A mobile manipulator in this study is a manipulator mounted on a mobile platform. Assuming the end point of the manipulator is guided, e.g., by a human operator to follow an arbitrary trajectory, it is desirable that the mobile platform is able to move as to position the manipulator in certain preferred configurations. Since the motion of the manipulator is unknown a priori, the platform has to use the measured joint position information of the manipulator for motion planning. This paper presents a planning and control algorithm for the platform so that the manipulator is always positioned at the preferred configurations measured by its manipulability. Simulation results are presented to illustrate the efficacy of the algorithm. The use of the resulting algorithm in a number of applications is also discussed.