Observation of an object opposed to the observer in the space $\mathbb{R}^2$

A course of action is proposed for an observer $f$ tracking an object $t$ that moves along a shortest trajectory $\mathcal T$ enveloping a family $\{G_i\}$ of convex sets. The object can send a dangerous high-speed mini-object in the direction of the observer. Observation methods depend on the geometric properties of the trajectory $\mathcal T$, i.e., on the location of the segments and convex arcs that constitute it. The aim of the observer is to track the motion of the object along the largest possible part of the trajectory $\mathcal T$.