Step-crossing control of two-wheeled transporter based on Takagi-Sugeno approach: Comparison between state and descriptor form

In this paper, a new control design for a two-wheeled self-balanced mobile robot (TWMR) is considered. The aim is to propose a strategy for a controlled and safe crossing step in order to extend the use of TWMR by disabled persons. The crossing step problem is formulated as a stabilisation problem of an Acrobot which is a two-link robot analogous to gymnast swinging on a high bar. The dynamic model is given in the quasi-LPV formulation, through the so-called Takagi-Sugeno (TS) fuzzy model. Based on the stabilization conditions of Lyapunov and derived into Linear Matrix Inequalities (LMIs), two different approaches are compared. The first one involves the state-space representation which is the widely used model for designing controller. The second approach involves the natural descriptor form inherited from mechanical modeling and then leads to a natural way to describe a mechanical system with time varying-inertia. The purpose of this comparison is to show the interest of keeping the natural descriptor form of the mechanical systems for the synthesis of TS-based controllers.