Solving Path Following Problem for Car-Like Robot in the Presence of Sliding Effect via LMI Formulation

One of the main problems of car-like robot is robust path following in the presence of sliding effect. To tackle this problem, a robust mix H2/H∞ static state feedback control method is selected. This method is the well-known linear robust controller which is robust against external disturbance as well as model uncertainty. In this paper, the path following problem is formulated as linear matrix inequality for the kinematic model of car-like robot, which includes sliding effect. The robustness and path following performance of the proposed controller are investigated based on the comparison of suggested controller with an optimal proportional integral controller. The simulation results, which have been performed by MATLAB Simulink, shows the presented controller is able to follow various paths including simple, linear and more complex function path like square, and sine function path even in the presence of sliding effect. In addition, the robustness and correctness of closed-loop system in the simulations are demonstrated based on the nonlinear analysis of equilibrium point.