4 Suppose that you are working with the robot in Exercise 3 and you are given the problem of finding a path from the starting configuration of figure 31 to the ending configuration.

Consider a potential function

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D(A, Goal)+D(B, Goal) + 1 D(A, B) where D(A, B) is the distance between the closest points of A and B. a. Show that hill climbing in this potential field will get stuck in a local minimum. b. Describe a potential field where hill climbing will solve this particular problem. You need not work out the exact numerical coefficients needed, just the general form of the solution. (Hint: Add a term that "rewards" the hill climber for moving A out of B's way, even in a case like this where this does not reduce the distance from A to B in the above sense.)