Aerial manipulators have great potential in accomplishing a variety of aerial tasks. One class of aerial manipulators, multi-UAV parallel robots, consists of multiple UAVs connected to a payload or an end-effector by passive kinematic chains. The primary limitation of such aerial manipulators is the dependence on motion capture (MOCAP) systems that provide precise and high-rate exteroceptive pose measurements of all bodies in a common inertial frame, but which are impractical in the majority of real applications. This paper proposes a novel methodology of controlling multi-UAV parallel robots, using a Flying Parallel Robot (FPR) as a case study, that could be deployed without a system of external localisation. Intrinsic measurements acquired onboard the UAVs are used to recover a set of robot states that avoid using coordinates derived from a global frame and allow control of the robot by teleoperation. Two decentralized control methods are proposed, based on inter-UAV communicating or non-communicating scenarios. Experiments with intrinsic measurements emulated by MOCAP are carried out to show the performance of the proposed method.