""" This file implements a grid with a 3d reservation matrix with dimensions for x, y, and time. There is also infrastructure to generate dynamic obstacles that move around the grid. The obstacles' paths are stored in the reservation matrix on creation. """ import numpy as np import matplotlib.pyplot as plt from enum import Enum from dataclasses import dataclass @dataclass(order=True) class Position: x: int y: int def as_ndarray(self) -> np.ndarray: return np.array([self.x, self.y]) def __add__(self, other): if isinstance(other, Position): return Position(self.x + other.x, self.y + other.y) raise NotImplementedError( f"Addition not supported for Position and {type(other)}" ) def __sub__(self, other): if isinstance(other, Position): return Position(self.x - other.x, self.y - other.y) raise NotImplementedError( f"Subtraction not supported for Position and {type(other)}" ) def __hash__(self): return hash((self.x, self.y)) @dataclass class Interval: start_time: int end_time: int class ObstacleArrangement(Enum): # Random obstacle positions and movements RANDOM = 0 # Obstacles start in a line in y at center of grid and move side-to-side in x ARRANGEMENT1 = 1 """ Generates a 2d numpy array with lists for elements. """ def empty_2d_array_of_lists(x: int, y: int) -> np.ndarray: arr = np.empty((x, y), dtype=object) # assign each element individually - np.full creates references to the same list arr[:] = [[[] for _ in range(y)] for _ in range(x)] return arr class Grid: # Set in constructor grid_size: np.ndarray reservation_matrix: np.ndarray obstacle_paths: list[list[Position]] = [] # Obstacles will never occupy these points. Useful to avoid impossible scenarios obstacle_avoid_points: list[Position] = [] # Number of time steps in the simulation time_limit: int # Logging control verbose = False def __init__( self, grid_size: np.ndarray, num_obstacles: int = 40, obstacle_avoid_points: list[Position] = [], obstacle_arrangement: ObstacleArrangement = ObstacleArrangement.RANDOM, time_limit: int = 100, ): self.obstacle_avoid_points = obstacle_avoid_points self.time_limit = time_limit self.grid_size = grid_size self.reservation_matrix = np.zeros((grid_size[0], grid_size[1], self.time_limit)) if num_obstacles > self.grid_size[0] * self.grid_size[1]: raise Exception("Number of obstacles is greater than grid size!") if obstacle_arrangement == ObstacleArrangement.RANDOM: self.obstacle_paths = self.generate_dynamic_obstacles(num_obstacles) elif obstacle_arrangement == ObstacleArrangement.ARRANGEMENT1: self.obstacle_paths = self.obstacle_arrangement_1(num_obstacles) for i, path in enumerate(self.obstacle_paths): obs_idx = i + 1 # avoid using 0 - that indicates free space in the grid for t, position in enumerate(path): # Reserve old & new position at this time step if t > 0: self.reservation_matrix[path[t - 1].x, path[t - 1].y, t] = obs_idx self.reservation_matrix[position.x, position.y, t] = obs_idx """ Generate dynamic obstacles that move around the grid. Initial positions and movements are random """ def generate_dynamic_obstacles(self, obs_count: int) -> list[list[Position]]: obstacle_paths = [] for _ in range(0, obs_count): # Sample until a free starting space is found initial_position = self.sample_random_position() while not self.valid_obstacle_position(initial_position, 0): initial_position = self.sample_random_position() positions = [initial_position] if self.verbose: print("Obstacle initial position: ", initial_position) # Encourage obstacles to mostly stay in place - too much movement leads to chaotic planning scenarios # that are not fun to watch weights = [0.05, 0.05, 0.05, 0.05, 0.8] diffs = [ Position(0, 1), Position(0, -1), Position(1, 0), Position(-1, 0), Position(0, 0), ] for t in range(1, self.time_limit - 1): sampled_indices = np.random.choice( len(diffs), size=5, replace=False, p=weights ) rand_diffs = [diffs[i] for i in sampled_indices] valid_position = None for diff in rand_diffs: new_position = positions[-1] + diff if not self.valid_obstacle_position(new_position, t): continue valid_position = new_position break # Impossible situation for obstacle - stay in place # -> this can happen if the oaths of other obstacles this one if valid_position is None: valid_position = positions[-1] positions.append(valid_position) obstacle_paths.append(positions) return obstacle_paths """ Generate a line of obstacles in y at the center of the grid that move side-to-side in x Bottom half start moving right, top half start moving left. If `obs_count` is less than the length of the grid, only the first `obs_count` obstacles will be generated. """ def obstacle_arrangement_1(self, obs_count: int) -> list[list[Position]]: obstacle_paths = [] half_grid_x = self.grid_size[0] // 2 half_grid_y = self.grid_size[1] // 2 for y_idx in