Suppose that you are working with the robot in Exercise 26.ABMA above and you are given the problem of finding a path from the starting configuration of figure ?? to the ending configuration. Consider a potential function 

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.

D(A, Goal)2 + D(B, Goal) + 1 D(A,B)