Question 2 (10 marks) There is a vacuum robot in a two-room space (see Figure 1)

Question

Question 2 (10 marks) There is a vacuum robot in a two-room space (see Figure 1). Its sensor can tell which room it is in (either A or B) and whether the room is Clean or Dirty. It can choose three possible actions: Right, Suck, Left with the restriction that if in room A, Left is not allowed and if in room B, Right is not allowed. Figure 1: Vacuum robot and space Answer the following questions: (a) We describe a system state as a tuple (Robot location, Room A's status, Room B's status). For example, the above state is given as (A, Dirty, Dirty). How many possible system states are there? (b) A memoryless strategy of the robot is a function fron its current sensor information to actions. For erample f(A, Dirty) = Suck, describes that when the robot senses that its is in room A and it is dirty, then it sucks up the dirts How many memoryless strategies are there?

Explanation / Answer

(a) Robot location, Room A's status and Room B's status are all independent of each other, and each has two states, which are

Robot location = {A, B}

Room A's status = {Clean, Dirty}

Room B's status = {Clean, Dirty}

So total tuples, viz. system states are 2 x 2 x 2 = 8

(b) Following memoryless strategies are feasible for the robot under given restrictions

f(A, Dirty) = Suck

f(A, Clean) = Right ? (Cannot move to the left)

f(B, Dirty) = Suck

f(B, Clean) = Left (Cannot move to the right)

So there are 4 memoryless strategies.

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