwIfnGN5I5c6quDKDbGAMAaDQzZiRf/Wrywx+W1+PGJT/6UfKhD1VaFsAK6nQMQFgFaFR33JF87nPJQw+V14cemvzv/52sskq1dQEsHzOrAE1lu+2Se+5JTjopGTAg+clPkne8I7n00mTJjQiAhqGzCtAMpk4tXdbf/ra8/uhHkx/8IFlvvUrLAlgGOqsATWuTTZLbbkt+/ONkxIjkxhvL4QFnnZUsWFB1dQDLTWcVoNk891xyzDHJZZeV1+9+dwmxEyZUWxfAkrnBCqBXuf765AtfSKZNS/r1K/uzHnxwMn580qfTfycAVElYBeh1Zs4se7GefXY5UCBJNtgg2WefZNKkZJttnIQF1IWwCtBr/fnPZS/Wq69OXnihY32ttTqC63bblQ4sQDWEVYBer6UlufPOchLWVVeVEYF2o0cne+9dguuOOyYrrVRdnUBvJKwCsJC2tuSuu0pwvfLK5PHHO94bMSLZc88SXHfZJRk8uLo6gd5CWAVgMdrakvvvL93WK69MpkzpeG/o0GS33UpwnTgxGTasujqBZiasArCUHn64Y1Tg7rs71gcNSv75n5NTT3VjFtDVhFUAlsMTT3R0XO+8s6x95jPJeee5IQvoSsIqACto8uRkr72SWbOS/fdPLrrIjVhAVxFWAegCd9xRZldfe60E11/+Mhk4sOqqgMYnrALQRe66K/nwh5Pp05Nddy37tw4ZUnVVQGMTVgHoQvffn+y8c/Lii8n225fjXYcPr7oqoHEJqwB0salTk512Sv761+Q970luvDEZObLqqoDGJKwC0A0ef7wE1iefTLbcMrnppnIaFsCy6TSs2iQPgBWz4YbJb3+bjBuX3Htv8qEPJc8+W3VVQJMQVgFYceusk9x+e7LZZsmDD5YZ1qeeqroqoAkIqwB0jTXWSG67LXnXu5LHHks+8IHyDLAChFUAus6oUckttyTbbls6q9tvXzqtAMvJDVYAdL2ZM5M99iid1jFjkilT7BIAvBU3WAHQQ4YNS37969JhffbZ5Gtfq7oioEHprALQfR58MBk/PmlpSe68M3nve6uuCKgvnVUAetimmybHH5+0tSWHH54sWFB1RUCDEVYB6F5f/3qy3nrJffcl3/9+1dUADcYYAADd79e/TnbbLRk6NHnoobIvK8CijAEAUJGJE5NJk5LXX0+OOabqaoAGorMKQM945plkk03KtlbXXlu2tgLooLMKQIXWWis5+eRyffTRpcsK8BaEVQB6zpFHJhMmJE8+mXzzm1VXAzQAYwAA9Kw//rHst9qvX3LPPcnmm1ddEVAPxgAAqIFttkmOOKLsuXr44Ulra9UVATWmswpAz5sxo9xs9fzzyXnnJYceWnVFQPU67awKqwBU45JLkgMPTFZZJZk6NRk9uuqKgGoZAwCgRg44oMyuvvxycuONVVcD1JSwCkA1+vQpQTVJxo2rthagtowBAFCNp58ux64OH15Ca//+VVcEVMsYAAA1csst5fmDHxRUgcUSVgGoxm9+U5533LHaOoBaE1YB6HltbR2d1Z12qrYWoNbMrALQ8x5+uOyzOnp08txzSV+9E8DMKgB10d5V3XFHQRVYIv+EAKDnGQEAlpIxAAB6VktL+fp/+vTk8ceTDTaouiKgHowBAFAD995bguq66ybrr191NUDNCasA9Kz2Lat22qmcYgWwBMIqAD3LvCqwDMysAtBz5s1LRo5MZs1Knn02WWONqisC6sPMKgAV+/3vS1DdbDNBFVgqwioAPeeJJ8rzsGHlFCuAtyCsAtBzdt+9jAH84Q/JdddVXQ3QAIRVAHrOKqsk//qv5fr445P586utB6g9YRWAnnXEEcnYsckjjyQ//GHV1QA1ZzcAAHreNdckH/tYsuqqyaOPltEAoLezGwAANbHXXsn22ycvvZScckrV1QA1prMKQDXuvjvZaqtkwIDkwQeTDTesuiKgWjqrANTIu9+dHHRQOSjgxBOrrgaoKZ1VAKrz9NPJRhsls2cnd9yRvP/9VVcEVEdnFYCaWXvt5LjjyvWXvpS0tlZbD1A7OqsAVGvmzGTcuOS555KLL04+8YmqKwKqobMKQA0NG5acfHK5PvHEMhIA8HfCKgDV+8xnki22SJ56Kvne96quBqgRYwAA1MPkyckuuyTDh5dDA3bYIenT6beCQHMyBgBAje28c7LHHslrryU77ZRMmJBceGHZ2grotXRWAaiP115LzjorOffc5IUXytqYMcmRRyaHH16OZwWaVaedVWEVgPqZMye55JLkzDOTBx4oa4MHl0MEvvjFZJNNqq0P6A7CKgANpq0tueWWElpvvLFjfbfdkmOPTXbc0VwrNA9hFYAG9tBDyXe/W+ZY58wpa1tsUULrJz6RDBxYbX3AihJWAWgCL76Y/J//k5xzTvL882Vt9dWTo44qc62jRlVbH7C8hFUAmsjcuWWu9ayzkvvvL2uDBpW51hNOSDbcsNr6gGUlrALQhNrakt/8poTWG24oa2PGJH/9a7V1ActKWAWgyd1zT/KudyVDhyYzZ1ZdDbBsHAoAQJMbM6Y8Dx1abR1AlxFWAWge7d3UYcOqrQPoMsIqAM3