Energy-efficient flocking with nonlinear navigational feedback

Modeling collective motion in multi-agent systems has gained significant attention. Of particular interest are sufficient conditions for flocking dynamics. We present a generalization of the multi-agent model of Olfati--Saber with nonlinear navigational feedback forces. Unlike the original model, ours is not generally dissipative and lacks an obvious Lyapunov function. We address this by proposing a method to prove the existence of an attractor without relying on LaSalle's principle. Other contributions are as follows. We prove that, under mild conditions, agents' velocities approach the center of mass velocity exponentially, with the distance between the center of mass and the virtual leader being bounded. In the dissipative case, we show existence of a broad class of nonlinear control forces for which the attractor does not contain periodic trajectories, which cannot be ruled out by LaSalle's principle. Finally, we conduct a computational investigation of the problem of reducing propulsion energy consumption by selecting appropriate navigational feedback forces.