An adaptive control scheme for emergency braking of vehicles is designed based on a LuGre dynamic model for the tire-road friction. The wheel angular speed and longitudinal vehicle acceleration information are used to design a fast convergence observer to estimate the vehicle velocity and the internal state of the friction model. The unknown parameters of the dynamic friction model are estimated through a parameter adaptation law. A Lyapunov-based state estimator and a stabilizing braking controller are designed to achieve near to maximum braking capability of the vehicle. Underestimation of the maximum friction coefficient, a very desirable feature from the perspective of safety, is guaranteed by a proper choice of adaptation gains and initial values of the estimated friction parameters.
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Álvarez et al. (2004) studied this question.
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