j9dfLs7AKTUNYBaB5tHdWjQFA0xBWAWgeOqvQdIRVAJqHzio0HWEVgObhBitoOsIqAM3DGAA0HWEVgOZhDACajrAKQPMwBgBNR1gFoHm0jwHorELTEFYBaB46q9B0hFUAmocbrKDpCKsANI/2zuq11yZPPlltLUCXEFYBaB477FCer7giGTs2OeSQ5JFHqq0JWCF92tralvT+Et8EgNqZMiU59dTkkkuS1takb99kv/2Sr30teec7q64OWLw+nS4KqwA0pcceS047LbnggmT+/LK2117Jv/xLsvXW1dYGdEZYBaAXmjYtOf305Mc/TubMKWu77lpC6/bbV1sbsDBhFYBe7PnnkzPPTH7wg44bsT7wgeTrX0922SXp0+m/J4GeI6wCQF56KTn77PKYMaOsbbVVCa177FFmXIEqCKsA8A+vvpr8x38k3/lO8uKLZW3zzcuNWPvum/TvX2190PsIqwDwJrNmlXnW009PnnmmrI0Zkxx0UHLwwcnGG1dbH/QewioALNbcuWXngO98Z9G9Wd/3vrJf6377JcOHV1cfND9hFQDeUltbcuedyc9+lvzylx03Yw0ZUsYDDjmk3JjlhizoasIqACyTmTOTK69MfvrT5PbbO9Y33LCMCBx0ULLOOl33+1pakscfLwcbTJmSPPBA8te/Jm9/ezmRq/0xblyyyioCM81GWAWA5fbYY8n555dH+2xrnz5lz9aDDy4HDgwatHSf1dqaPPHEoqF0ypRk6tSOvWDfyogRi4bXhcPs6NGCLI1IWAWAFdbSkkyeXLqt11yTzJtX1keOTD75yRJcJ0woYbGtrRxK8MZQ+uCD5cauzqyzTtmVYLPNymOddZKnniph+bHHkkcfLc+vvbb4Glde+c2d2LFjky22KO9BPQmrANClXn45ufjiElzvuadjfYstyozrgw+WLbI6M2bMoqF0882TTTddujDZ1la221o4vLZfP/ro4n/n6NGloztkyDL/VaEHCKsA0G3uvbfclPWLX5SDB9qNHt15KF1lle6po62t/P6FQ+xjjyVXXVVGDB5/PNlgg+753bBihFUA6HZz5ya33poMHFjC6WqrVV1RsckmycMPJw89VK6hfjoNq47nAICuNHBg8pGPVF3Fmw0YUJ7bZ2yhQTgAGQB6g4EDy/PcudXWActIWAWA3kBnlQYlrAJAbyCs0qCEVQDoDdrDqjEAGoywCgC9QfvMqs4qDUZYBYDewBgADUpYBYDeQFilQQmrANAbmFmlQQmrANAbmFmlQQmrANAbGAOgQQmrANAbGAOgQQmrANAbtIfVO+5IXnih2lpgGQirANAbjB9fnn/1q2TddZOjjkqeeKLSkmBpCKsA0BsccEDyu98le+2VzJmTnHtuMnZs8ulPJw88UHV1sFh92tralvT+Et8EABrQlCnJaaclF1+ctLSUtT32SL761WTbbautjd6sT6eLwioA9FJPPpmccUZy3nml25okH/xgcuKJyYc/nPTpNDtAd+PJyxYAAAglSURBVBFWAYBOvPBCcvbZyTnnJK+8UtYmTCihddKkpF+/auujtxBWAYAlePXV5Ic/TM48M3n++bI2dmxywgnJQQd1HCwA3UNYBQCWwpw5yfnnJ6efnvzlL2VtzJjkS19KPv/5ZPjwSsujaQmrAMAyWLAgufzy5NvfTu6/v6xttFHy298mq61WbW00I2EVAFgObW3JjTcmxx+fPPhgmWe99dbkbW+rujKai7AKAKyA559PttsueeyxZPvtk//8z2Tw4Kqronl0GlYdCgAALJ3VV09uvjlZa63k9tuT/fdP5s+vuiqanLAKACy99dZLbropWWWV5LrrkkMPTVpbq66KJiasAgDLZtNNywzr0KHJRReVXQKWPFYIy01YBQCW3TbbJNdckwwYkHzve8nJJ1ddEU3KDVYAwPK78spkv/3KKMC55yZf+ELVFdG43GAFAHSxSZPKqVdJctRRySWXVFsPTUdnFQBYcaedlpx4YtK/f/KrXyUTJy7f57S2JtOmJQ8/nEydWp4feyzZfPPkG99IRozo2rqpE/usAgDd6IQTyhGtgweXHQO2227xP/vaa8kjj3QE0vZw+uijyezZnf+ZNdYo87H77pv06TTX0NiEVQCgG7W1JYcdlvzkJ+V0q1tvTUaOfHMgffjh5K9/XfznrLFGsvHGHY911km++93kzjvL+xMnlvnY9dbrkb8WPUZYBQC62YIF5bCAq65a8s8NHJiMG9cRSDfZpOO6s2NcW1uT884r3dtXXkmGDElOOin54hfL6AHNQFgFAHrA3LnJ3nuX41jHjOk8kK67btKv37J/9nPPJccem1x6aXm95ZbJj36UbL111/4dqIKwCgD0kNbWZM6c0gHtDjfeWLbJeuKJMr961FFlr9eVV+6e30dPEFYBgCby+uvJv/978p3vJC0tyVprJeecU7q6NCJhFQBoQvfdl3zuc8kf/1he77VX8v3vlxuzaCQOBQAAmtD48WWngHPOSYYPL/u8brpp2eaqpaXq6lhBOqsAQPN45pnkmGPKMbBJstVWZSutLbaoti6WhjEAAKCXuO665Mgjy2lYI0Ykf/hDstFGVVfFkgmrAEAvMnNmcuCBJbhuvHEJrJ3t4UpdCKsAQC8zc2ay7bbJAw+Uk6+uvXb59nelJ7jBCgDoZYYNKwF11VWTX/86+drXqq6IZaSzCgA0v9tuS3bZpRwHe9FFyac+VXVFvJnOKgDQS33oQ8nZZ5frz362Y09Wak9nFQDoPY44IvnhD5M110zuuqs8UxdusAIAerl588o4wO23J9tsk/z3fyeDBlVdFYUxAACglxswILniimTddcsowOc+lyy5cUfFhFUAoHcZPbrsEDB0aLnZ6jvfqboilsAYAADQO111VTJpUtKnT3LDDclHP1p1Rb2dMQAAgH/YZ5/kpJPKGMABByRTp1ZdEZ3QWQUAeq/W1mS//ZIrr0zGjUsuuyzZcsuqq+qtdFYBABbRt29ywQXJ+PHJo48mEyYku++e/O53VVfG3wmrAEDvNnRoMnlycuyxyZAhZX71fe9LdtwxueUWuwVUTFgFABg1KjnzzOSJJ5KvfS1ZeeXk1luTnXdOtt02uf76xgitd9yRTJyYHH108uqrVVfTJcysAgC80YwZybnnJmedlbz0UlkbP74E2UmTkn79qq3vjaZOTU48MfnVrzrW1l03+dnPkh12qK6uZWNmFQBgqYwYkfzLvyRPPlk6rmPGJPfdl+y/f7LZZsn55yfz51ddZfLss8nhhyebb16C6pAhJbS+612l9h13TI45Jpk1q+pKl5vOKgDAW5kzpwTU004rowJJ6Vx+5SvJwQf3/JGtr72WnHFGecyaVTq9n/1s8q//WoL1/PnJt76VnHxysmBBstFG5Uay9763Z+tcNp12VoVVAIClNX9+csklyamnduzLOmZM8uUvJ5//fDJsWPf//vPOS/7t35IXXihre+9d6tlkkzf//N13J//0T8mUKWXng698pQTagQO7t87lI6wCAHSJlpZyAtYpp5TxgCRZddVk113L9lftj1VX7Zrf19aWXH118tWvJo88Uta23TY5/fTk/e9f8p+dM6cE1NNPL5/zzncmF15Yx/1khVUAgC7V1pb8+tfl6/bf//7N76+zzqLhdcKEstan01zWuTvuSE44oWPv13Hjkm9/O/nYx5btc+68s3RZH3ss6d+/BNgTTyzX9SCsAgB0i7a20mG9667knnvK4/77O7+xadVVS1dz4QC70UZv3mFg6tTSSb3mmvJ6tdXK1/+f/Wyy0krLV+frr5eAes455fXWW5dZ1ne8Y/k+r2sJqwAAPaalpXxl3x5e2x8vv/zmnx0yJNlii47wevfdZTa1paW8d/zxZS52+PCuqe2WW8qNYdOmlfnVb30r+eIXy1xrdYRVAIBKtbWVgHjPPcm993YE2KeeevPPvvEO/672yivJl76U/PSn5fX225d9WTfYoOt/19IRVgEAaumllxYNr4MGlW5qZ3f4d7Xrr08OOyx57rly9OyPfpQceGD3/943E1YBAOjESy8lRx2VXHppMnlystNOVVQhrAIAsAT33FNmZqshrAIAUFudhtVKb/kCAIAlEVYBAKgtYRUAgNoSVgEAqC1hFQCA2hJWAQCoLWEVAIDaElYBAKgtYRUAgNoSVgEAqC1hFQCA2hJWAQCoLWEVAIDaElYBAKgtYRUAgNoSVgEAqC1hFQCA2ur/Fu/36ZEqAACgEzqrAADUlrAKAEBtCasAANSWsAoAQG0JqwAA1JawCgBAbf1/JxvSCpSjyR4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VC4PZloI5aGS"
      },
      "source": [
        "Discuss and implement a suitable method to visualize your results."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K8g1ubH85kjW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d14cf5d5-11a9-42f4-8452-b3b221167f33"
      },
      "source": [
        "# install\n",
        "\n",
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from matplotlib import animation, rc\n",
        "from IPython.display import HTML, Image\n",
        "\n",
        "# equivalent to rcParams['animation.html'] = 'html5'\n",
        "rc('animation', html='html5')\n",
        "\n",
        "!apt install imagemagick"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "imagemagick is already the newest version (8:6.9.7.4+dfsg-16ubuntu6.11).\n",
