Optimality of Motion Camouflage Under Escape Uncertainty

TL;DR

This paper develops a dynamic programming framework to determine optimal motion camouflage strategies for pursuers under uncertainty about evader escape timing, with applications to biological pursuit scenarios.

Contribution

It introduces a novel continuous-time dynamic programming approach to analyze motion camouflage under escape uncertainty, incorporating biologically informed models and solving Hamilton-Jacobi-Bellman PDEs.

Findings

Optimal pursuit strategies depend on the evader's sensing abilities.

Motion camouflage is optimal under certain conditions of escape uncertainty.

The framework can predict when pursuit tactics are most effective.

Abstract

This letter proposes a novel continuous-time dynamic programming framework to determine when it is optimal for a pursuer to use MC amidst uncertainty in the evader's escape attempt time. We motivate this framework through the model problem of an energy-optimizing male hover fly pursuing a female hover fly for mating. The time at which the female fly initiates an escape is modeled to occur as the result of a non-homogeneous Poisson point process with a biologically informed rate function, and we obtain and solve two Hamilton-Jacobi-Bellman (HJB) PDEs which encode the pursuer's optimal trajectories. Our numerical experiments and statistics illustrate when it is optimal to use MC pursuit tactics amidst uncertainty and how MC optimality is affected by certain properties of the evader's sensing abilities.