Flexible manipulators play an important role in ocean development and carrying astronauts for underwater training. In this paper; a controller with global convergence is designed by using backstepping method and the adaptive law of neural network (NN) is introduced to solve the unknown disturbance. To further suppress the residual vibration; an optimal control scheme is proposed. The dynamic modelling and controlling of underwater manipulators are developed in ADAMS and SIMULINK. The simulation results show that the output position is converged to the desired trajectory quickly; and the proposed composite controller has the high-precision trajectory tracking performance and can effectively restrain the vibration of flexible manipulators.


Underwater vehicle-manipulator system(UVMS) is an indispensable tool for deep-sea resource development; and is widely used in deep-sea scientific exploration; seabed resource surveying and underwater object search ( Satja ; Joseph and Edin; 2018). In the past; the research of underwater manipulators mainly focused on rigid manipulators. Due to the advantages of high speed; low energy consumption; small size and light weight; flexible robots have been used in space robots in recent years (Lochan; Roy and Subudhi; 2016). The flexibility of the underwater manipulators can meet the requirements of high performance and has better anti-collision characteristic in practical applications (Liu; He; Xie and Tao; 2017); so it has high research value and application prospects.

Compared with land fixed-base manipulators and space manipulators; underwater flexible manipulators are usually interfered by additional mass forces; water resistance; buoyancy; and some uncertain factors when they move in the water. These effects and interference are highly nonlinear and time-varying; so it is difficult to obtain precise dynamics control equations (Ishitsuka and Ishii; 2005; Farivarnejad and Moosavian; 2014). At the same time; underwater flexible manipulators will undergo torsion and elastic deformation during the movement process; and produce elastic displacement at the end of the manipulator. Conventional control methods are difficult to effectively suppress flexible vibration and eliminate tracking errors; which seriously affects its work efficiency and accuracy (Sakawa ;1985; Yin ; Li and Li ;2017). The operation process of the underwater flexible manipulator system is a complex fusion of hydrodynamics and flexible multi-body dynamics. The combination of complex water environment and flexible vibration of the manipulator brings great difficulties to the modeling and precise control of the manipulator. At present; there are few studies on underwater flexible manipulators. The precise dynamic modeling and control of underwater flexible manipulators has become a very challenging and urgent problem in marine development.

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