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The continuous inverse kinematic problem amounts to computing a configuration of a mobile manipulator capable of producing a prescribed trajectory in the taskspace. By adopting a control system representation of kinematics of the mobile manipulator this problem is made equivalent to the problem of exact or asymptotic output tracking that may be solved by the dynamic extension algorithm. We study the continuous inverse kinematic problem for a mobile manipulator comprising a 3 DOF RTR manipulator mounted on a kinematic car type mobile platform. Our main result is a continuous asymptotic inverse kinematics algorithm employing dynamic state feedback. The performance of this inversion algorithm has been examined in computer simulations.