When performing robotic electrical work, the mechanical arm will come into contact with wires, bolts, and gold tools. In order to prevent the robot from being shocked or vibrating excessively during this process, as well as to accurately control the screwing bolt angle issue, the robot force control issue should be taken into account. Based on the theory of higher order sliding mode control for such non-linear systems, a differential observer-based higher order sliding mode control method is proposed in this study. In order to build a type of controller based on the differential observer, the differential observer is used to observe the information of the derivative of the angular velocity and the information of the derivative order sliding variables of the higher-order sliding mode. The outcomes demonstrate the control method’s applicability to powered robots, as well as its ability to successfully suppress the jitter issue associated with conventional sliding mode control and achieve good control performance.