We have presented a method to estimate on-line the changes in road condition. To achieve this goal we have introduced dynamical friction models that, one hand provide a more accurate description of the contact friction, and one the other hand, allow us to characterize road condition variations via a single parameter.
It has been shown that the distributed parameter version of these model also capture stationary shape profiles between normalized friction and slip rate that are similar to the ones obtained from experimental data (i.e. magic formula).
We have introduced a model-base observer that ensure asymptotic tracking of road condition, under mild conditions implying a non-vanishing evolution of the slip rate. This condition are quite natural in this context (they imply that the vehicle should operate away to the ideal pure rolling condition). Mathematically, this condition correspond to the persistently excitation condition, which is well known in the adaptive control literature. In the context of nonlinear observers, this condition appear as being the characterization of “good” inputs, which are required to recover state observability.
The observer presented here has been derived in a general framework allowing to extend our study to the case where the vehicle velocity is not measurable. In particular, assumption A2 — (ii) will allows for this extension, if it can be shown that the assumption A3, also holds. This study and the introduction of other factors like: wheel vertical deformation, and suspension dynamics, are currently under study.