Spatial target path following control based on Nussbaum gain method for underactuated underwater vehicle

• The virtual target point on the desired spatial path is not the nearest point to UUV.
• The line-of-sight navigation is introduced.
• Hyperbolic tangent functions were employed to prevent actuators from saturation.
• Nussbaum gains were employed to estimate unknown parameters.

This paper investigates path following problem of underactuated underwater vehicle (UUV) which follows desired spatial path with constraint control inputs. Three dimensional path following error dynamics in Serret–Frenet coordinate frame is set up. The virtual target point on the desired spatial path is not the nearest point to UUV, which relaxes the restrictions on the initial conditions of controller. Considering speed of UUV and introducing the line-of-sight navigation, path following errors can converge rapidly. Hyperbolic tangent functions are employed to design path following controller which generates amplitude-limited control signals to prevent the actuators from the saturation. This improves the transient performance for large initial tracking errors in path following problem. Moreover, Nussbaum gains are incorporated into the control laws in order to estimate unknown parameters. This makes the controller realizable. The control method was proposed based on Lyapunov theory and backstepping technique. Theoretical proof and simulation experiment showed that the proposed method is effective to deal with path following problem of UUV.