In this thesis, a new approach is presented for the modelling and control of an automated polishing/deburring process that utilizes a dual-purpose complaint toolhead mounted on a parallel tripod robot. This toolhead has a pneumatic spindle that can be extended and retracted by three pneumatic actuators to provide tool compliance. By integrating a pressure sensor and a linear encoder, this toolhead can be used for polishing and deburring. For the polishing open-loop control, the desired tool pressure is pre-planned based on the given part geometry. To improve control performance, a closed-loop controller is applied for pressure tracking through pressure sensing. For the deburring control, another closed-loop controller is applied to regulate the tool length through tool extension sensing. The two control methods have been tested and implemented on a polishing/deburring robot, and the experiment results demonstrate the effectiveness of the presented methods.To future improve the control performance, an adaptive controller is developed to deal with the uncertainties in the compliant tool. This control method combines the adaptive control theory with the constant stress theory of the contact model. A recursive last squares (RLS) estimator is developed to estimate the pneumatic plant model, and then a minimum-degree pole placement (MDPP) is applied to design a self-tuning controller. Afterwards, the simulation and experiment results of the proposed controller are presented and discussed. Finally, a nonlinear model of the pneumatic plant is developed. The nonlinear controller developed by using feedback linearization method is applied on the nonlinear pneumatic system of the compliant toolhead. The simulation is carried out to test the effectiveness of the pressure tracking for the polishing process.