Authors G. E. Veselov, A. A. Sklyarov, M. N. Garcia
Month, Year 05, 2018 @en
Index UDC 681.51
Abstract The paper presents a solution of the problem of non-linear control law design for a group of mobile robots. A mobile robot on omni-directional wheels was chosen as an agent of the swarm, because this kind of mobile robot is the most maneuverable and designed to work in closed spaces. The type of chassis is designed to perform tasks in warehouses. To take into account the nonlinear characteristics of this type of mobile robot chassis, the analysis of the mathematical model of a mobile robotic platform was considered. The paper also provides a survey of modern methods and approaches to group control, discusses the use of methods for optimizing collective behavior, artificial potential fields, heuristic methods based on the recognition of the situation and the development of appropriate actions and methods based on the use of fuzzy logic. It is shown that when applying these methods, the problem of analyzing the stability of the obtained closed-loop control system is complex. From the survey of modern methods, the basic conditions imposed on the synthesized law of group control of robots are highlighted. These conditions are adaptability to the external environment and asymptotically stable movement of mobile robots to a given point in space with a given type of order. Therefore, the paper presents a reasons for the use of new non-linear approaches to the control of mobile robots’ swarm, in particular, synergetic control theory. The main method, within the framework of this theory, is the method of analytical design of aggregated regulators, which allows to synthesize control laws for complex non-linear systems of large dimensions without applying linearization procedures or other simplifications, therefore this method is used to synthesize synergetic laws of group control. The application of the method of analytical design of aggregated regulators allows us to solve the problem of studying the stability of the resulting closed-loop control system, due to the sequential decomposition of the original system, which is shown in the analytical synthesis procedure of the group control strategy of mobile robots using full non-linear motion models.

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Keywords Group control; omni-wheel robot; non-linear mathematical model; synergetic control theory.
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