In order to solve the problem of assembly position deviation caused by external stress interference during the working process of the robotic arm, a monitoring system based on a combination of multiple fiber optic grating sensors is designed in this paper. Based on the range of motion angles of the robotic arm, the stress field distribution characteristics of the outer and inner robotic arms are simulated and analyzed after applying stress in different directions at two characteristic positions. Based on the distribution characteristics of the stress field, a multi-FBG sensing array is designed, and the corresponding relationship between different FBG responses and external interference stresses is calculated. The experiment used 16 FBGs for online monitoring of the gripping process of the FS-MP1C small machinery, with a random external interference stress set to 2~20 N. The response linearity of 16FBGs is above 0.99, with maximum positive and negative wavelength responses of 1354 pm and -984 pm, respectively. In 100 layered interference tests, the detection rate of X-axis and Y-axis interference stress is better than 80.0%, and the detection rate of Z-axis interference stress is better than 97.5%. The average false detection rate of the system is less than 4.0%. It can be seen that this design can achieve real-time monitoring of external interference stress online, which has certain practical value.