The general design of the wheeled vibration-driven robot is developed in the SolidWorks software on the basis of the double-mass semidefinite oscillatory system. The idea of implementing the vibro-impact working regimes of the internal (disturbing) body is considered. The corresponding mathematical model describing the robot motion conditions is derived using the Euler–Lagrange equations. The numerical modeling is carried out by solving the obtained system of differential equations with the help of the Runge-Kutta methods in the Mathematica software. The computer simulation of the robot motion is conducted in the MapleSim and SolidWorks software under different robot’s design parameters and friction conditions. The experimental prototype of the wheeled vibration-driven robot is developed in the Vibroengineering Laboratory of Lviv Polytechnic National University. The corresponding experimental investigations are carried out in order to verify the correctness of the obtained results of the numerical modeling and computer simulation. All the results are presented in the form of time dependencies of the robot’s basic kinematic characteristics: displacements, velocities, accelerations of the wheeled platform and disturbing body. The influence of the impact gap value on the average translational speed of the robot’s wheeled platform is studied, and the corresponding recommendations for designers and researchers of the similar robotic systems are stated. The prospective directions of further investigations on the subject of the present paper and on similar vibration-driven locomotion systems are considered.