Hybrid three-dimensional formation control for unmanned helicopters

This paper presents a hybrid supervisory control framework for the three-dimensional leader–follower formation control of unmanned helicopters. In particular, a spherical abstraction of the state space is proposed. Utilizing the properties of multi-affine functions over the partitioned space, a finite state model is obtained, which is shown to be bisimilar to the original continuous-variable dynamical system. Then, in the discrete domain, a logic supervisor is modularly designed for the abstracted model, which can be recaptured as a hybrid controller for the original continuous-variable dynamics. The designed hybrid supervisor is able to bring the unmanned helicopters to the desired formation, starting from any initial point inside the control horizon, and then maintain the formation. Moreover, a collision avoidance mechanism is embedded in the designed supervisor. The algorithm is verified through hardware-in-the-loop simulations.