Methods for tracking an object moving in $\mathbb{R}^3$ under conditions of its counteraction

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.