This paper describes the development and use of the cooperative control scheme used by the intelligent pneumatic arm movement (iPAM) system to deliver safe, therapeutic treatment of the upper limb during voluntary reaching exercises. A set of clinical and engineering requirements for the control scheme are identified and detailed, which entail controlled, coordinated movement of a dual robot system with respect to the human upper limb. This is achieved by using a 6-DOF model of the upper limb that forms the controller's coordinate system. An admittance control scheme is developed by using this coordinate system such that robotic assistance can be varied as appropriate. Key controller components are derived, including kinematic and force transformations between the upper limb model and the dual robot task space. The controller is tested using a computational simulation and with a stroke subject in the iPAM system. The results demonstrate that the control scheme can reliably coordinate the dual robots to assist upper limb movements. A discussion considers the ramifications of using the system in practice, including the effects of measurement errors and controller limitations. In conclusion, the iPAM system has been shown to be effective at delivering variable levels of assistance to the upper limb joints during therapeutic movements in a clinically appropriate manner.