Unmanned ground vehicles designed for exploring unstructured unknown environments usually move at very low speed because they can encounter different types of obstacles. For some tasks, however, they need to move faster, which increases the risk of tipping over and taking off the ground. This paper compares a new suspension, build with both vertical and longitudinal dampers (Susp-4D), to a classical vertical-only damping suspension (Susp-3D) through geometric and kinematic models, and experimental tests. The rover equipped with Susp-4D endured a lower deceleration from the shock with the obstacle, and lost less speed and less kinetic energy. The vehicle with Susp-4D did not pitch down against the obstacle, but rather pitched up, which should allow it to cross any obstacle easier than with a classical suspension.