planning_utils.py

from enum import Enum
from queue import PriorityQueue
from bresenham import bresenham
from scipy.spatial import Voronoi
import numpy as np
import numpy.linalg as LA


def create_grid(data, drone_altitude, safety_distance):
    """
    Returns a grid representation of a 2D configuration space
    based on given obstacle data, drone altitude and safety distance
    arguments.
    """

    # minimum and maximum north coordinates
    north_min = np.floor(np.min(data[:, 0] - data[:, 3]))
    north_max = np.ceil(np.max(data[:, 0] + data[:, 3]))

    # minimum and maximum east coordinates
    east_min = np.floor(np.min(data[:, 1] - data[:, 4]))
    east_max = np.ceil(np.max(data[:, 1] + data[:, 4]))

    # given the minimum and maximum coordinates we can
    # calculate the size of the grid.
    north_size = int(np.ceil(north_max - north_min))
    east_size = int(np.ceil(east_max - east_min))

    # Initialize an empty grid
    grid = np.zeros((north_size, east_size))

    # Populate the grid with obstacles
    for i in range(data.shape[0]):
        north, east, alt, d_north, d_east, d_alt = data[i, :]
        if alt + d_alt + safety_distance > drone_altitude:
            obstacle = [
                int(np.clip(north - d_north - safety_distance - north_min, 0, north_size-1)),
                int(np.clip(north + d_north + safety_distance - north_min, 0, north_size-1)),
                int(np.clip(east - d_east - safety_distance - east_min, 0, east_size-1)),
                int(np.clip(east + d_east + safety_distance - east_min, 0, east_size-1)),
            ]
            grid[obstacle[0]:obstacle[1]+1, obstacle[2]:obstacle[3]+1] = 1

    return grid, int(north_min), int(east_min)

# Here you'll modify the `create_grid()` method from a previous exercise
# In this new function you'll record obstacle centres and
# create a Voronoi graph around those points
def create_grid_and_edges(data, drone_altitude, safety_distance):
    """
    Returns a grid representation of a 2D configuration space
    along with Voronoi graph edges given obstacle data and the
    drone's altitude.
    """
    # minimum and maximum north coordinates
    north_min = np.floor(np.min(data[:, 0] - data[:, 3]))
    north_max = np.ceil(np.max(data[:, 0] + data[:, 3]))

    # minimum and maximum east coordinates
    east_min = np.floor(np.min(data[:, 1] - data[:, 4]))
    east_max = np.ceil(np.max(data[:, 1] + data[:, 4]))

    # given the minimum and maximum coordinates we can
    # calculate the size of the grid.
    north_size = int(np.ceil(north_max - north_min))
    east_size = int(np.ceil(east_max - east_min))

    # Initialize an empty grid
    grid = np.zeros((north_size, east_size))
    # Initialize an empty list for Voronoi points
    points = []
    # Populate the grid with obstacles
    for i in range(data.shape[0]):
        north, east, alt, d_north, d_east, d_alt = data[i, :]
        if alt + d_alt + safety_distance > drone_altitude:
            obstacle = [
                int(np.clip(north - d_north - safety_distance - north_min, 0, north_size-1)),
                int(np.clip(north + d_north + safety_distance - north_min, 0, north_size-1)),
                int(np.clip(east - d_east - safety_distance - east_min, 0, east_size-1)),
                int(np.clip(east + d_east + safety_distance - east_min, 0, east_size-1)),
            ]
            grid[obstacle[0]:obstacle[1]+1, obstacle[2]:obstacle[3]+1] = 1
            # add center of obstacles to points list
            points.append([north - north_min, east - east_min])

    # TODO: create a voronoi graph based on
    # location of obstacle centres
    graph = Voronoi(points)

    # TODO: check each edge from graph.ridge_vertices for collision
    edges = []
    for v in graph.ridge_vertices:
        p1 = graph.vertices[v[0]]
        p2 = graph.vertices[v[1]]
        cells = list(bresenham(int(p1[0]), int(p1[1]), int(p2[0]), int(p2[1])))
        hit = False

        for c in cells:
            # First check if we're off the map
            if np.amin(c) < 0 or c[0] >= grid.shape[0] or c[1] >= grid.shape[1]:
                hit = True
                break
            # Next check if we're in collision
            if grid[c[0], c[1]] == 1:
                hit = True
                break

