Problem $2(15$ Points$)$

Using the Lumesky$-$Bug method I for robot navigation

i$.$ For the following maze, assume that the robot starts at the Start point and needs to navigate to the Goal point. Inside the maze there are different obstacles as shown in the graphics.

ii$.$ Assume that the length is the horizontal axis X and the width is the vertical axis Y

iii. The overall dimensions of the maze are length $=144ft,$ width $=72ft.$

iv$.$ That the origin of the maze has coordinates $(0,0)$ and is located on the bottom left corner

v$.$ The start is located at coordinates $(136,16)$

vi$.$ The goal is located at coordinates $(6,64)$

Answer the following questions:

a$)$ Give the value of the starting angle $$ in degrees and radians that the robot should take in order to reach the goal.

Angle $$ degrees

Angle $$ radians

b$)$ Give the equation that can be used to calculate the main trajectory that the robot will follow if there were no obstacles?

Equation:

c$)$ Calculate the Euclidian distance from the start to the goal.

Euclidian Distance $$

d$)$ Draw the path that gives the shortest Manhattan distance and calculate its value.

Manhattan Distance $$