Moving object in \(\mathbb{R}^2\) and a group of observers (Q721511)

The author considers the problem of finding an optimal trajectory of an object moving in \(\mathbb R^2\) space. The optimal trajectory is under given constraints as far as possible from a group of observers with fixed visibility cones. A formal general formulation of the optimization problem is given, properties of the optimal trajectories are studied, and a method of construction of these trajectories is proposed for a special case. In the special case trajectories consist of segments of straight lines circular arcs, and segments of the boundary of a corridor within which the object moves. The corridor is defined by the visibility cones.