        # If the edge does not hit on obstacle
        # add it to the list
        if not hit:
            # array to tuple for future graph creation step)
            p1 = (p1[0], p1[1])
            p2 = (p2[0], p2[1])
            edges.append((p1, p2))

    return grid, int(north_min), int(east_min), edges

# Assume all actions cost the same.
class Action(Enum):
    """
    An action is represented by a 3 element tuple.

    The first 2 values are the delta of the action relative
    to the current grid position. The third and final value
    is the cost of performing the action.
    """

    WEST = (0, -1, 1)
    EAST = (0, 1, 1)
    NORTH = (-1, 0, 1)
    SOUTH = (1, 0, 1)
    NORTHWEST = (-1, -1, 2**(1/2))
    NORThEAST = (-1, 1, 2**(1/2))
    SOUTHWEST = (1, -1, 2**(1/2))
    SOUTHEAST = (1, 1, 2**(1/2))

    @property
    def cost(self):
        return self.value[2]

    @property
    def delta(self):
        return (self.value[0], self.value[1])


def valid_actions(grid, current_node):
    """
    Returns a list of valid actions given a grid and current node.
    """
    valid_actions = list(Action)
    n, m = grid.shape[0] - 1, grid.shape[1] - 1
    x, y = current_node

    # check if the node is off the grid or
    # it's an obstacle

    if x - 1 < 0 or grid[x - 1, y] == 1:
        valid_actions.remove(Action.NORTH)
    if x + 1 > n or grid[x + 1, y] == 1:
        valid_actions.remove(Action.SOUTH)
    if y - 1 < 0 or grid[x, y - 1] == 1:
        valid_actions.remove(Action.WEST)
    if y + 1 > m or grid[x, y + 1] == 1:
        valid_actions.remove(Action.EAST)

    return valid_actions


def a_star(graph, h, start, goal):
    """Modified A* to work with NetworkX graphs."""

    path = []
    path_cost = 0
    queue = PriorityQueue()
    queue.put((0, start))
    visited = set(start)

    branch = {}
    found = False

    while not queue.empty():
        item = queue.get()
        current_node = item[1]
        if current_node == start:
            current_cost = 0.0
        else:
            current_cost = branch[current_node][0]

        if current_node == goal:
            print('Found a path.')
            found = True
            break
        else:
            for next_node in graph[current_node]:
                cost = graph.edges[current_node, next_node]['weight']
                branch_cost = current_cost + cost
                queue_cost = branch_cost + h(next_node, goal)

                if next_node not in visited:
                    visited.add(next_node)
                    branch[next_node] = (branch_cost, current_node)
                    queue.put((queue_cost, next_node))

    if found:
        # retrace steps
        n = goal
        path_cost = branch[n][0]
        path.append(goal)
        while branch[n][1] != start:
            path.append(branch[n][1])
            n = branch[n][1]
        path.append(branch[n][1])
    else:
        print('**********************')
        print('Failed to find a path!')
        print('**********************')
    return path[::-1], path_cost



def heuristic(n1, n2):
    return LA.norm(np.array(n2) - np.array(n1))

def closest_point(graph, current_point):
    """
    Compute the closest point in the `graph`
    to the `current_point`.
    """
    closest_point = None
    dist = 100000
    for p in graph.nodes:
        d = LA.norm(np.array(p) - np.array(current_point))
        if d < dist:
            closest_point = p
            dist = d
    return closest_point

def point(p):
    return np.array([p[0], p[1], 1.]).reshape(1, -1)

def collinearity_check(p1, p2, p3, epsilon=1e-6):
    m = np.concatenate((p1, p2, p3), 0)
    det = np.linalg.det(m)
    return abs(det) < epsilon

def prune_path(path):
    pruned_path = [p for p in path]
    # TODO: prune the path!

    i = 0
    while i < len(pruned_path) - 2:
        p1 = point(pruned_path[i])
        p2 = point(pruned_path[i+1])
        p3 = point(pruned_path[i+2])

        # If the 3 points are in a line remove
        # the 2nd point.
        # The 3rd point now becomes and 2nd point
        # and the check is redone with a new third point
        # on the next iteration.
        if collinearity_check(p1, p2, p3):
            # Something subtle here but we can mutate
            # `pruned_path` freely because the length
            # of the list is check on every iteration.
            pruned_path.remove(pruned_path[i+1])
        else:
            i += 1
    return pruned_path