A-Star-City.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Your Way In The City\n",
    "\n",
    "In this notebook you'll combine the work of previous exercises to calculate a minimal series of waypoints in order to get from a start location to a goal location.\n",
    "\n",
    "You'll reuse and modify your algorithms from:\n",
    "\n",
    "- A*\n",
    "- Configuration Space\n",
    "- Collinearity and/or Bresenham"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from grid import create_grid\n",
    "from planning import a_star, heuristic, actual_path\n",
    "from colinear import prune_path, collinearity_check, point\n",
    "%matplotlib inline\n",
    "\n",
    "#from bresenham import bresenham\n",
    "from bresenham import bresenham"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#testing modules\n",
    "import argparse\n",
    "import time\n",
    "import msgpack\n",
    "from enum import Enum, auto\n",
    "import utm\n",
    "import numpy as np\n",
    "\n",
    "#from planning_utils import a_star, heuristic, create_grid\n",
    "from planning import * #modified version of a_star containing diagonal movement, np.linalg.norm Heuristic\n",
    "from grid import *\n",
    "#from udacidrone import Drone\n",
    "#from udacidrone.connection import MavlinkConnection\n",
    "#from udacidrone.messaging import MsgID\n",
    "#from udacidrone.frame_utils import global_to_local\n",
    "from geo_ned import *  #to convert from geo to ned freely. vice versa\n",
    "from colinear import * #contains prune_path and other useful definitions/functions/algorithms\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = 12, 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-3-0f44b287cd63>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-3-0f44b287cd63>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    x =\u001b[0m\n\u001b[1;37m        ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "x = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll notice we've imported `create_grid`, and `a_star`. These are functions you've implemented in previous exercises, and here you'll use them to create a map and find a path from a starting position to a goal position.\n",
    "\n",
    "To read the function signature and documentation execute `?` followed by the function name in a cell. In the example below we'll check the documentation for `create_grid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "?create_grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you would like to alter these implementations, you can modify [grid.py](/edit/grid.py) and [planning.py](/edit/planning.py) in the current directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-310.2389   -439.2315     85.5         5.          5.         85.5     ]\n",
      " [-300.2389   -439.2315     85.5         5.          5.         85.5     ]\n",
      " [-290.2389   -439.2315     85.5         5.          5.         85.5     ]\n",
      " ...\n",
      " [ 257.8061    425.1645      1.75852     1.292725    1.292725    1.944791]\n",
      " [ 293.9967    368.3391      3.557666    1.129456    1.129456    3.667319]\n",
      " [ 281.5162    354.4156      4.999351    1.053772    1.053772    4.950246]]\n"
     ]
    }
   ],
   "source": [
    "# This is the same obstacle data from the previous lesson.\n",
    "filename = 'colliders.csv'\n",
    "data = np.loadtxt(filename, delimiter=',', dtype='Float64', skiprows=2)\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Static drone altitude (meters)\n",
    "drone_altitude = 5\n",
    "\n",
    "# Minimum distance stay away from obstacle (meters)\n",
    "safe_distance = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Use `create_grid` to create a grid configuration space of\n",
    "# the obstacle data.\n",
    "grid, north_min, east_min = create_grid(data, drone_altitude, safe_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17dab7d32e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# equivalent to\n",
    "# plt.imshow(np.flip(grid, 0))\n",
    "plt.imshow(grid, origin='lower') \n",
    "\n",
    "plt.xlabel('EAST')\n",
    "plt.ylabel('NORTH')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next you'll compute the path from a start location to a goal location using A*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start and goal coordinates in *(north, east)*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "start_ne = (316, 445)\n",
    "goal_ne = (326, 455)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a heuristic function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def heuristic_func(position, goal_position):\n",
    "    # TODO: write a heuristic approach!\n",
    "    #Manhattan Graph or Euclidean Distance.\n",
    "    #Manhattan is used in this approach\n",
    "        \n",
    "    return np.abs(goal_position[0] - position[0]) + np.abs(goal_position[1] - position[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the lowest cost path with `a_star`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found a path.\n",
      "11 14.142135623730955\n"
     ]
    }
   ],
   "source": [
    "# TODO: use `a_star` to compute the lowest cost path\n",
    "path, cost = a_star(grid, heuristic_func, start_ne, goal_ne)\n",
    "print(len(path), cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(316, 445), (317, 446), (318, 447), (319, 448), (320, 449), (321, 450), (322, 451), (323, 452), (324, 453), (325, 454), (326, 455)]\n"
     ]
    }
   ],
   "source": [
