The significant advantage of ground mobile robots (GMRs) is their accessibility to areas that are inaccessible for humans. One difficulty of current GMR technology is that the external driving mechanisms, such as wheel, track, and leg, restrict its applications. In order to solve this limitation, the present paper proposes a novel driving mechanism using a novel GMR called the double-pendulum driven cart (DPDC). The DPDC, which employs only internal thrust and static friction, is capable of steering by two parallel pendulums mounted on the cart, and is able to implement planar elemental motions by designing the pendulum trajectory properly. The paper first studies the dynamic modelling and the motion control issues of the DPDC. A closed-loop controller using the partial feedback linearization technique is then designed for the tracking control of the parallel pendulums to guarantee accurate motion of the cart. Extensive simulation results verify the proposed model and the efficiency of the motion control strategy.