## 1 Introduction  
Through visual feedback, human beings can perform various tasks in an unknown environment without a priori knowledge. Human can adapt to unforeseen changes by fast visual responses and dexterous hand manipulations. For example, a person can easily move his hand to grip a tool at different positions and in varying orientations. It seems that human beings do not require thorough understanding of the kinematics and dynamics of the human eye-to-hand system. This flexibility to adapt to unknown variations might arise from the consequences of low-speed hand motions and high-gain sensorimotor control. Nevertheless, a well-designed and flexible robot control system should be able to adapt to parametric variations in kinematics and dynamics to meet the demands of industrial-robot applications that require high-speed manipulations for better productivity and low control energy for better efficiency [1]. Adaptive tracking control schemes in joint space have been proposed for more than two decades to deal with parametric uncertainties in dynamics [2; 3; 4; 5]. For instance, [PERSON] and [PERSON] [3] investigated the adaptive control of rigid link manipulator systems using linear estimation techniques together with a computed torque control. The proposed adaptive control algorithms were shown to be globally convergent and do not require acceleration measurements. [PERSON] and [PERSON] [4] proposed an adaptive inverse dynamics control for rigid robots to relax the assumption that the inverse of the estimated inertia matrix must remain bounded. Furthermore, using linear parameterization and skew-symmetric properties from the inertia matrix, [PERSON] and [PERSON] [5] defined a sliding vector and proposed an adaptive control algorithm that does not require the measurement of joint acceleration. In general, task-space control algorithms can use vision sensors to provide visual feedback and thus compute the joint control torque using the Jacobian matrix, defined as a transformation from the joint space to the image space. Assuming kinematics is known, adaptive control schemes in the joint space can be extended to the adaptive tracking control in the task space. Therefore, kinematic uncertainties such as unforeseen changes of object positions and/or orientation and unknown camera parameters must be considered for accurate tracking control in the task space. The dynamic effects in visual servo control can be ignored if the robot's inertia is small and the tracking velocity is low. However, for high-speed trajectory tracking, a task-space robot control scheme that can adapt to the kinematic and dynamic uncertainties is important for improving the performance of future robots. Recently, researchers have considered dynamic and kinematic uncertainties in robot manipulators and have proposed many means of task-space adaptive tracking control [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. In particular, [PERSON] et al. [7] extended the classic Slotine-Li adaptive algorithms [5] for manipulator control to task-space adaptive algorithms that can deal with dynamic uncertainties and unknown kinematic properties such as uncertain camera parameters. Nevertheless, the formulation of the dynamic regressor requires the exact Jacobian matrix that may not be available due to the parametric uncertainty in kinematics. [PERSON] [11] presented a unified approach and discussed the duality property of the transpose Jacobian and inverse Jacobian PD (Proportional-Derivative) control for the task-space regulation of robot manipulators. For the transpose Jacobian approach, in general, it is assumed that the Jacobian matrix is nonsingular for the control schemes in the task space. [PERSON] and [PERSON] [17] developed a global task-space adaptive robot control strategy to address the problems of singularity of the Jacobian matrix and limited sensing zone. The authors proved the global dynamic stability of the proposed task-space control strategy that can smoothly transit between regional feedback and avoid discontinuous switching.