In this study, a continuous robust-adaptive operational space controller that ensures asymptotic end-effector tracking, despite the uncertainties in robot dynamics and on the velocity level kinematics of the robot, is proposed. Specifically, a smooth robust controller is applied to compensate the parametric uncertainties related to the robot dynamics while an adaptive update algorithm is used to deal with the kinematic uncertainties. Rather than formulating the tracking problem in the joint space, as most of the previous works on the field have done, the controller formulation is presented in the operational space of the robot where the actual task is performed. Additionally, the robust part of the proposed controller is continuous ensuring the asymptotic tracking and relatively smooth controller effort. The stability of the overall system and boundedness of the closed loop signals are ensured via Lyapunov based arguments. Experimental results are presented to illustrate the feasibility and performance of the proposed method.