Reactive synthesis is a class of methods to construct a provably-correct
control system, referred to as a robot, with respect to a temporal logic
specification in the presence of a dynamic and uncontrollable environment. This
is achieved by modeling the interaction between the robot and its environment
as a two-player zero-sum game. However, existing reactive synthesis methods
assume both players to have complete information, which is not the case in many
strategic interactions. In this paper, we use a variant of hypergames to model
the interaction between the robot and its environment; which has incomplete
information about the specification of the robot. This model allows us to
identify a subset of game states from where the robot can leverage the
asymmetrical information to achieve a better outcome, which is not possible if
both players have symmetrical and complete information. We then introduce a
novel method of opportunistic synthesis by defining a Markov Decision Process
(MDP) using the hypergame under temporal logic specifications. When the
environment plays some stochastic strategy in its perceived sure-winning and
sure-losing regions of the game, we show that by following the opportunistic
strategy, the robot is ensured to only improve the outcome of the game -
measured by satisfaction of sub-specifications - whenever an opportunity
becomes available. We demonstrate the correctness and optimality of this method
using a robot motion planning example in the presence of an adversary.Comment: Submitted to Conference on Decision and Control 201