The paper presents the motion control of the ceiling based service robot platform ACROBOTER that contains two main subsystems. The climbing unit is a serial robot, which realizes planar motion in the plane of the ceiling. The swinging unit is hoisted by the climbing unit and it is actuated by windable cables and ducted fans. The two subsystems form a serial and subsequent closed-loop kinematic chain segments. Because of the complexity of the system we use natural (Cartesian) coordinates to describe the configuration of the robot, while a set of algebraic equations represents the geometric constraints. Thus the dynamical model of the system is given in the form of differential-algebraic equations (DAE). The system is under-actuated and the the inverse kinematics and dynamics cannot be solved in closed form. The control task is defined by the servo-constraints which are algebraic equations that have to be considered during the calculation of control forces. In this paper the desired control inputs are determined via the numerical solution of the resulting DAE problem using the Backward Euler discretization method.