Control and Stability of the Multi-Robots System

Abstract

The problem of coordination of two or more mechanical systems (robots) cooperating in the same control task is considered in the paper. The coordination of the robots in time and in space is left to upper control levels. The executive control level has to ensure tracking of the trajectories imposed by the upper control levels, i.e. it has to ensure practical stability of the complete system around nominal trajectory. However, during the operation, the robots may come in the mechanical contacts with each other or operate without contacts. Therefore, the structure of the global system changes during operation. This means that the executive control level has to ensure practical stability of the whole (global) system under the structural perturbations of the system. The executive control level is synthesized in decentralized form: for each degree of freedom (subsystem) of each mechanical system local controller is synthesized. The aggregation-decomposition method is used for stability analysis of the complete multi-robot system. To ensure practical stability of the system under structural perturbations we have to consider connective stability of the system. This method for stability analysis can guarantee the stability of the complex system with changes in structure of interconnections between the subsystems. This method is used to establish an algorithm for iterative synthesis of local controllers which are capable to withstand structural perturbations in the system and thus stabilize multi-robots system. Also we suggested the introduction of global control which can reduce the coupling between the subsystems and compensate for changes in interconnection structure. En example of two particular robotic manipulators cooperating in the same control task is presented.