This paper presents the study of both steering and speed control algorithms of an off-road mobile robot in order to accurately guide, forward or backward, the position of its trailer with respect to a planned trajectory, whatever ground conditions and trajectory shape. The proposed algorithms are based on an extended kinematic model of the system, accounting for sliding effects with additional sliding parameters. An observer is developed to obtain a relevant on-line estimation of these parameters. An original steering control algorithm is then proposed, considering the implement as an independent virtual vehicle: A first control law calculates the direction of the linear velocity vector at the hitch point that would ensure the convergence of this virtual vehicle to the planned trajectory. Next, a reference angle between the tractor and the implement leading to such a velocity vector is inferred, and finally a second control law is designed to stabilize the actual tractor implement angle on this reference angle. The capabilities of the proposed algorithms are investigated through full-scale experiments.