State-feedback control of robot manipulators using polytopic LPV modelling with fuzzy-clustering

Abstract

This paper proposes a new algorithm to full state systematic feedback control design for robot manipulators based on fuzzy-clustered polytopic model. At first, a linear parameter varying (LPV) representation of the system is generated via linearization of usual Lagrangian equation about a desired state trajectory and a vector of scheduling signals from the desired trajectory information is produced to construct an initial polytopic model. Then a fuzzy-clustering algorithm is introduced to categorize the vertices of the initial polytopic model in several clusters such that a sufficient condition of asymptotic stability of the closed loop models in each cluster is satisfied. Hence, the number of vertices is reduced to the number of clusters and a new reduced polytopic model is generated with the representative models of the clusters. The proposed algorithm is applied to control of a two-degree-of-freedom (DOF) robotic manipulator that illustrates the validity of the proposed scheme. Keywords: Fuzzy clustering, Linear matrix inequality, Polytopic models, Robot control