Add expanded node set to SpaceTime AStar (#1183)

* speed up spacetime astar

* forgot to include hash impl on Position

* add condition to test on node expansions

* remove heuristic from Node __hash__ impl

* update rst with note about optimization

PathPlanning/TimeBasedPathPlanning/GridWithDynamicObstacles.py

@@ -30,6 +30,9 @@ class Position:
             f"Subtraction not supported for Position and {type(other)}"
         )
 
+    def __hash__(self):
+        return hash((self.x, self.y))
+
 
 class ObstacleArrangement(Enum):
     # Random obstacle positions and movements

PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar.py

@@ -20,7 +20,7 @@ from collections.abc import Generator
 import random
 from dataclasses import dataclass
 from functools import total_ordering
-
+import time
 
 # Seed randomness for reproducibility
 RANDOM_SEED = 50
@@ -48,11 +48,17 @@ class Node:
             return NotImplementedError(f"Cannot compare Node with object of type: {type(other)}")
         return (self.time + self.heuristic) < (other.time + other.heuristic)
 
+    """
+    Note: cost and heuristic are not included in eq or hash, since they will always be the same
+          for a given (position, time) pair. Including either cost or heuristic would be redundant.
+    """
     def __eq__(self, other: object):
         if not isinstance(other, Node):
             return NotImplementedError(f"Cannot compare Node with object of type: {type(other)}")
         return self.position == other.position and self.time == other.time
 
+    def __hash__(self):
+        return hash((self.position, self.time))
 
 class NodePath:
     path: list[Node]
@@ -86,6 +92,8 @@ class SpaceTimeAStar:
     grid: Grid
     start: Position
     goal: Position
+    # Used to evaluate solutions
+    expanded_node_count: int = -1
 
     def __init__(self, grid: Grid, start: Position, goal: Position):
         self.grid = grid
@@ -98,7 +106,8 @@ class SpaceTimeAStar:
             open_set, Node(self.start, 0, self.calculate_heuristic(self.start), -1)
         )
 
-        expanded_set: list[Node] = []
+        expanded_list: list[Node] = []
+        expanded_set: set[Node] = set()
         while open_set:
             expanded_node: Node = heapq.heappop(open_set)
             if verbose:
@@ -110,23 +119,25 @@ class SpaceTimeAStar:
                 continue
 
             if expanded_node.position == self.goal:
-                print(f"Found path to goal after {len(expanded_set)} expansions")
+                print(f"Found path to goal after {len(expanded_list)} expansions")
                 path = []
                 path_walker: Node = expanded_node
                 while True:
                     path.append(path_walker)
                     if path_walker.parent_index == -1:
                         break
-                    path_walker = expanded_set[path_walker.parent_index]
+                    path_walker = expanded_list[path_walker.parent_index]
 
                 # reverse path so it goes start -> goal
                 path.reverse()
+                self.expanded_node_count = len(expanded_set)
                 return NodePath(path)
 
-            expanded_idx = len(expanded_set)
-            expanded_set.append(expanded_node)
+            expanded_idx = len(expanded_list)
+            expanded_list.append(expanded_node)
+            expanded_set.add(expanded_node)
 
-            for child in self.generate_successors(expanded_node, expanded_idx, verbose):
+            for child in self.generate_successors(expanded_node, expanded_idx, verbose, expanded_set):
                 heapq.heappush(open_set, child)
 
         raise Exception("No path found")
@@ -135,7 +146,7 @@ class SpaceTimeAStar:
     Generate possible successors of the provided `parent_node`
     """
     def generate_successors(
-        self, parent_node: Node, parent_node_idx: int, verbose: bool
+        self, parent_node: Node, parent_node_idx: int, verbose: bool, expanded_set: set[Node]
     ) -> Generator[Node, None, None]:
         diffs = [
             Position(0, 0),
@@ -146,13 +157,17 @@ class SpaceTimeAStar:
         ]
         for diff in diffs:
             new_pos = parent_node.position + diff
+            new_node = Node(
+                new_pos,
+                parent_node.time + 1,
+                self.calculate_heuristic(new_pos),
+                parent_node_idx,
+            )
+
+            if new_node in expanded_set:
+                continue
+
             if self.grid.valid_position(new_pos, parent_node.time + 1):
-                new_node = Node(
-                    new_pos,
-                    parent_node.time + 1,
-                    self.calculate_heuristic(new_pos),
-                    parent_node_idx,
-                )
                 if verbose:
                     print("\tNew successor node: ", new_node)
                 yield new_node
@@ -166,9 +181,12 @@ show_animation = True
 verbose = False
 
 def main():
-    start = Position(1, 11)
+    start = Position(1, 5)
     goal = Position(19, 19)
     grid_side_length = 21
+
+    start_time = time.time()
+
     grid = Grid(
         np.array([grid_side_length, grid_side_length]),
         num_obstacles=40,
@@ -179,6 +197,9 @@ def main():
     planner = SpaceTimeAStar(grid, start, goal)
     path = planner.plan(verbose)
 
+    runtime = time.time() - start_time
+    print(f"Planning took: {runtime:.5f} seconds")
+
     if verbose:
         print(f"Path: {path}")
 

docs/modules/5_path_planning/time_based_grid_search/time_based_grid_search_main.rst

@@ -16,6 +16,23 @@ Using a time-based cost and heuristic ensures the path found is optimal in terms
 The cost is the amount of time it takes to reach a given node, and the heuristic is the minimum amount of time it could take to reach the goal from that node, disregarding all obstacles.
 For a simple scenario where the robot can move 1 cell per time step and stop and go as it pleases, the heuristic for time is equivalent to the heuristic for distance.
 
+One optimization that was added in `this PR <https://github.com/AtsushiSakai/PythonRobotics/pull/1183>`__ was to add an expanded set to the algorithm. The algorithm will not expand nodes that are already in that set. This greatly reduces the number of node expansions needed to find a path, since no duplicates are expanded. It also helps to reduce the amount of memory the algorithm uses.
+
+Before::
+
+    Found path to goal after 204490 expansions
+    Planning took: 1.72464 seconds
+    Memory usage (RSS): 68.19 MB
+
+
+After::
+
+    Found path to goal after 2348 expansions
+    Planning took: 0.01550 seconds
+    Memory usage (RSS): 64.85 MB
+
+When starting at (1, 11) in the structured obstacle arrangement (second of the two gifs above).
+
 References:
 ~~~~~~~~~~~
 

tests/test_space_time_astar.py

@@ -28,6 +28,7 @@ def test_1():
     # path should end at the goal
     assert path.path[-1].position == goal
 
+    assert planner.expanded_node_count < 1000
 
 if __name__ == "__main__":
     conftest.run_this_test(__file__)