            "0 upgraded, 0 newly installed, 0 to remove and 40 not upgraded.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "2i-Fc4-UKTYS",
        "outputId": "f1cdd5b3-0adf-4b60-b4d4-496958847539"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.offsetbox import OffsetImage, AnnotationBbox\n",
        "from matplotlib.cbook import get_sample_data\n",
        "\n",
        "def main(positions, image_paths):\n",
        "    x = positions[:, 0]\n",
        "    y = positions[:, 1]\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.imshow(np.flipud(floorplan.T), extent=figure_bounds, cmap='Greys_r')          # images and matrixes are indexed differently. Use this to plot floorplan image.\n",
        "    ax.scatter(position_robot[0], position_robot[1], c='b')\n",
        "    imscatter(x, y, image_paths, zoom=0.05, ax=ax)\n",
        "    ax.scatter(x, y, color='r')\n",
        "    #plt.show()\n",
        "\n",
        "def imscatter(x, y, images, ax=None, zoom=1):\n",
        "    # display the relevent images at each (x, y) location\n",
        "    if ax is None:\n",
        "        ax = plt.gca()\n",
        "\n",
        "    x, y = np.atleast_1d(x, y)\n",
        "    artists = []\n",
        "    for x0, y0, i0 in zip(x, y, images):\n",
        "        try:\n",
        "          img = plt.imread(i0)\n",
        "        except TypeError:\n",
        "          # Likely already an array...\n",
        "          pass\n",
        "        im = OffsetImage(img, zoom=zoom)\n",
        "        ab = AnnotationBbox(im, (x0, y0), xycoords='data', frameon=False)\n",
        "        artists.append(ax.add_artist(ab))\n",
        "    ax.update_datalim(np.column_stack([x, y]))\n",
        "    ax.autoscale()\n",
        "    return artists\n",
        "\n",
        "\n",
        "positions = position_customers\n",
        "image_paths = []\n",
        "for i in range(len(position_customers)):\n",
        "  image_paths.append(os.path.join(f\"customers/{i}\", os.listdir(f\"customers/{i}\")[0]))\n",
        "\"\"\" # example for reading image paths\n",
        "image_paths = []\n",
        "for i in range(len(position_customers)):\n",
        "  image_paths.append(os.path.join(f\"customers/{i}\", os.listdir(f\"customers/{i}\")[0]))\n",
        "\"\"\"\n",
        "\n",
        "main(positions, image_paths)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "bAov8ksgK0xd",
        "outputId": "520fb941-d322-42ca-f67a-54e73777b4b4"
      },
      "source": [
        "# First set up the figure, the axis, and the plot element we want to animate\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "# values\n",
