Combined control of guaranteed search for a moving object with geometric constraints.

In this paper we consider the problem of locating an object moving on a horizontal plane, whose initial position is known to be from a given subset of points of the plane. The search is carried out by the means of accelerating an object through space, which adheres to certain geometrical constraints on the vertical plane such as that the object cannot move past a certain maximum elevation. A combined control algorithm has been developed, that is guaranteed to locate the object by means of a varying linear and curvilinear trajectories, modeled as circles with varying radii. Geometrical and physical parameters have been calculated which allow to solve the problem of guaranteed positioning.