Trajectory of an observer tracking object motion around convex obstacles in $\mathbb{R}^2$ and $\mathbb{R}^3$

An autonomous object moves at a constant speed along the shortest path, while bypassing an ordered collection of pairwise disjoint convex sets. The object is tracked by an observer. The goal of the observer is to find a trajectory of motion along which the object can be tracked at each moment of time and can be followed at a given distance at possibly low speed. Options for the observer’s trajectories with an indication of the speed limit are proposed.