Higher-order sliding mode observer for estimation of tyre friction in ground vehicles

The estimation of friction coefficient for a vehicle when it traverses on different surfaces has been an important issue. In this work, the longitudinal vehicle dynamics, the torsional tyre dynamics and the non-linear LuGre friction dynamics are integrated to model the quarter vehicle dynamics. The road adhesion coefficient in the vehicle dynamics is unknown and varies with the contact surface. To address this issue, the authors consider a class of non-linear uncertain systems that covers the vehicle dynamics and develop a higher-order sliding mode observer based on supertwisting algorithm for state and unknown input estimations. Under Lipschitz conditions for the non-linear functions, the convergence of the estimation error is established. By estimating the road adhesion coefficient, the coefficient of friction can be estimated. Simulation results demonstrate the effectiveness of the proposed observer for state and unknown input estimation.