Straight-Line Segments Joining - Convex Polygonal Obstacles - Engineering Assignment Help

Assignment Task :

Ques  1 Consider the problem of finding the shortest path between two points on a plane that has convex polygonal obstacles  . This is an idealization of the problem that a robot has to solve to navigate in a crowded environment.  
a) Suppose the state space consists of all positions (x,y) in the plane. How many states are there? How many paths are there to the goal? 
The state space consists of corners, starting points, and endpoints that are encoded into x, y positions. The number of state spaces is dictated by the number of corners in the obstacles. The path are drawn from one corner to the next, avoiding the interior of the obstacles.
b) Explain briefly why the shortest path from one polygon vertex to any other in the scene must consist of straight-line segments joining some of the vertices of the polygons. Define a good state space now. How large is this state space?  

The shortest path is to go straight to the corner instead of going around it. The shortest path consists of the segments joining corners. The state space should consist of the x, y values of the corner and the position of the goal. This state space of eight polygons has thirty-five states.

c) Define the necessary functions to implement the search problem, including an ACTIONS function that takes a vertex as input and returns a set of vectors, each of which maps the current vertex to one of the vertices that can be reached in a straight line.  

The state space implemented as Coordinate class includes the coordinate position, the goal, and predecessor. This class includes methods to access, the predecessor, test equality, compute the distance from the goal, and to test if the state itself is the goal. A class called CoordinateSuccessorFunction has a method called getSuccessors. This method will take the current state as input and return a list of its successors as an array list data structure.

d) Theoretically, apply any one of the algorithms from chapter 03(uninformed searches) to the above problem.  

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