1. A control device for a mobile robot which has a plurality of links interconnected through joints and actuators for driving the joints and in which a power transmitting system located between each joint and each actuator is provided with a spring member which converts the power generated by the actuator into an elastic force and imparts the elastic force to the joint, the control device comprising: a motion state amount desired value determining processor which determines a motion state amount desired value, which is a desired value related to a predetermined type of motion state amount of the mobile robot which has a value dependent on the value of a generalized variable vector of the mobile robot, the vector including the following components: the displacement amount of each joint of the mobile robot and the position and the posture of a predetermined representative link of the mobile robot on a global coordinate system; a desired driving force determining processor which receives the determined motion state amount desired value and determines a desired driving force to be imparted to each joint of the mobile robot by carrying out processing of inverse dynamics calculation, using at least the motion state amount desired value; and an actuator control processor which controls the operation of the actuator on the basis of at least the determined desired driving force, wherein the motion state amount desired value includes at least a desired value of a vertical component of a first-order differential value of a total translational momentum of the mobile robot, and the motion state amount desired value determining processor determines the desired value of the vertical component of the first-order differential value of the translational momentum such that the observed value of the vertical position of an overall center-of-gravity point of the mobile robot is converged to a predetermined desired value according to a feedback control law.