Optimal sensor deception in stochastic environments with partial observability to mislead a robot to a decoy goal

Deception is a common strategy adapted by autonomous systems in adversarial settings. Existing deception methods primarily focus on increasing opacity or misdirecting agents away from their goal or itinerary. In this work, we propose a deception problem aiming to mislead the robot towards a decoy goal through altering sensor events under a constrained budget of alteration. The environment along with the robot's interaction with it is modeled as a Partially Observable Markov Decision Process (POMDP), and the robot's action selection is governed by a Finite State Controller (FSC). Given a constrained budget for sensor event modifications, the objective is to compute a sensor alteration that maximizes the probability of the robot reaching a decoy goal. We establish the computational hardness of the problem by a reduction from the $0/1$ Knapsack problem and propose a Mixed Integer Linear Programming (MILP) formulation to compute optimal deception strategies. We show the efficacy of our MILP formulation via a sequence of experiments.