Authors A. I. Diveev, E. Yu. Shmalko
Month, Year 09, 2017 @en
Index UDC 004.896, 519.688, 004.023
Abstract The paper presents the results of our research in application of modern numerical methods of symbolic regression for the automatic synthesis of synergistic control for robots group interac-tion. Synergetic control is determined by the presence of such manifolds in the state space that must have the properties of an attractor, in particular terminal manifolds, as well as domains through which solutions of the system do not pass or have repeller properties, for example, the domain of phase constraints. In this paper we formulated a multipoint numerical criterion for ensuring the properties of an attractor for manifolds in the state space. The presented criterion takes into account not only the hit of the solution to the neighborhood of the manifold, but also the behavior of the solution in the neighborhood of the manifold. The proposed criterion turns out to be especially important for one-dimensional manifolds, for which it is necessary not only to get into the neighborhood of a manifold, but also to provide a definite form of variation of the solution in time in the neighborhood of the manifold. The paper presents the results of computational experiments on the effective application of the proposed criterion. As an application object, we consider the problem of synthesizing the control for group of robots. Additional complexity of the task of controlling a group of robots is the presence of dynamic phase constraints that determine the absence of collisions between robots. These dynamic constraints seriously complicate the process of finding the optimal solution for both the control synthesis and optimal control problems. The complexity of the search is mainly dictated by changing the convexity properties of the search area. The paper shows by computational experiments that the solution of the synthesis problem and the problem of optimal control is most effectively performed for control objects that have the property of local stability with respect to a given point in the state space. Therefore, when solving these problems, the proposed two-stage approach is applied when firstly the problem of synthesis of the stabilization system is to be solved in advance to ensure the stability of the object relative to a given point in the state space, and secondly problems of synthesis and optimal control are solved as problems of controlling the stabilization point in the state space. To synthesize control, we use the methods of symbolic regression, which allow us to find the coded mathematical expression of the required synthesizing function using evolutionary algorithms. When searching for optimal trajectories we use various evolutionary and gradient algorithms of nonlinear programming.

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Keywords Control of group of robots; synergetic control; symbolic regression methods; attractors.
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