Sistemas Autónomos/Autonomous Systems Mestrado em Engª. Electrotécnica e de Computadores 1º Teste 18 de Dezembro de 2014 1º Semestre

NUMBER  _______________            NAME_____________________________________________________________________________________________  

Each question have an associated grade of 1,0 point for correct answers, -0,1 points for incorrect answers and 0 points for no answer. Mark an “X” on the ¨ corresponding to the correct answer. In case you change your mind about the correct answer later, cross the former “X”, and mark another “X” corresponding to your new decision.

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1. Situation calculus attempts to solve problems associated to representation and reasoning under changes by:

¨ a) Representing the world state (robot position) by a (x,y) tuple, whose value changes according to received perceptions and executed actions; the world “dynamics” is described by differential equations, which express how the world evolves.

¨ b) Representing the world state by a probability density function over the possible states (belief), which changes according to received perceptions and executed actions; the world “dynamics” is described by diachronic rules, which express how the world evolves.

¨ c) Representing the world state by a proposition set, which only changes according to received perceptions.

X d) Representing the world state by a proposition set, which changes according to received perceptions and executed actions; the world “dynamics” is described by diachronic rules, which express how the world evolves.

2. In situation calculus, a situation S1 representing a state of the world: X a) Is added as an extra argument of predicates characterizing properties of

world components (which may change between situations) and is generated from another situation S0 by executing an action a, as described by the function Result (S1=Result(a,S0)).

¨ b) Is added as an extra argument of predicates representing actions and is generated from another situation S0 by executing an action a, as described by the function Result (S1=Result(a,S0)).

¨ c) Is characterized by the actions available in that world state and their uncertain effects.

¨ d) None of the above.

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3. The situation calculus axioms can be listed as:

¨ a) effect axioms that describe what does not change after an action is executed; frame axioms that describe the changes due to action effects; and successor state axioms that merge frame and effect axioms.

X b) effect axioms that describe the changes due to action effects; frame axioms that describe what does not change after an action is executed; and successor state axioms that merge frame and effect axioms.

¨ c) effect axioms that describe the small changes due to action effects; frame axioms that describe the large changes due to action effects; and successor state axioms that merge frame and effect axioms.

¨ d) effect axioms that describe the changes due to action effects; frame axioms that describe the changes in object frames due to action effects; and successor state axioms that combine all frame and effect axioms in one single axiom.

4. When planning in a dynamic and uncertain environment, which of the following assumptions is not satisfied:

¨ a) Agent does not know everything that is relevant for the planning problem.

¨ b) Agent does not know exactly how its available actions can change the world state from one state to another.

X c) The planning agent is in control of the world – the only state changes are the result of its deliberate actions.

¨ d) The agent’s preferred world states (or the goal states) may change during a planning episode.

5. The Stanford Research Institute Problem Solver (STRIPS) uses:

X a) A set of world models, each of them described by a clause set, and operators which, when selected, add and remove clauses from the world state that is active before the operator is applied, to create a new world state.

¨ b) Decision-theoretic methods that generate a policy mapping world states into actions.

¨ c) Effect and frame axioms, as in situation calculus, to infer knew knowledge until a goal state is reached.

¨ d) A set of operators, each of them described by a clause set, and world states which are updated by operators.

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6. Imagine a parking lot autonomously controlled to ensure the number of slots is never exceeded and burglars are detected. This can be modelled as a discrete event system where:

¨ a) Events correspond to the detection of a burglar and the opening of the entrance and exit gates, and states correspond to the exit and entrance of cars in the parking lot.

¨ b) Events correspond to the number of cars in the parking lot, and states correspond to the exit and entrance of cars in the parking lot. as well as to the detection of a burglar.

X c) States correspond to the number of cars and whether a burglar is present or not in the parking lot, and events correspond to the exit and entrance of cars in the parking lot, as well as to the detection of a burglar.

¨ d) States correspond to the number of cars and burglars entering the parking lot in a given instant, and events correspond to the number of cars and burglars exiting the parking lot in a given instant.

7. Which of the following is not a Petri net (assume the usual graphical notation for places and transitions):

¨ a)

¨ b)

X c)

¨ d)

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8. Consider the following marked Petri net:

After firing the sequence of transitions t1t2 which of the following markings corresponds to the state of the new marked Petri net

X a) (1 0 3)

¨ b) (1 0 2)

¨ c) (0 0 3)

¨ d) (0 0 2)

9. In the Petri net representation of a robot task plan introduced in class:

¨ a) Places with tokens represent events and transitions are associated to primitive actions running.

¨ b) Places with tokens represent uncontrolled state changes, while events representing decisions to start a primitive action are associated to transitions.

¨ c) Places represent only primitive actions running, while all events represent decisions to start a primitive action and are associated to transitions.

X d) Places with tokens represent resources available and primitive actions running, while events representing decisions to start a primitive action or uncontrolled state changes are associated to transitions.

p1#

p2#

p3#

t1#

t2#

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10. Under given conditions, stochastic Petri nets have a marking graph which is equivalent to a Continuous Time Markov Chain only when:

¨ a) Timed transitions have an associated normal probability density function

X b) Timed transitions have an associated exponential probability density

function.

¨ c) Timed places have an associated normal probability density function.

¨ d) Timed places have an associated exponential probability density function.

11. Concerning the analysis of robot task models represented by discrete event systems: X a) Qualitative/logical analysis problems rely on untimed events, while

quantitative analysis problems require timed events.

