Dynamic Modeling and Sliding Mode Control of a 2-DOF Spherical Parallel Mechanism With a Passive Branch

This paper presents a dynamic analysis and a sliding mode control approach for high speed tracking control of a 2-DOF spherical parallel mechanism with a redundant branch. The kinematics of this mechanism is briefly introduced, two of three branches are actuated and the rest one is a passive branch. The dynamic model is built based on Lagrange method and simplified to develop a real-time controller. The control scheme is designed given that only the angle and angular velocity of actuators are measureable. First a Quasi-sliding mode control algorithm is proposed to compensate the parameter perturbation and reduce the chattering phenomenon, and then the trending law is introduced to decrease the regulation time of tracking control. Lyapunov theory is performed to guarantee that the controller design is stable. Finally, experiment based on a prototype of SPM is carried out to verify the effectiveness of the proposed method.