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With a wheeled robot based on step motor drive for the study, Lyapunov direct method control algorithm is proposed through the establishment of a kinematic model. Then the dynamic model is established and the restriction strategy of speed and acceleration is used to limit the maximum speed and the maximum acceleration of the output from the kinematic model. Finally, the relationship between the speed and time is generated, which can better meet actual working conditions. The simulation results show that the control algorithm can adjust the trajectory error quickly, and there will be no speed mutation during the adjustment process. It can also track the desired trajectory steadily and react quickly when the trajectory changes. The pulse data generated by the control algorithm is compiled and downloaded to the STM32F407 microcontroller for experiment, without additional C code programming.