¨ b) Qualitative/logical analysis problems rely on timed events, while quantitative analysis problems require untimed events..

¨ c) Qualitative/logical analysis problems rely on untimed states, while quantitative analysis problems require timed events.

¨ d) Qualitative/logical analysis problems rely on untimed events, while quantitative analysis problems require timed states.

12. Which of the following is an example of a quantitative analysis problem for robot tasks modelled by Petri nets:

¨ a) Determining if a plan to accomplish the robot task will ever reach a dead-lock state.

¨ b) Determining if a plan to accomplish the robot task will visit unsafe states.

¨ c) Determining if a plan to accomplish the robot task requires an unbounded amount of resources.

X d) Determining the probability of success of a plan to accomplish the robot task.

13. The goal of a Markov Decision Process (MDP) is:

¨ a) to determine the policy (mapping states onto actions) that maximizes the expected accumulated discounted reward of an agent described by a Markov chain.

X b) to determine the policy (mapping states onto actions) that maximizes the

expected accumulated discounted reward of an agent, requiring the definition of the agent states, actions, state transition probabilities and the reward function, under the Markov assumption.

¨ c) to solve Markov chains.

¨ d) none of the above.

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14. Which of the following is a Bellman equation for discrete action and state space MDP, whose solution are the state values VT

π (x) = E RTπ xt = x{ } for a given policy π, using

the course notation for transition probabilities, states, actions, rewards and discount factor (V* stands for the optimal value): X a) VT

π (x) = p(x ' | u, x) r(x,u)+γVT−1π (x ')"# $%

x '∑ .

¨ b) VTπ (x) = π (x,u) r(x,u)+γVT−1

π (x ')"# $%u∑ .

¨ c) VTπ (x) = p(x ' | u, x) r(x,u)+γVT−1

* (x ')"# $%x '∑ .

¨ d) VTπ (x) = π (x,u) r(x,u)+γVT−1

* (x ')"# $%u∑ .

15. Which of the following statements is true regarding the Q-learning reinforcement learning algorithm to solve an MDP: ¨ a) Model-free (does not require knowledge of the transition probabilities)

algorithm that estimates the policy mapping each state to its optimal action.

¨ b) Model-based (requires knowledge of the transition probabilities) algorithm that estimates the policy mapping each state to its optimal action.

X c) Model-free (does not require knowledge of the transition probabilities) algorithm that estimates the value of the Q(x,u) function for a given (state, action) pair.

¨ d) Model-based (requires knowledge of the transition probabilities) algorithm that estimates the value of the Q(x,u) function for a given (state, action) pair.

16. The exploration vs exploitation trade-off in the Q-learning reinforcement learning algorithm to solve an MDP:

X a) Consists of giving a chance to less promising actions at each iteration of the algorithm, not always picking the best action, so as to meet the algorithm’s sufficient conditions for convergence.

¨ b) Consists of always picking the best action at each iteration, so as to meet the algorithm’s sufficient conditions for convergence.

¨ c) Consists of giving a chance to less promising actions at each iteration of the algorithm, not always picking the best action, to ensure the stochastic approximation algorithm’s conditions for convergence.

¨ d) Consists of always picking the best action at each iteration, so as to achieve the maximum value of Q.

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17. In cooperative perception problems for a team of sensors (some static, some mobile):

¨ a) Only the uncertainty about the localization of the mobile sensors is considered.

¨ b) Only the measurement uncertainty of the sensors must is considered.

¨ c) No uncertainty must be considered.

X d) The uncertainty about the localization of the mobile sensors and the measurement uncertainty of the sensor must be combined.

18. In a N-sensor team where the sensors are linearly ordered from 1 to N, Pr(zo(1)

W , zo(2)W ,…, zo(N )

W ) =C.Pr(zo(1)W | zo(2)

W )Pr(zo(2)W | zo(3)

W )...Pr(zo(N−1)W | zo(N )

W )Pr(zo(N )W ) (where

zWo(i) is the vector of position coordinates expressed in the world frame W, for an

object o seen by sensor i, and C is a probability normalization factor) represents the joint probability of the position of o observed by the N sensors when

¨ a) The probability of each sensor observation is independent of the observations of all the other sensors.

¨ b) There is full dependence among all sensor measurements.

X c) The probability of each sensor observation only depends on the observation of one of its neighbours (in the sense of the defined ordering).

¨ d) None of the above.

19. Task plans for cooperative robots include two types of communication signals for relational behaviours:

¨ a) Data-sharing and commitment.

X b) Commitment and synchronization.

¨ c) Synchronization and data-sharing.

¨ d) Synchronous and asynchronous data-sharing.

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20. The major difference between hierarchical and heterarchical functional architectures for robot systems regarding the access to the system sensors and actuators is:

X a) The heterarchical architecture provides access to sensors and actuators to all functional modules from any layer, while hierarchical architectures only grant sensor and actuator access to the functional modules at the bottom hierarchical level.

¨ b) The hierarchical architecture provides access to sensors and actuators to all functional modules from any layer, while heterarchical architectures only grant sensor and actuator access to the functional modules at the bottom level

¨ c) The heterarchical architecture provides access to sensors and actuators to all functional modules from any layer, while hierarchical architectures only grant sensor and actuator access to the functional modules at the top hierarchical level.

¨ d) There is no difference regarding actuator access, but heterarchical architecture provides access to sensors to all functional modules from any layer, while hierarchical architectures only grant sensor access to the functional modules at the bottom hierarchical level.