Granular terrains, such as those found in desert and extraterrestrial environments, present unique challenges for mobile robots due to high resistance, unpredictable slip, and lift-induced instability. This paper introduces a vibration-driven robot powered by dual eccentric motors and enhanced by a novel nonlinear spring-damper structure. The proposed design enables whole-body motion through periodic inertial forces, allowing the robot to move without external actuators, wheels, or limbs. Experimental results demonstrate that the robot achieves stable and efficient locomotion across varying granular substrates, including fine sand, coarse sand, and inclined slopes. The addition of lateral spring-damper assemblies significantly reduces lateral drift and enhances straight-line stability. Obstacle avoidance tests confirm the robot’s high maneuverability, while slope-climbing experiments reveal performance constraints due to terrain collapse. Overall, the robot’s compact, enclosed design, combined with its vibration-based actuation strategy, offers a promising solution for navigating unstructured and deformable terrains in planetary exploration and disaster response scenarios.