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An Algorithm of Route Planning Through the Set of Nonconvex Obstacles

Sergey Kruglikov, Alexei Kruglikov
Navigation and routes planning for a group of vessels jointly moving in complex environment, including circumvention of seashore and islands, are important applications of computer-based decision-making support systems. A group of objects as an open complex system includes several levels of a hierarchy and is controlled by a decision-maker supported by an information-analytical soft and methodical maintenance. One stage of management is planning, including an a priori phase – determination routes for all objects in the group, coordinated in both time and directions of approach to the target set restricted by a set of obstacles. A discrete system of priorities reflects the relative preferences of the decision-maker and allows choosing the routes optimal in different senses. Such tasks could be formalized in terms of different mathematical models including control problems of formation motion, the theory of extreme networks and interval analysis. Constructions discussed in the paper are based on guaranteed approach to control of dynamic objects under uncertainty. Unified mathematical descriptions of shores, routes of isolated objects and the whole group may be given in terms of hierarchic (i)-systems. That allows to reconcile data on geography, environment, object characteristics, peculiarities of control systems and data transmission, including sources and causes of uncertainty, and to describe movement of a group as an extreme problem of control and estimation. The results of computer simulation are considered. Similar models may be used to explore economic aspects of application a heterogenic complex of surface and underwater vessels.
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