        "obstacles = np.asarray(np.where(floorplan == 0)).T\n",
        "obs = set()\n",
        "for i in range(len(obstacles)):\n",
        "  obs.add((obstacles[i, 0], obstacles[i, 1]))\n",
        "s_start = tuple(position_robot)\n",
        "s_goal = tuple(position_customers[int(name)])\n",
        "result = path\n",
        "result = np.asarray(result)\n",
        "# visited = # write code - list of visited nodes\n",
        "\n",
        "# unanimated parts of plot\n",
        "obs_x = [x[0] for x in obstacles]\n",
        "obs_y = [x[1] for x in obstacles]\n",
        "ax.plot(obs_x, obs_y, \"sk\")\n",
        "\n",
        "ax.plot(s_start[0], s_start[1], \"rs\")\n",
        "ax.plot(s_goal[0], s_goal[1], \"bs\")\n",
        "plt.axis('equal')\n",
        "\n",
        "# v_x = [x[0] for x in visited]\n",
        "# v_y = [x[1] for x in visited]\n",
        "# ax.scatter(v_x, v_y, color='grey')\n",
        "imscatter(positions[:, 0], positions[:, 1], image_paths, zoom=0.045, ax=ax)\n",
        "# line to animate\n",
        "line, = ax.plot([], [], lw=2)\n",
        "\n",
        "def init():\n",
        "    line.set_data([], [])\n",
        "    return (line,)\n",
        "    \n",
        "def animate(i):\n",
        "    # at time i, draw from 0th frame to ith frame \n",
        "    line.set_data(result[:i, 0], result[:i, 1])\n",
        "    return (line,)\n",
        "\n",
        "# call the animator. blit=True means only re-draw the parts that \n",
        "# have changed.\n",
        "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=100, interval=20, blit=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "id": "Qk74pOcfK1_J",
        "outputId": "fd6fc2af-91b1-4186-ccb8-2a85112cb33f"
      },
      "source": [
        "# display\n",
        "anim\n",
        "\n",
        "## save animation\n",
        "#anim.save('animation.gif', writer='imagemagick', fps=60)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-13-da6b53eb3c80>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# display\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0manim\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m## save animation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;31m#anim.save('animation.gif', writer='imagemagick', fps=60)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'anim' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VCiUUMZMR3iJ"
      },
      "source": [],
      "execution_count": null,
      "outputs": []
    }
  ]
}