    "print(path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the path!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17dab84cba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(grid, cmap='Greys', origin='lower')\n",
    "\n",
    "#fix the plot error\n",
    "#path = actual_path(actions, start_ne)\n",
    "\n",
    "\n",
    "# For the purposes of the visual the east coordinate lay along\n",
    "# the x-axis and the north coordinates long the y-axis.\n",
    "plt.plot(start_ne[1], start_ne[0], 'x')\n",
    "plt.plot(goal_ne[1], goal_ne[0], 'x')\n",
    "\n",
    "pp = np.array(path)\n",
    "plt.plot(pp[:, 1], pp[:, 0], 'g')\n",
    "\n",
    "plt.xlabel('EAST')\n",
    "plt.ylabel('NORTH')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty neat! Unfortunately this path is impractical, the drone would be constantly stopping and going since each grid cell visited is synonymous with a waypoint. Ideally, we'd like to only consider a new waypoint when the drone's direction changes. Path pruning is one way to achieve this result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Path Pruning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\ndef point(p):\\n    return np.array([p[0], p[1], 1.]).reshape(1, -1)\\n\\ndef collinearity_check(p1, p2, p3, epsilon=1e-6):   \\n    m = np.concatenate((p1, p2, p3), 0)\\n    det = np.linalg.det(m)\\n    return abs(det) < epsilon\\n'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "def point(p):\n",
    "    return np.array([p[0], p[1], 1.]).reshape(1, -1)\n",
    "\n",
    "def collinearity_check(p1, p2, p3, epsilon=1e-6):   \n",
    "    m = np.concatenate((p1, p2, p3), 0)\n",
    "    det = np.linalg.det(m)\n",
    "    return abs(det) < epsilon\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complete the `prune_path` function below. It should return a new path much shorter than the original."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# We're using collinearity here, but you could use Bresenham as well!\\ndef prune_path(actual_path):\\n    #pruned_path = [p for p in actual_path]\\n    # TODO: prune the path!\\n    #startp = point(pruned_path[0])\\n    #goalp = point(pruned_path[len(pruned_path)-1])\\n    #bres_path = list(bresenham(startp[0], startp[1], goalp[0], goalp[1]))\\n    \\n    #return bres_path\\n    pruned_path = [p for p in actual_path]\\n    # TODO: prune the path!\\n    \\n    i = 0\\n    while i < len(pruned_path) - 2:\\n        p1 = point(pruned_path[i])\\n        p2 = point(pruned_path[i+1])\\n        p3 = point(pruned_path[i+2])\\n        \\n        #If the 3 points are in a line remove\\n        # the 2nd point.\\n        # The 3rd point now becomes and 2nd point\\n        # and the check is redone with a new third point\\n        # on the next iteration.\\n        if collinearity_check(p1, p2, p3):\\n            # Something subtle here but we can mutate\\n            # `pruned_path` freely because the length\\n            # of the list is check on every iteration.\\n            pruned_path.remove(pruned_path[i+1])\\n        else:\\n            i += 1\\n    return pruned_path\\n\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "# We're using collinearity here, but you could use Bresenham as well!\n",
    "def prune_path(actual_path):\n",
    "    #pruned_path = [p for p in actual_path]\n",
    "    # TODO: prune the path!\n",
    "    #startp = point(pruned_path[0])\n",
    "    #goalp = point(pruned_path[len(pruned_path)-1])\n",
    "    #bres_path = list(bresenham(startp[0], startp[1], goalp[0], goalp[1]))\n",
    "    \n",
    "    #return bres_path\n",
    "    pruned_path = [p for p in actual_path]\n",
    "    # TODO: prune the path!\n",
    "    \n",
    "    i = 0\n",
    "    while i < len(pruned_path) - 2:\n",
    "        p1 = point(pruned_path[i])\n",
    "        p2 = point(pruned_path[i+1])\n",
    "        p3 = point(pruned_path[i+2])\n",
    "        \n",
    "        #If the 3 points are in a line remove\n",
    "        # the 2nd point.\n",
    "        # The 3rd point now becomes and 2nd point\n",
    "        # and the check is redone with a new third point\n",
    "        # on the next iteration.\n",
    "        if collinearity_check(p1, p2, p3):\n",
    "            # Something subtle here but we can mutate\n",
    "            # `pruned_path` freely because the length\n",
    "            # of the list is check on every iteration.\n",
    "            pruned_path.remove(pruned_path[i+1])\n",
    "        else:\n",
    "            i += 1\n",
    "    return pruned_path\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prune the path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "pruned_path = prune_path(path)\n",
    "print(len(pruned_path))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(316, 445), (326, 455)]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pruned_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replot the path, it will be the same as before but the drone flight will be much smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17dab88fd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(grid, cmap='Greys', origin='lower')\n",
    "\n",
    "plt.plot(start_ne[1], start_ne[0], 'x')\n",
    "plt.plot(goal_ne[1], goal_ne[0], 'x')\n",
    "\n",
    "pp = np.array(pruned_path)\n",
    "plt.plot(pp[:, 1], pp[:, 0], 'g')\n",
    "plt.scatter(pp[:, 1], pp[:, 0])\n",
    "\n",
    "plt.xlabel('EAST')\n",
    "plt.ylabel('NORTH')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the waypoints symbolize a change in direction, much better!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[solution](/notebooks/A-Star-City-Solution.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}