Abstract: Nonholonomicity arises in many mechanical systems subjected to nonintegrable velocity constraints or nonintegrable conservation laws. Due to nonholonomic constraints, the motion planning and control of a nonholonomic mutilbody system is much more difficult than that of a conventional system. Nonholonomic characteristic and controllable condition are investigated using the infinite dimension optimization and the control theory, regarding the system's dissipation energy as a target function and considering the nonholonomic characteristic, a numerical method for the nonholonmic motion planning without drift is proposed. The effectiveness of the numerical algorithm is demonstrated by numerical simulation.