Authors A.I. Diveev, E.Yu. Shmalko
Month, Year 10, 2015 @en
Index UDC 004.896
Abstract We consider the problem of automatic synthesis of feedback controller for a robotic team. To synthesize a feedback control means to find a multidimentional nonlinear control function that depends on objects’ state. Such functions implemented to on-board computers will be able to produce control signals that transfer the control objects from the initial state to the terminal manifold with optimal value of quality criteria. The problem of control synthesis for the group of robots relates to the general problem of control synthesis and has additional dynamic constraints in the state space in order to avoid collisions of robots with each other in the process of movement towards the control objective. The review presents the three main approaches to constructing feedback control systems for groups of robots. These are methods that use navigation functions, that decompose the configuration space into cells and symbolic regression methods. In contrast to the first two approaches on multi robot coordination, symbolic regression methods allows synthesizing feedback controllers completely automatically, realizing the evolutionary search for the optimal control and its parameters in the space of possible solutions. Such an approach to the synthesis problem is versatile and not limited to the particular application problem. In the present paper we use such method of symbolic regression as the network operator method. The basic idea is to code any mathematical expression in the form of integer matrix which elements correspond to variables, parameters and elementary functions. The mathematical expression that meets the overall control objective with the best value of quality functional is searched by the genetic algorithm on the basis of the principle of small variations of basic solution. Our principle of small variations of the basic solution narrows the search space and reduces the computation time. When building a basic solution a specialist can use well-known analytical methods, such as analytical construction of aggregated controllers. The better the basic solution the faster a computer solves the problem. We validate our approach by presenting the results of applying the network operator method to the task of two mobile robots parking.

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Keywords Control system synthesis; robotic team; dynamic constraints; symbolic regression; genetic algorithm.
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