Spherical Formation Tracking Control of Non-Holonomic UAVs with State Constraints and Time Delays

Abstract

This paper addresses a novel spherical formation tracking control problem of multiple UAVs with time-varying delays in the directed communication network, where the dynamics of each UAV is non-holonomic and in the presence of spatiotemporal flowfields. The state constraints (that is, position and velocity constraints) are derived from our previous differential geometry method and the F–S formulas. The state constraints and time delays in the directed communication network bring many difficulties to controller design. To this end, a virtual-structure-like design is given to achieve a formation with delayed information by using Lyapunov–Krasovskii functionals, and then proposing a barrier Lyapunov function for the satisfaction of state constraints to design a novel spherical formation tracking algorithm. The general assumption of the rate of change of time-varying delays, and a certain initial position and velocity adjustment range are given. Simulation results show the feasibility and effectiveness of the proposed algorithm.