Methods for Tracking an Object Moving in \({{\mathbb{R}}^{3}}\) under Conditions of Its Counteraction

Abstract

We propose ways of acting an observer f when tracking an object \(t\) moving in \({{\mathbb{R}}^{3}}\) along the shortest trajectory \(\mathcal{T}\) bypassing a collection \(\{ {{G}_{i}}\} \) of convex sets. The object has high-speed miniobjects threatening the observer. The tracking methods depend on the geometric properties of \({{G}_{i}}\) and \(\mathcal{T}\). The observer’s task is to track the motion of the object over as long a segment of \(\mathcal{T}\) as possible.