13 In this exercise, we examine hill climbing in the context of robot navigation, using the environment in Figure 31, from the chapter “Solving Problems by Searching”, as an example.

a. Repeat Exercise 11 using hill climbing. Does your agent ever get stuck in a local minimum? Is it possible for it to get stuck with convex obstacles?

b. Construct a nonconvex polygonal environment in which the agent gets stuck.

c. Modify the hill-climbing algorithm so that, instead of doing a depth-1 search to decide where to go next, it does a depth-k search. It should find the best k-step path and do one step along it, and then repeat the process.

d. Is there some k for which the new algorithm is guaranteed to escape from local minima?

e. Explain how LRTA∗ enables the agent to escape from local minima in this case.