Abstract: Aiming at the balancing control problem of a cubical robot, a system balancing on its corner was modeled by taking the physical prototype as research object, and least system variables were defined for expressing system movement attributes. The energy function and generalized forces of the system were calculated, and the dynamic model of the cubical robot balancing on its corner was derived based on Lagrange method. The correctness of the model was analyzed in theory by numerical simulation, and the model precision was verified with basically indetical response results about zero-input experiment in comparision betweeen the model and virtual prototype. A balancing controller designed based on the dynamic model was applied in balancing control of the virtual prototype. The experiment results show that the cubical robot can balance effectively by the controller, then the effectiveness of the model is verified further. The dynamic model provides an important foundation for the further research on balancing control of the cubical robot.