Consider an idealization of a problem where a robot has to navigate its way around obstacles. The goal is to find the shortest distance between two points on a plane that has convex polygonal obstacles. The shortest path from one polygon vertex to any other in the scene consists of straight-line segments joining some of the vertices of the polygon. (Note that the start and the end goal points may be considered polygons of size 0).

Polygon 1: ((220, 616), (220, 666), (251, 670), (272, 647))

Polygon 2: ((341, 655), (359, 667), (374, 651), (366, 577))

Polygon 3: ((311, 530), (311, 559), (339, 578), (361, 560), (361, 528), (336, 516))

Polygon 4: ((105, 628), (151, 670), (180, 629), (156, 577), (113, 587))

Polygon 5: ((118, 517), (245, 517), (245, 577), (118, 557))

Polygon 6: ((280, 583), (333, 583), (333, 665), (280, 665))

Polygon 7: ((252, 594), (290, 562), (264, 538))

Polygon 8: ((198, 635), (217, 574), (182, 574))

Question: Implement an algorithm to find the shortest path from the start node to the end node using an A* (A-star) heuristic search. Use the straight-line distance to the end node as a heuristic function. Show your pseudo code for this algorithm.

Hint: Define the necessary functions to implement the search problem. This should include a function that takes a vertex as input and returns the set of vertices that can be reached in a straight line from the given vertex. You may need to implement a function that detects whether or not two line segments intersect. The problem can be solved using shortest path algorithms but you are required to use A*.