Collaborative probabilistic search for a randomly and evasively moving target using optimized time-periodic orbits of multi-searchers

Authors: Muhan Zhao, and Thomas R. Bewley

Submitted to: Automatica (2025)

Abstract:
This paper optimizes the orbits of multiple unmanned heterogeneous vehicles looking for an unseen, evasively and randomly moving target. The evasiveness of target is simply its tendency to flee away from searchers, whereby this behavior is modeled by:
(1) the repulsion of searchers, and this added repulsive force peaks at searchers’ locations, and
(2) the increased skittishness, again, peaks at searchers’ locations
Those evasiveness is integrated in the target dynamics described by the stochastic ordinary differential equation, and further reflected by the advection and diffusion terms of the forced Fokker-Planck equation, which models the probability density function of target position. The goal of searchers is to distribute search efforts along their orbits with the minimal probability of failing to detect the target. We propose an encircled formation search strategy, whereby searchers gather in the zone where the probability of finding the target is maximal. Such searchers’ orbits are iteratively optimized by nonlinear programming methods, facilitated by the derivation of relevant adjoint fields. Numerical examples are presented to showcase the efficiency of proposed search strategies and computational framework.