This paper presents the design, implementation and validation of the three-wheel holonomic motion system of a mobile robot designed to operate in homes. The holonomic motion system is described in terms of mechanical design and electronic control. The paper analyzes the kinematics of the motion system and validates the estimation of the trajectory comparing the displacement estimated with the internal odometry of the motors and the displacement estimated with a SLAM procedure based on LIDAR information. Results obtained in different experiments have shown a difference on less than 30 mm between the position estimated with the SLAM and odometry, and a difference in the angular orientation of the mobile robot lower than 5° in absolute displacements up to 1000 mm.