Game tree search for minimizing detectability and maximizing visibility

Abstract

We introduce and study the problem of planning a trajectory for an agent to carry out a scouting mission while avoiding being detected by an adversarial opponent. This introduces a multi-objective version of classical visibility-based target search and pursuit-evasion problem. In our formulation, the agent receives a positive reward for increasing its visibility (by exploring new regions) and a negative penalty every time it is detected by the opponent. The objective is to find a finite-horizon path for the agent that balances the trade off between maximizing visibility and minimizing detectability. We model this problem as a discrete, sequential, two-player, zero-sum game. We use two types of game tree search algorithms to solve this problem: minimax search tree and Monte-Carlo search tree. Both search trees can yield the optimal policy but may require possibly exponential computational time and space. We first propose three pruning techniques to reduce the computational time while preserving optimality guarantees. When the agent and the opponent are located far from each other initially, we present a variable resolution technique with longer planning horizon to further reduce computational time. Simulation results show the effectiveness of the proposed strategies in terms of computational time.