On the Optimal Policies for Visibility-Based Target Tracking

TL;DR

This paper studies optimal pursuit strategies for a mobile observer tracking a target amid obstacles, deriving switching conditions and extending solutions to complex environments with polygonal obstacles.

Contribution

It introduces a novel formulation of the pursuit-evasion game as an optimal control problem with state constraints and develops techniques for constructing pursuit fields in complex environments.

Findings

Identification of two regimes in optimal pursuit strategies.

Derivation of equations for switching times between regimes.

Development of pursuit fields guiding observer motion.

Abstract

In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple environment. We show that for some initial conditions, there are two different regimes in the optimal strategy of the pursuer depending on whether the state-constraint is activated. We derive the equations that characterize the switching time between the two regimes. The pursuer's optimal tracking strategy in a simple environment is further extended to a general environment with multiple polygonal obstacles. We propose techniques to construct a "pursuit field" based on the optimal solutions to guide the motion of the observer in a general environment.