Optimal planning of networks of mobile objects under uncertainty

When solving a given common task, a swarm of moving objects coordinates the state of its individual members. When planning swarm operations, there is a need to take into account the possibility of its operational regrouping, since at the time of planning the exact purpose of the swarm operation may be either not yet defined, or secret, or determined by a number of random circumstances. At the same time, the swarm resources are insufficient for one-time coverage of all possible targets in a given service area. Therefore, the execution of the operation of the swarm begins to resolve the aforementioned uncertainties. In this case, the operation time can be significantly reduced. This problem is solved by methods of the percolation theory. A concept of programmable percolation of the service area, which is implemented in two phases, is introduced. The value of the concentration of objects in a basic stochastic swarm is obtained numerically — using the results of statistical modeling of two-phase operations — and analytically, providing a minimum total cost of the two-phase operation. The synergy of information interaction between the swarm objects when implementing a programmable percolation path is analyzed.