Computed Torque Control of the Stewart platform with uncertainty for lower extremity robotic rehabilitation

Abstract

Parallel manipulators play a key role in robotic rehabilitation. In reality, such systems operate under uncertainty due to the changes in the characteristics of the patients and lack of knowledge about the physical and geometrical properties of the system. In this paper, we present a robust control scheme to control a six-degree-of-freedom Stewart platform. In this application, it is aimed to follow a desired pure rotational motion required in the robotic rehabilitation of the foot for patients with diabetic neuropathy. It is assumed that uncertainty exists in the mass of the foot of the patients (the proposed approach can also be used when disturbance exists). To perform this, the method of polynomial chaos expansion (PCE) is extended and integrated with the computed torque control law (CTCL) to control the system. In PCE scheme, uncertainty is introduced to the system by compactly projecting each stochastic response output and random input onto the space of appropriate independent orthogonal polynomial basis functions. CTCL uses a feedback linearization technique which provides the necessary force/torque to enforce the system to follow a prescribed trajectory. This papers presents a successful implementation of the PCE-base CTCL on a Stewart platform. Finally, a comparison between the efficiency and accuracy of the Monte Carlo and PCE is conducted.