Optimizing the Control of a Group of Mobile Objects under Uncertainty

A swarm of moving objects coordinates the position of its individual objects in order to simultaneously solve a general problem set in a distributed manner. Planning the swarm operations comes across a problem of taking into account the possibility of operational regrouping of the swarm as the exact purpose of the swarm operation is not yet determined, or is a secret, or is set by a number of random circumstances. At the same time, the swam resources are not sufficient to simultaneously cover all possible targets in the operating region. Therefore, it is advisable to carry out the swarm operation in two phases and begin the first preliminary phase before resolving the mentioned uncertainties by creating a basic network with a relatively low concentration of swarm objects therein. In this case, one can significantly reduce the operation time. In the second phase of the operation, one locally simultaneously regroups the swarm objects, which takes a minimum time, to form a programmable percolation path that provides targeted coverage of the operating region. The solution to this problem is carried out by methods of the programmed percolation theory. The value of the swarm object concentration is obtained numerically using the results of statistical modeling of two-phase operations and analytically, thereby providing a minimum of total cost of the two-phase operation. The synergetics of information interaction of the swarm of objects in the implementation of a programmable percolation path is considered.