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[Feature Request] Improve Hybrid A* with Reeds-Shepp Paths and Reversing Support #49

Description

@ShisatoYano

Description
Currently, the existing sample code of Hybrid A* Path Planning doesn't support reversing movement.
To make it more practical and professional -- similar to those used in autonomous valet parking -- we need to upgrade the heuristic and the motion model.

I would like to propose an enhancement to the Hybrid A* algorithm by integrating the Reeds-Shepp curves.

Tasks

  • Integration of Reeds-Shepp Paths: Use Reeds-Shepp curves as the analytic expansion (shot-to-goal) to improve search efficiency and path quality.
  • Support for Reversing: Update the motion model to allow the vehicle to move to backward.
  • Direction Change Penalty: Implement a cost function that penalizes switching between forward and backward to ensure smooth paths.
  • Heuristic Update: Improve the heuristic considering the non-holonomic constraints.

Reference Code
Current version of Hybrid A* Global Path Planning

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