## 1 Introduction  
Recently, with the exhaustion of land resources, underwater resources are at the center of attention, especially the resources hidden in the deep sea [1]. Therefore, many underwater works and operations are now being performed both in the scientific and business communities, such as salvage, marine resource investigation, ship engineering, marine construction, etc. [2]. Owing to the extremely poor working conditions in the deep sea, underwater manipulators, often equipped on the remotely operated underwater vehicles or autonomous and remotely operated underwater vehicles, are considered to be the most suitable tool to work instead of human beings. Hydraulic underwater manipulators and electric underwater manipulators are the most commonly existing commercially available underwater manipulators and most of the experimental/prototype underwater manipulators [3]. In recent years, with the development and combination of artificial intelligence technology and robot technology, the research of electric underwater manipulators hasattracted considerable attention due to their capability for precise motion and force/torque control as they perform in the industrial fields [3]. Typical electric underwater manipulators are the manipulator 7E of Eca Robotics [3], the UMA manipulator developed by Graal Tech SRL in Italy for the TRIDENT project [4], the modified commercial electric manipulator ARM 5E [5], etc. Owing to the extremely high pressure in the deep-sea environment, the electric underwater manipulator is watertight and oil compensated from bearing the deep-sea water pressure [6; 7]. The oil-filled joint actuator of electric underwater manipulator, which is commonly composed of a brushless, direct-drive motor with reduction gearbox featuring low backlash and a large reduction ratio [3], will suffer from oil stirring loss [7; 8; 9; 10] resulting from the rotation viscos between the high speed rotor and oil, output shaft dynamic seal loss [10] deriving from the high-pressure action and high-speed rotation friction on the rubber seal rings, and core loss [9; 10] caused by the high-pressure action on the motor cores. Therefore, the oil-filled joint actuator will show different characteristics and response performance compared with its common use. For the oil-filled joint actuator, the oil stirring viscos loss and output shaft dynamic seal loss can be considered as part of unknown internal disturbance and external disturbance respectively, while the core loss usually directly leads to the physical parameter deviations of the motor, which can be treated as dynamic uncertainties. Furthermore, due to the compact and lightweight requirements, usually only the angular position sensor is available for the oil-filled joint actuator, and thus joint velocity is immeasurable for the control. Consequently, the oil-filled joint actuator will suffer from an unmeasured system state, dynamic uncertainties, and unknown disturbances when it works in the deep-sea environment, and its achievable control performance could be severely deteriorated by these adverse factors. To handle immeasurable system states, observers have been widely used [11; 12; 13; 14; 15]. In [11], a neural-based full-order Luenberger adaptive observer was designed for sensorless linear induction motor control. In [12], a sliding mode observer was proposed to observe the back electromotive force for obtaining the velocity and position of the mover of a permanent magnet synchronous linear motor. In [13], an approximate high-gain observer was employed to observe the speed signals for an induction motor control. In [14], a third-order nonlinear extended-state observer (ESO) was constructed for position and speed estimation for a permanent magnet synchronous motor control. In [15], the oxygen excess ratio was estimated via an extended-state observer (ESO) from the measurements of the compressor flow rate, the load current, and the supply manifold pressure, which was used in the output feedback controller design of the oxygen excess ratio control system.