The problem of manipulating objects cooperatively for multi-link multi-degree of freedom space manipulator is very challenging because of the multisource disturbances, including nonlinear coupling, model uncertainties, and external disturbances. To solve this issue, a composite hierarchical control strategy is proposed, which has two layers. In inner layer, uncertainty and disturbance estimator (UDE) is employed to estimate the composite uncertainty that comprises the effect of multisource disturbances and compensate for it, producing the decoupled system. Furthermore, taking the error in UDE estimation into consideration, the chattering–eliminating sliding mode control is designed to suppress it in the outer layer. However, the obtained controller requires the measurement of joint velocities apart from joint positions. To address this issue, a robust velocity observer that employs the UDE-estimated uncertainty is proposed. The notable feature of the proposed design is that it requires neither accurate plant model nor any information about the uncertainty. Also, the design requires only joint position measurements for its implementation. Finally, to demonstrate the effectiveness of the composite hierarchical controller, the simulations of a planar dual-arm manipulator system and the comparisons of the proposed method with the other existing designs are presented.