Multiple robot manipulators cooperating in a common manipulation task can accomplish complex tasks that a single manipulator would be unable to complete. To achieve physical cooperation with multiple manipulators working on a common object, interaction forces need to be controlled throughout the motion. The aim of this research is to develop an inverse dynamics model-based cooperative force and position control scheme for multiple robot manipulators. An extended definition of motion is proposed to include force demands based on a constrained Lagrangian dynamics and Lagrangian multipliers formulation. This allows the direct calculation of the inverse dynamics with both motion and force demands. A feedforward controller based on the proposed method is built to realise the cooperative control of two robots sharing a common load, with both motion and force demands. Furthermore, this thesis develops a method to design an optimal excitation trajectory for robot dynamic parameter estimation utilising the Schroeder Phased Harmonic Sequence. This method yields more precise and accurate inverse dynamics models, which result in better control. The proposed controller is then tested in an experimental set-up consisting of two robot manipulators and a common load. Results show that in general the proposed controller performs noticeably better position and force tracking, especially for higher speed motions, when compared to traditional hybrid position/force controllers.