Nonlinear vehicle side-slip estimation with friction adaptation

Nonlinear Observer for Vehicle Velocity with Friction and Road Bank Angle Adaptation - Validation and Comparison with an Extended Kalman Filter

“…where K vy , K r , Γ 1 and Γ 2 are positive gains, Λ is a (possibly time-varying, state-dependent) positive scaling factor, and ξ and ζ can be interpreted as partial derivatives of f y and f r with respect to v y (evaluated using the estimated states, see [6] for details). The friction forces on wheel i (in the wheel coordinate system) are calculated via a friction model,…”

“…Fortunately, most of the uncertainty in the friction model can be lumped into one parameter denoted µ H (the maximum tire-road friction coefficient), which can be said to characterize the road surface; from µ H ≈ 0.1 on wet ice to µ H ≈ 1.0 on dry asphalt. Based on a friction model parameterized in µ H , the above observer can be extended with adaptation of µ H , using the techniques in [7,6].…”

“…, based on the estimated state variables and the measurements, and an estimate of the maximum friction coefficient, µ H (see below and [7,6]). Based on this,f y =…”

“…The implemented observer can be described by a number of ordinary differential equations derived using nonlinear observer theory [12,11,7,6] based on the dynamic model of the vehicle and the friction model. The sensors used are three-axis accelerometers (a x , a y and a z ) in addition to yaw rate r (angular rate about vertical axis).…”

“…This is an overall velocity observer with adaptation of the maximum friction coefficient and the road bank angle. The detailed development of the different parts of the observer is described in [12,11,7,6,10], * Also affiliated with NTNU, Department of Engineering Cybernetics, N-7491 Trondheim, Norway and will be briefly summarized herein. Furthermore, we want to assess, to a certain degree, its performance in terms of accuracy and robustness, tuning, and computational complexity, in comparison with the EKF [19] applied to the same problem.…”