## 1 Introduction  
Many robot manipulators work in environments with vibrations and are concurrently subject to payload uncertainty. These two factors cause a significant nonlinear disturbance torque that affects the dynamic behavior of the controllers, which complicates the issue of tracking control [1]. Therefore, considering the disturbance while controlling the position of manipulators has been a topic of interest in recent years. Some researchers count the disturbance as part of uncertain dynamics while dealing with trajectory tracking control. Others consider the dynamics as known and deal with the disturbance separately. For this purpose, a variety of linear and nonlinear control tools have been tested. In [2], the trajectory tracking problem was treated in the presence of an unknown payload using adaptive control theory. The same theory was used in [3] to suppress disturbances and track desired trajectories uniformly by assuming that an accurate dynamic model of the manipulator is available. The authors of [4] considered the uncertain load as part of unmodeled dynamics and represented it by a single disturbance force to be rejected utilizing a proportional derivative (PD control law). [PERSON] et al. [5] depended on the definition that the disturbance can be bounded [3] to show that if the PD controller gains are chosen to be greater than that bound plus the other uncertain dynamics and the initial value of the tracking error is considered, then that error is uniformly bounded (UB). In [6], the author derived a control law and proved that the tracking error is uniformly ultimately bounded (UUB) depending on the inertia parameters of the robot. The control effort in [2; 3] is superior to that in [4; 5; 6], but this kind of controller performs poorly in the presence of disturbances, such as unknown payload or external vibration. Some other works [7; 8] used the theory of variable structure (VSS) to drive the tracking error to a switching surface so that the disturbance will not affect the tracking control (i.e., asymptotic result). However, the drawback of controllers that use VSS theory is the discontinuity/high-frequency of the control input, which makes it difficult to implement. Furthermore, other works take into account the case that the disturbance cannot be linearly parameterized and thus incorporate function approximation methods (neural network and fuzzy logic) into the above mentioned works and presented UUB results for the tracking error. In [9], the fuzzy logic method was used to develop a robust tracking control for robot manipulators in the presence of unknown perturbations. In [10], the authors showed that a combination of robust model-based control and neural network payload estimation has the potential to provide payload-invariant high-speed trajectory tracking. In [11], a universal robust neural network controller was presented for motion control of rigid-link electrically-driven robots with unknown dynamics. This controller does not require an off-line training-phase, as compared with other neural network approaches. [PERSON], [PERSON] et al. [12] developed a neural network controller for vibration suppression of a two-link flexible robotic manipulator and they showed UUB results. The mentioned works require velocity measurements to design the controllers. Further research has been conducted to eliminate the measurement of velocity and show global asymptotic and global UUB for joint position tracking [13; 14]. However, these controllers are restricted by many assumptions during the design process. To overcome these restrictions, other efforts utilize the differentiable property of the uncertain terms and/or use robust integral of the sign of the error (RISE) feedback to develop new controllers for high-order dynamic systems and many other systems. In [15], a robust adaptive control is presented for a multiple-input-multiple-output system that guarantees the tracking error is asymptotically driven to zero in the presence of bounded disturbances with bounded time derivatives.