Currently, there is considerable interest in the principles of locomotion driven by vibrations, particularly in the field of mobile robotics. Among the various types of robotic chasses, wheeled ones are the most commonly utilized. The primary objective of this research is to define the dynamic and force characteristics of a wheeled vibratory robot driven by an imbalanced rotor (centrifugal exciter) and equipped with overrunning clutches providing one-way rotation of the robot’s wheels. The latter allows the robot to move in a single direction. The research methodology contains several main stages: developing the dynamic diagram of the robot’s mechanical system and deducing the locomotion equations; modeling (simulation) of the robot’s dynamic behavior in Mathematica software under specific operational conditions; creating the 3D design of the wheeled platform in SolidWorks software; and finally, constructing the laboratory prototype of the vibration-driven robot and carrying out the full-scale experimental investigations. The obtained outcomes illustrate the time dependencies of the platform’s speed, displacement, and consumed power under specific operating conditions. The primary scientific contribution of this research is establishing the relationships between the parameters of the platform’s mechanical system and its dynamic and force characteristics at specific operating conditions. The investigations can be valuable for designers and researchers who work on mobile vibration-driven robotic vehicles, capsule-type robots, pipeline cleaning systems, vessel inspection devices, and similar applications. Further research on the considered topic may be focused on optimizing the excitation conditions to maximize the average locomotion velocity and minimize the power consumption.