This paper studies the high performance robust motion control of electro-hydraulic servo-systems driven by double-rod hydraulic actuators. The dynamics of hydraulic systems are highly non-linear and the system may be subjected to non-smooth and discontinuous non-linearities due to directional change of valve opening, friction and valve overlap. Aside from the non-linear nature of hydraulic dynamics, hydraulic servosystems also have large extent of model uncertainties. To address these challenging issues, the recently proposed adaptive robust control (ARC) is applied and a discontinuous projection based ARC controller is constructed. The resulting controller is able to take into account the effect of the parameter variations of the inertia load and the cylinder hydraulic parameters as well as the uncertain non-linearities such as the uncompensated friction forces and external disturbances. Non-differentiability of the inherent non-linearities associated with hydraulic dynamics is carefully examined and addressing strategies are provided. Compared with previously proposed ARC controller, the controller in the paper has a more robust parameter adaptation process and may be more suitable for implementation. Finally, the controller guarantees a prescribed transient performance and final tracking accuracy in the presence of both parametric uncertainties and uncertain non-linearities while achieving asymptotic tracking in the presence of parametric uncertainties.