The objective of this paper is to design a discrete-time multivariable controller for a class of robot manipulators without using joint velocities while possessing tracking ability and yielding smooth torque signals. The structure of the control law is a proportional derivative (PD) controller plus gravity compensation with some plausible partial compensation of the friction and Coriolis/centripetal forces. However, we show that the controller requires the derivative part of the controller for stability, that is, joint velocities are needed. In order to resolve this dilemma, we develop a suboptimal stochastic controller, which assumes noisy measurement of joint positions and velocities. The optimality is in the sense that the time-varying PD controller gains aim at per-discrete-time instant minimization of the mean-square state error. Stability analyses of the proposed controller are provided. While implementing the controller we use fictitious measurement of the joint velocities, which depend on the current measured positions. In order to overcome the discrepancy resulting from such inaccurate measurements, we associate large measurement error covariance corresponding to joint velocities. It is shown that tracking errors can be made arbitrary small in probability while adopting sufficiently large sample rate. We demonstrate the effectiveness of our proposed approach numerically and experimentally on a seven-degree-of-freedom robot manipulator.