This paper presents the model predictive control of Hilare-type robot on a slippery 3D terrain having known ground conditions, while avoiding wheel slip. The controller is developed based on the dynamic model of the Hilare-type robot on a 3D terrain. So, the terrain's gradient appears in the dynamic model, and is fedback in real-time for more precise trajectory tracking. Nonlinear model predictive control incorporates constraints such as maximum affordable longitudinal and lateral wheels static friction, to avoid slip and control input saturation. The Hilare-type robot is simulated while moving on a slippery hill with known static friction. The simulation exhibits accurate trajectory tracking of the autonomous mobile robot on a slippery 3D terrain having known surface conditions, while eliminating wheel slip.