Three dimensional path-following control for an under-actuated airship

A new three dimensional path-following control algorithm for under-actuated airships based on guidance vector field is presented in this paper. Firstly, the vector field theory is described. Nextly the under-actuated airship dynamic is established based on Newton-Euler equations. Based on this model and the vector field theory, the guidance vector field is constructed to obtain the desired attitude angles and desired velocity. Then the path-following controller is proposed by using Backstepping technique and PD control technique. Command filters are utilized to estimate derivatives of the virtual controls during the controller design progress such that complex analytical calculations can be avoided. The resultant control system possesses a cascaded structure, which consists of a guidance vector field subsystem, an attitude stabilization control loop and a velocity tracking control loop. The stability analysis shows that path-following error of the airship is ultimately uniformly bounded. Finally, simulation results for the airship are illustrated to verify the effectiveness of the proposed design.