We define a mobile manipulator as a complex robotic system composed of a mobile platform and a stationary manipulator mounted on the platform. The platform motion is subject to nonholonomic velocity constraints. The task of the mobile manipulator amounts to placing its end effector at a prescribed position and orientation in the taskspace. The kinematics of the mobile manipulator are represented by a driftless control system with outputs. We consider a motion planning problem that consists in computing an endogenous configuration (i.e. a control function of the platform and a joint position of the manipulator) capable of driving the end effector to a desirable position and orientation, and of avoiding obstacles present in the taskspace. The motion planning problem is solved locally by the extended Jacobian inverse kinematics algorithm furnished with an extra motion component belonging to the null space of analytic Jacobian of the mobile manipulator. A performance of this motion planning algorithm is examined by computer simulations.