Simulation-Based Analysis of a Linear Switched System Based on Human Arm’s Dynamics

Abstract

The article outlines the process of developing a mathematical model of the human arm. The model arm consists of two joints connected by the rotational link. Each of them is represented as a truncated cone prism which changes its shape during motion. The shape change instant depends on the two-state coordinates being the angular displacements q1 and q2. Based on the analysis of the arm motion a mathematical model is proposed. The design process is made on the basis of switched systems theory. We present a transition from the general equation of a two-link arm’s dynamics to the state equation for stationary linear models. Based on previous step a mathematical model is presented as a switched linear system. The article also shows that the dependency of the switching rule on the two components of the state vector.