Spatial Curvilinear Path Following Of Underactuated UUV Based On Sliding Mode Theory

The spatial curvilinear path following control is the essential basis of underactuated Unmanned Underwater Vehicle's (UUV) mission implement, such as seabed survey, submarine pipeline monitoring, and cable maintenance. This paper deals with the characteristics of nonholonomic restriction for underactuated UUV, considering the nonlinear of dynamic motion, the dynamic coupling between the degrees of freedom, the uncertainties of hydrodynamic and unsteady ocean current disturbance. Sliding mode control theory for underactuated UUV as well as its practical applications in curve path following control are deeply investigated in this paper, and the main contents contain the following four parts:The first section:the motion and modeling of a certain underactuated UUV are fully investigated and its characteristics of the control system are studied in this paper.Firstly, in order to improve the mathematical models of underactuated UUV motion for six degrees of freedom, the nonlinear mathematical models of actuators and the disturbance model of ocean current are established. The motion models include the nonlinear terms and coupling characteristics of hydrodynamic, also contain the saturation characteristics of actuators and the equilibrium point characteristics under the disturbance of ocean current. Thus the accuracy of digital models are improved and the validity of the models is verified through the maneuverability experiments.Secondly, the underactuated UUV motion models are investigated based on the theory of nonholonomic system and differential geometry. It is proved that the underactuated UUV is second-order nonholonomic system, which has the small-time local controllability. It is demonstrated there is no continuous time-invariant feedback control law that makes underactuated UUV asymptotically stabilization to a single equilibrium, but the system is small-time local controllable. All of that lay a theoretical foundation for motion controller design.The second section:the line-of-sight method is proposed to design the adaptive PID controller, thus the spatial curvilinear path following control for underactuated UUV is actualized.Firstly, aiming at the problem that there is no continuous time-invariant feedback control law to make system be asymptotically stabilized to a single equilibrium, the line-of-sight method is proposed to establish the space movement error models of underactuated UUV. Then the problem of position error's stabilization control is turned into the asymptotic stability design of the speed error, heading error and pitch error, by which the nonholonomic stabilization can be transformed into control problems of holonomic systems. Thus the restrictions of Brockett theorem are avoided and the traditional control methods could be applied to the spatial path following control for underactuated UUV.Secondly, according to the classical PID parameters are difficult to setting, the motion controller is designed based on adaptive PID algorithm for underactuated UUV. The adaptive PID parameters'setting are independent of the accurate mathematical models, which on-line adjustment could realize real-time control. It also has the advantages of simple structure, high reliability as the PID controller. The validity of the method is test and verified through the simulation experiments for spatial curvilinear path following control under the different velocity of underactuated UUV.The third section:the nonlinear iterative sliding mode control based on virtual guide method is proposed, thus the accuracy and robustness of path following are improved under the time-varying ocean current disturbance.Firstly, in allusion to the discontinuity tracking errors which result in saturation characteristic of actuators in LOS method, the virtual guide method is proposed to establish the space movement error models of underactuated UUV. Considering the characteristic of spatial curve and the movement characteristics of underactuated UUV, the smooth continuous space movement error model is established based on virtual guide method, which gives a speed on the path could avoid the occurrence of a singularity.Secondly, aiming at the difficulty for adaptive PID controller to restrain the time-varying ocean current disturbance, the iterative sliding mode control method based on increment feedback is proposed to design the spatial curve path following controller. The recursive sliding mode designing procedure could avoid the problem of the chattering, the increment feedback control method could reduce the overshoot and static error. The anti-interference ability of controller is verified by the simulation experiments for spatial curvilinear path following control under the time-varying continuous ocean current disturbance.The fourth section:the discrete-time sliding mode predictive control method is proposed to achieve the path following receding-horizon control.According to the problem that the ISMC which designed based on continuous-time system can't attain the satisfying control performance, The single-value sliding mode predictive control algorithm is introduced, which is convenient for engineering realization. Feedback correction and receding horizon optimization approaches are employed to compensate the uncertainties of dynamic model and the influence of steady discontinuous ocean current disturbances, thus the spatial curve path following control system possesses stronger robustness and higher accuracy for underactuated UUV.