Question $2$

Machine Learning

$[16]$

Three $(3)$ engineers $($Alex$,$ Brianna, and Chris$)$ are working late at a robotics lab located on one side of a large, automated warehouse. To exit the building, they need to pass through a secured door on the other side. However, the only way to reach the door is by using a small, automated cart that runs along a narrow track across the warehouse. While searching for a solution, they find two interns who have been using the cart to move small items between sections of the warehouse. The engineers ask the interns if they can use the cart to reach the exit. The interns agree, but explain that due to the cart's size, it can only carry either both interns together or just one engineer at a time. We can assume that everyone knows how to operate the cart.

$($a$)$ Define a state using a mathematical notation $($pictures or any form of graphical notation will not be accepted$).$ Discuss the appropriateness of your choice and provide an example to show that it will be suitable to be employed during a search.

$($b$)$ Define the start and goal states using your representation.

$($c$)$ Define an appropriate cost function or functions for this problem.

$($d$)$ Provide a formal definition of a valid action function for this problem $-$ you need not provide a formal definition for the operation of the function. Discuss the operation of the function and provide an example to illustrate its use.