Add expanded node set to SpaceTime AStar

[SchwartzCode]

Reference issue

What does this implement/fix?

This change speeds up the SpaceTime A* algorithm by adding an expanded set. 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.

Also adds a timer to the SpaceTimeAStar.py script

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 arrangement1

Additional information

CheckList

• Did you add an unittest for your new example or defect fix?
• Did you add documents for your new example?
• All CIs are green? (You can check it after submitting)

[Copilot]

PR Overview

This PR improves the performance of the SpaceTime AStar algorithm by introducing an expanded node set to avoid duplicate expansions and adds timing information to measure planning runtime.

• Implements an expanded set and list to track visited nodes
• Adds a timer in the main function to track planning duration
• Updates the unit test to assert that the number of expanded nodes remains below a threshold

Reviewed Changes

File	Description
PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar.py	Incorporates an expanded set to avoid duplicate node expansions and adds timer functionality
tests/test_space_time_astar.py	Updates the test to assert a maximum bound on expanded nodes
PathPlanning/TimeBasedPathPlanning/GridWithDynamicObstacles.py	Adds a hash method to the Position class for proper use in hashed collections

Copilot reviewed 3 out of 3 changed files in this pull request and generated 1 comment.

[Copilot]

The hash method in Node includes the heuristic value, but eq only compares position and time. This inconsistency can lead to unexpected behavior in hashed collections; consider using only position and time in both methods.

Suggested change

	return hash((self.position, self.time, self.heuristic))
	return hash((self.position, self.time))

[AtsushiSakai]

@SchwartzCode What do you think this?

[SchwartzCode]

Ayo, that is a nice catch! Go copilot 🎉
I removed self.heuristic and added a note why that & cost are not included in __eq__ or __hash__:
eecb5c8

[AtsushiSakai]

Could you add an explanation about this speed-up technique to the RST documentation? Something like the PR description plus a little more would be fine.

[SchwartzCode]

@AtsushiSakai added some information to the RST doc for this algorithm:
acb0773

Does that look good?

[AtsushiSakai]

LGTM