Multi agents' multi targets mission under uncertainty using probability navigation function

In this paper we consider the problem of cooperative control of a swarm of autonomous heterogeneous mobile agents that are required to intercept a group of moving targets while avoiding contacts with dynamic obstacles. Traditionally these type of problems are solved by decomposing the solution into several sub problems: targets assignments, coordinated interception control, motion planning and motion control. In this paper we present a simultaneous solution to these problems based on the Probabilistic Navigation Function (PNF). The proposed solution considers uncertainties in the targets and obstacles locations. such that the locations and geometries of the targets and obstacles are given by Gaussian probability distributions. These probabilities are convoluted with the agents', obstacles' and targets' geometries to provide a Global Probability Navigation Function — φ. The PNF provides an analytic solution, and guarantees a simultaneous interception of all targets while limiting the risk of the agents to a given value. The complexity of the solution is linear with the number of targets and agents, and therefore is not limited to small problems. Although the solution provided by the PNF is not optimal, it provides simple and efficient solution, making it suitable for a large range of real time applications.