Robust Control for a Planar Parallel (3-PPR) Manipulator based on Udwadia-Kalaba Theory

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.