range(0, min(obs_count, self.grid_size[1])): moving_right = y_idx < half_grid_y position = Position(half_grid_x, y_idx) path = [position] for t in range(1, self.time_limit - 1): # sit in place every other time step if t % 2 == 0: path.append(position) continue # first check if we should switch direction (at edge of grid) if (moving_right and position.x == self.grid_size[0] - 1) or ( not moving_right and position.x == 0 ): moving_right = not moving_right # step in direction position = Position( position.x + (1 if moving_right else -1), position.y ) path.append(position) obstacle_paths.append(path) return obstacle_paths """ Check if the given position is valid at time t input: position (Position): (x, y) position t (int): time step output: bool: True if position/time combination is valid, False otherwise """ def valid_position(self, position: Position, t: int) -> bool: # Check if new position is in grid if not self.inside_grid_bounds(position): return False # Check if new position is not occupied at time t return self.reservation_matrix[position.x, position.y, t] == 0 """ Returns True if the given position is valid at time t and is not in the set of obstacle_avoid_points """ def valid_obstacle_position(self, position: Position, t: int) -> bool: return ( self.valid_position(position, t) and position not in self.obstacle_avoid_points ) """ Returns True if the given position is within the grid's boundaries """ def inside_grid_bounds(self, position: Position) -> bool: return ( position.x >= 0 and position.x < self.grid_size[0] and position.y >= 0 and position.y < self.grid_size[1] ) """ Sample a random position that is within the grid's boundaries output: Position: (x, y) position """ def sample_random_position(self) -> Position: return Position( np.random.randint(0, self.grid_size[0]), np.random.randint(0, self.grid_size[1]), ) """ Returns a tuple of (x_positions, y_positions) of the obstacles at time t """ def get_obstacle_positions_at_time(self, t: int) -> tuple[list[int], list[int]]: x_positions = [] y_positions = [] for obs_path in self.obstacle_paths: x_positions.append(obs_path[t].x) y_positions.append(obs_path[t].y) return (x_positions, y_positions) """ Returns safe intervals for each cell. """ def get_safe_intervals(self) -> np.ndarray: intervals = empty_2d_array_of_lists(self.grid_size[0], self.grid_size[1]) for x in range(intervals.shape[0]): for y in range(intervals.shape[1]): intervals[x, y] = self.get_safe_intervals_at_cell(Position(x, y)) return intervals """ Generate the safe intervals for a given cell. The intervals will be in order of start time. ex: Interval (2, 3) will be before Interval (4, 5) """ def get_safe_intervals_at_cell(self, cell: Position) -> list[Interval]: vals = self.reservation_matrix[cell.x, cell.y, :] # Find where the array is zero zero_mask = (vals == 0) # Identify transitions between zero and nonzero elements diff = np.diff(zero_mask.astype(int)) # Start indices: where zeros begin (1 after a nonzero) start_indices = np.where(diff == 1)[0] + 1 # End indices: where zeros stop (just before a nonzero) end_indices = np.where(diff == -1)[0] # Handle edge cases if the array starts or ends with zeros if zero_mask[0]: # If the first element is zero, add index 0 to start_indices start_indices = np.insert(start_indices, 0, 0) if zero_mask[-1]: # If the last element is zero, add the last index to end_indices end_indices = np.append(end_indices, len(vals) - 1) # Create pairs of (first zero, last zero) intervals = [Interval(int(start), int(end)) for start, end in zip(start_indices, end_indices)] # Remove intervals where a cell is only free for one time step. Those intervals not provide enough time to # move into and out of the cell each take 1 time step, and the cell is considered occupied during # both the time step when it is entering the cell, and the time step when it is leaving the cell. intervals = [interval for interval in intervals if interval.start_time != interval.end_time] return intervals show_animation = True def main(): grid = Grid( np.array([11, 11]), num_obstacles=10, obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1, ) if not show_animation: return fig = plt.figure(figsize=(8, 7)) ax = fig.add_subplot( autoscale_on=False, xlim=(0, grid.grid_size[0] - 1), ylim=(0, grid.grid_size[1] - 1), ) ax.set_aspect("equal") ax.grid() ax.set_xticks(np.arange(0, 11, 1)) ax.set_yticks(np.arange(0, 11, 1)) (obs_points,) = ax.plot([], [], "ro", ms=15) # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect( "key_release_event", lambda event: [exit(0) if event.key == "escape" else None] ) for i in range(0, grid.time_limit - 1): obs_positions = grid.get_obstacle_positions_at_time(i) obs_points.set_data(obs_positions[0], obs_positions[1]) plt.pause(0.2) plt.show() if __name__ == "__main__": main()