A mobile manipulator is defined as a robotic system composed of a nonholonomic mobile platform and a holonomic manipulator fixed to the platform. The kinematics of the mobile manipulator, describing velocity constraints imposed on the platform and determining actual position and orientation of the end effector, are represented by a driftless control system with outputs. The motion planning problem considered in the paper consists in computing a control of the platform and a joint position of the manipulator, that produce a desirable position and orientation of the end effector in the taskspace at a prescribed instant of time. The motion planning problem can be solved globally, using methods of optimal control theory, or locally, by Jacobian methods employing the concept of analytic Jacobian. In the paper we concentrate on local methods, and present three Jacobian motion planning algorithms effective at regular configurations of the mobile manipulator. The performance and convergence of these algorithms is illustrated with computer simulations.