Hybrid 3-D Formation Control for Unmanned Helicopters
  Teams of Unmanned Aerial Vehicles (UAVs) form typical networked cyber-physical systems that involve the interaction of discrete logic and continuous dynamics. This paper presents a hybrid supervisory control framework for the three-dimensional leader follower formation control of unmanned helicopters. The proposed hybrid control framework captures internal interactions between the decision making unit and the path planner continuous dynamics of the system, and hence improves the system's overall reliability. To design such a hybrid controller, a spherical abstraction of the state space is proposed as a new method of abstraction. Utilizing the properties of multi-affine functions over the partitioned space leads to a finite state Discrete Event System (DES) model, 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. Due to the bisimilarity between the abstracted DES model and the original UAV dynamics, the designed logic supervisor can be implemented as a hybrid controller through an interface layer. This supervisor drives the UAV dynamics to satisfy the design requirements. In other words, the hybrid controller is able to bring the UAVs to the desired formation starting from any initial state inside the control horizon and then, maintain the formation. Moreover, a collision avoidance mechanism is embedded in the designed supervisor. Finally, the algorithm has been verified by a hardware-in-the-loop simulation platform, which is developed for unmanned helicopters. The presented results show the effectiveness of the algorithm. 
A. Karimoddini, H. Lin, B. M. Chen, T. H. Lee
cs.SY cs.MA cs.RO math.OC