Decentralized Control of a Group of Similar Objects Moving in a Two-Dimensional Environment with Obstacles

Abstract

The topic of the article is movement of a group of autonomous mobile objects during their functioning in the environments with stationary obstacles. The task is solved within the framework of the decentralized control systems. Thus the exchange of information between the mobile objects in a group is minimized. During the planning of the movement and control of the mobile objects the obstacles are transformed into repellers by means of synthesizable controls. The method of the potential fields and the method of control of the mobile objects with the use of unstable modes are the closest to the proposed method. The main difference of the developed method from the method of the potential fields is that a mobile object moves to the field of the forces depending not only on the relative positioning of the robot and an obstacle, but also on the additional dynamic variables. The dynamic way of formation of the repellent forces allows one to operate robots within the system of a decentralized control. The main difference of the offered approach from the method of position and trajectory control with the use of the unstable modes is the way of introduction of the unstable states. In the method of position and trajectory control the change of the parameters of the reference equation of a control system is used. In the offered method additional dynamic variables are used. Stable and unstable states of this variable depend on the state variables of a robot and the objects, next to it. In the local control systems of each mobile object the only values used are those of the own coordinates and speeds, and also coordinates and speeds of the neighboring objects. At that, a centralized algorithm of control is absent. Obstacles in the local algorithms are presented as mobile objects, which makes it possible to unify the control systems for the heterogeneous groups. An analysis was carried out, during which the existence and asymptotic stability of the steady movement modes were proved. The carried out numerical modeling confirmed the results of the analysis and synthesis.