The Method of Controlling an Object Identifying Trajectory Parameters of a Rectilinearly Moving Target on the Base of the Distances to it

Abstract

The article deals with the problem of object control in order to determine the parameters of the moving target trajectory. We consider the conditions under which a locality map is unknown and there are no external landmarks. There is no available target position information except for non-directional measurements of the distance between an object and a target. Such conditions can arise, for example, in the case of using Wi-Fi or radio signals, when by means of a signal strength the distance to a signal source can be determined, while the direction in which a signal source is located remains unknown. A general statement of the control problem is given. The solution of the problem in a particular case of rectilinear motion of a target and a piecewise linear motion of an object is proposed. It is proved that the estimations of the parameters of target motion can be obtained by using not less than 7 measurements of distances to a target. In addition, in the measurement process, an object twice has to change the direction of its motion at least two times. An immovable object cannot determine the trajectory of a target. The method of object control which enables to determine the parameters of a target trajectory is proposed. The conditions of control existence are obtained. It is also shown that in a special case of a parallel movement of a target and an object not less than 4 measurements are needed to determine target trajectory parameters. The problem solution time corresponding to different methods of solution is estimated. The results of research can be used in the robot control problem, particularly, in the problem of robot gathering. The presented approach gives an exact solution under condition of high accuracy of distance measuring. In practice, the accuracy of measurements is influenced by a large number of factors. Therefore, a challenging problem is to study the dependence of the target trajectory parameters problem solution on the accuracy of distance measurements.