Abstract: On-orbit servicing robots seem to be the best alternative for tasks such as satellite servicing, space construction missions, and orbital debris removal. Typically, space robots for on-orbit servicing consist of a base satellite and one or more manipulators attached to the base. Since the base is not fixed, the robot kinematics is more complicated than in the case of ground-fixed manipulators. This paper presents methods for solving the direct and inverse kinematics of a free floating robot for on-orbit servicing as well as its direct and inverse velocity kinematics. The presented approach employs dual quaternions for the kinematics solving, showing more computationally efficiently than the classical approach based on homogenous transforms. The velocity kinematics problems are solved by an introduction of the momentum conservation law into the kinematics model. The proposed methods are applicable to robots with an arbitrary number of manipulators and mixed prismatic and revolute joints. The methods are verified by computer simulation of a kinematic control process.