Adaptive Fast Non-Singular Terminal Sliding Mode Path Following Control for an Underactuated Unmanned Surface Vehicle with Uncertainties and Unknown Disturbances

Abstract

This paper focuses on an issue involving robust adaptive path following for the uncertain underactuated unmanned surface vehicle with time-varying large sideslips angle and actuator saturation. An improved line-of-sight guidance law based on a reduced-order extended state observer is proposed to address the large sideslip angle that occurs in practical navigation. Next, the finite-time disturbances observer is designed by considering the perturbations parameter of the model and the unknown disturbances of the external environment as the lumped disturbances. Then, an adaptive term is introduced into Fast Non-singular Terminal Sliding Mode Control to design the path following controllers. Finally, considering the saturation of actuator, an auxiliary dynamic system is introduced. By selecting the appropriate design parameters, all the signals of the whole path following a closed-loop system can be ultimately bounded. Real-time control of path following can be achieved by transferring data from shipborne sensors such as GPS, combined inertial guidance and anemoclinograph to the Fast Non-singular Terminal Sliding Mode controller. Two examples as comparisons were carried out to demonstrate the validity of the proposed control approach.

Keywords: fast non-singular terminal sliding mode control; line-of-sight; path following; sensor application; unmanned surface vehicle.

Figure 1

Schematic diagram of USV path-following guidance.

Figure 2

The Block Diagram of The Path Following Controller.

Figure 3

The Shipborne Sensors for “Lanxin”.

Figure 4

Comparison results of straight line trajectory tracking at moderate speed.

Figure 5

Along-track error $$x_e$$ and cross-track error $$y_e$$ at middle speed.

Figure 6

Sideslip angle estimations at moderate speed.

Figure 7

Comparison results of $$u_e$$ and $${\psi }_e$$ at moderate speed.

Figure 8

The lumped disturbances and their estimations at moderate speed.

Figure 9

The force $${\tau }_u$$ and moment $${\tau }_r$$ at moderate speed.

Figure 10

Comparison results of straight line trajectory tracking at fast speed.

Figure 11

Along-track error $$x_e$$ and cross-track error $$y_e$$ at fast speed.

Figure 12

Sideslip angle estimations at fast speed.

Figure 13

Comparison results of $$u_e$$ and $${\psi }_e$$ at fast speed.

Figure 14

The lumped disturbances and their estimations at fast speed.

Figure 15

The force $${\tau }_u$$ and moment $${\tau }_r$$ at fast speed.

Figure 16

Comparison results of curve line trajectory tracking at moderate speed.

Figure 17

Along-track error $$x_e$$ and cross-track error $$y_e$$ at moderate speed.

Figure 18

Sideslip angle estimations at moderate speed.

Figure 19

Comparison results of $$u_e$$ and $${\psi }_e$$ at moderate speed.

Figure 20

The lumped disturbances and their estimations at moderate speed.

Figure 21

The force $${\tau }_u$$ and moment $${\tau }_r$$ at moderate speed.

Figure 22

Comparison results of curve line trajectory tracking at fast speed.

Figure 23

Along-track error $$x_e$$ and cross-track error $$y_e$$ at fast speed.

Figure 24

Sideslip angle estimations at fast speed.

Figure 25

Comparison results of $$u_e$$ and $${\psi }_e$$ at fast speed.

Figure 26

The lumped disturbances and their estimations at fast speed.

Figure 27

The force $${\tau }_u$$ and moment $${\tau }_r$$ at fast speed.

Figure 28

Comparison results of curve line trajectory tracking under severe disturbance.

Figure 29

Along-track error $$x_e$$ and cross-track error $$y_e$$ under severe disturbance.

Figure 30

Sideslip angle estimations under severe disturbance.

Figure 31

Comparison results of $$u_e$$ and $${\psi }_e$$ under severe disturbance.

Figure 32

The lumped disturbances and their estimations under severe disturbance.

Figure 33

The force $${\tau }_u$$ and moment $${\tau }_r$$ under severe disturbance.