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The task-space tracking control of robots without the exact knowledge of kinematics and dynamics has been studied before with the assumption that the joint velocities are available for controller designs. However, the velocity measurements can be contaminated by noises, thereby resulting in poor system performance, or even leading to instability problems. Therefore, in this paper, we propose a new tracking controller for robots in the task space without the use of both task-space and joint-space-velocity measurements, under the condition that both the robot kinematics and dynamics are unknown. To overcome these incapacities without the velocity measurements, we introduce the well-known sliding-observer-design techniques to estimate the joint velocities for the purpose of our controller design. Our main concern, i.e., the stability analysis of our controller design incorporated with the siding observer, is presented with the help of Lyapunov-analysis methodology and the sliding-patch concept. Simulation results are presented to show the performance of our controller-observer designs.