Add theta star planner

[Musab1Blaser]

Reference issue

Enhance: #1286

What does this implement/fix?

It implements the Theta Star Planner, which performs a simple path compression on the A* planner by allowing the robot to define its heading based on far-away nodes so long as there is a clear path to it. This means the robot can travel in more than the 8 defined directions, which allows it to avoid unnecessary small turns.

Additional information

Demo (Submitted for PR in GIFs repo):

One can also disable Theta* and see how the angles of arrows become limited to only 8 directions, leading to a more choppy path.

The implementation was done by:

• Theta* Path Compression algorithm as detailed in: (https://cdn.aaai.org/AAAI/2007/AAAI07-187.pdf)
• Line of sight determined by using Bresenham's line algorithm to determine cells on the line and then verifying those nodes

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)

[AtsushiSakai]

@codex review

[Copilot]

Pull Request Overview

This PR implements the Theta* path planning algorithm, which enhances A* by enabling path compression through line-of-sight checks. This allows the robot to follow more natural, less constrained paths by connecting to non-adjacent ancestor nodes when a clear path exists, resulting in smoother trajectories with fewer unnecessary turns compared to standard grid-based planners.

Key Changes:

• Implements Theta* algorithm with Bresenham's line algorithm for line-of-sight verification
• Adds visualization showing parent-child node relationships with cyan arrows
• Includes comprehensive test coverage and documentation

Reviewed Changes

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

File	Description
PathPlanning/ThetaStar/theta_star.py	Core implementation of ThetaStarPlanner class with line-of-sight checking and path compression
tests/test_theta_star.py	Unit test verifying the planner runs successfully
docs/modules/5_path_planning/grid_base_search/grid_base_search_main.rst	Documentation entry for Theta* algorithm with animation reference

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[chatgpt-codex-connector]

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[Musab1Blaser]

@AtsushiSakai I have removed the extra loop as per the code review.

[Musab1Blaser]

@AtsushiSakai I have added some more details to the documentation. I can also add even more, but I was unsure how much to add to match with the docs of the neighboring algorithms.

[AtsushiSakai]

@Musab1Blaser Thank you!

[Musab1Blaser]

yay!
One small note. Just noticed that I slightly messed up with the consistency of using Theta* vs Theta star. I was trying to use it as Theta Star in the actual paragraphs but in one place I mixed it up :(
Doesn't effect understanding, just noting.

[AtsushiSakai]

If you want to fix it, PR is welcome.

[Musab1Blaser]

I'll try to go over the whole website soon for some more similar typos, which tbh could be very easily done with an LLM. and i'll try to make a PR of all the obvious errors I can find.