3D Circle Formation Control of VTOL Vehicles Without Distance Measurement

This paper studies a novel circle formation problem in 3D space using a team of vehicles that are able to vertically take off and land (VTOL). The target formation can be in any plane with any non-horizontal orientation in 3D space, which, combined with the complicated nonlinear dynamics of vehicles, makes the problem difficult. We design a distributed control law to solve this problem. The control law has three nice properties. The first is that it can be transformed into the local frame of each vehicle, and the resulting form is independent of any global values, which means it is fully distributed. The second is that the control law requires no distance measurements, which facilitates practical application. The third is that our controller generates bounded values of control inputs. To validate it, we carry out theoretical analysis using Lyapunov function and graph theory, where we show successively that the vehicles will move to the target plane, the target circle, and the desired spacing. Finally, we execute numerical simulations to show the effectiveness of the proposed control law and further perform formation tasks in our built multi-UAV simulation platform to demonstrate the applicability.