Properties of interconnected negative imaginary systems and extension to formation-containment control of networked multi-UAV systems with experimental validation results

This paper extends the properties of a positive feedback interconnection of two negative imaginary (NI) systems to multi-agent NI systems and proposes a new formation-containment control methodology relying on the characteristic loci technique. Inspired by recent applications of NI and passivity-based control techniques in the multi-agent systems (MAS) domain, a new formation-tracking and containment control scheme is developed for a class of networked multi-UAV systems. The proposed scheme offers a two-stage and two-loop control configuration where the inner loop uses a cascaded PID controller to ensure stable hovering of the UAVs, and the outer loop deploys a distributed "mixed" SNI and strictly passive controller to achieve the formation-containment objectives. This scheme works with a dynamic output feedback control strategy; hence, it offers advantages when the full-state measurement is not possible. In contrast to the well-known Lyapunov theory-based cooperative control schemes, the present one exploits the characteristic loci technique to prove the formation-tracking and containment phenomena theoretically. The paper also provides experimental validation results on a fleet of Crazyflie 2.1 nano quadcopters.