in this paper the second version of the omnidirectional mobile robot with steerable omnidirectional wheels (OMR-SOW) is presented. This robot can operate in either the omnidirectional or the differential drive mode depending on the drive conditions. in the omnidirectional mode, it has 3 DOFs in motion and 1 DOF in steering which can function as a continuously-variable transmission (CVT). The CVT function can be used to enhance energy efficiency of the robot operation by increasing the range of velocity ratio of the robot velocity to wheel velocity. Kinematics and dynamics of this robot are examined. in the proposed steering algorithm, the steering angle is controlled so that motors may operate in the region of high velocity and low torque, thus generating the maximum energy efficiency. Various tests show that motion control of the OMR-SOW works satisfactorily and the proposed steering algorithm for CVT can provide higher energy efficiency than the algorithm using a fixed steering angle. in addition, it is shown that the differential drive mode can give better energy efficiency the omnidirectional drive mode.