Representing the model of impedance controlled robot interaction with feedback delay in polytopic LPV form: TP model transformation based approach

Abstract

The aim of this paper is to transform the model of the impedance controlled robot interaction with feedback delay to a Tensor Product (TP) type polytopic LPV model whereupon Linear Matrix Inequality (LMI) based control design can be immediately executed. The paper proves that the impedance model can be exactly represented by a finite element TP type polytopic model under certain constrains. The paper also determines various further TP models with different advantages for control design. First, it derives the exact Higher Order Singular Value Decomposition (HOSVD) based canonical form, then it performs complexity trade-off to yield a model with less number of components but rather effective for LMI design. Then the paper presents various different types of convex TP model representations based on the non-exact model in order to investigate how convex hull manipulation can be performed on the model. Finally the presented models are analyzed to validate the accuracy of the transformation and the resulting TP type polytopic LPV models. The paper concludes that these prepared models are ready for convex hull manipulation and LMI based control design.