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Since Global Navigation Satellite systems are able to supply very accurate coordinates of a point (about 2 cm with a RTK GPS), such a sensor is very suitable to design vehicle guidance system. It is especially the case in agricultural tasks where a centimeter precision is often required (seeding, spraying,...). To answer to growing high precision agriculture principle demand, several control laws for automated vehicle guidance relying on this sensor have been developed. Such guidance systems are able to supply an acceptable steering accuracy as long as vehicle does not slide (path tracking on even ground with good adherence properties...), what alas inevitably occurs in agricultural tasks. Several principles are here presented to steer vehicle whatever properties of ground and path to be followed are. In this paper a new extended kinematic model with sliding accounted is presented which allows describing vehicle dynamics in all guidance conditions. Via this model a new nonlinear control law can be designed, which integrates sliding effects. Its capabilities are investigated through simulations and experimental tests.