An object bypassing convex sets and an observer's trajectory in two-dimensional space

An autonomous object $t$ moving under observation in $\mathbb{R}^2$ with constant speed along a shortest curve $\mathcal{T}_t$ with given initial and final points bypasses an ordered family of pairwise disjoint convex sets. The aim of the observer $f$, whose speed is upper bounded, is to find a trajectory $\mathcal{T}_f$ on which the distance to the observer is at each time a certain prescribed value. Possible variants of motion are given for the observer $f$, who tracks the object on different segments of the trajectory $\mathcal{T}_t$.