Coherent phantom track generation through controlling a group of electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, generating an optimal or even feasible coherent phantom trajectory in real-time is challenging due to the high dimensionality of the problem and severe geometric, as well as state, control, and control rate constraints. In this paper, the bio-inspired virtual motion camouflage based methodology, augmented with the derived early termination condition, is investigated to solve this constrained collaborative trajectory planning problem in two approaches: centralized (one optimization loop) and decentralized (two optimization loops). Specifically, in the decentralized approach, the first loop finds feasible phantom tracks based on the early termination condition and the equality and inequality constraints of the phantom track. The second loop uses the virtual motion camouflage method to solve for the optimal electronic combat air vehicle trajectories based on the feasible phantom tracks obtained in the first loop. Necessary conditions are proposed for both approaches so that the initial and final velocities of the phantom and electronic combat air vehicles are coherent. It is shown that the decentralized approach can solve the problem much faster than the centralized one, and when the decentralized approach is applied, the computational cost remains roughly the same for the cases when the number of nodes and/or the number of electronic combat air vehicles increases. It is concluded that the virtual motion camouflage based decentralized approach has promising potential for usage in real-time implementation.
Real-time kinematic positioning for unmanned air vehicles
