PurposeIn the high-altitude, high-voltage electromagnetic interference operation environment, due to the parameters perturbation for robot control model caused by uncertainties and disturbances, and with the poor effective of the conventional proportional–integral–derivative (PID) control to parameters perturbation system, the mathematical model of power cable live operation robot joint PID closed-loop control system is established.Design/methodology/approachThe corresponding joint motion robust PID control method is also proposed based on Kharitonov theory, the system robust stability conditions including the sufficient and necessary conditions are deduced and obtained and the solving process of robust PID control parameters stability region is provided.FindingsFinally, the simulation research on robot joint motion PID control system is also launched in MATLAB environment based on Kharitonov theory. The results show that the conventional PID control obtains better control effect only to nominal model but is ineffective to parameter perturbation system, while robust PID obtains sound control effect to parameter perturbation system. Compared with H8 robust PID, the Kharitonov robust PID has better control effect which meet the system design requirements of joint motor quickly response, high tracking accuracy and sound stability. Finally, the validity and engineering practicability are verified by 220-kV living replacing damper operation experiment.Originality/valueThis paper has described the development of a damper replacement power cable live maintenance robot experimental prototype, which greatly improves operation efficiency and deals with the safety problem of operation in a high-voltage environment. A general manipulator motion control model of the power cable robot is established; the Kharitonov theory-based parameter perturbation robust motion control method of damper replacement robot is also obtained. Through the simulation comparison, it is verified that the Kharitonov control has more superiority for dealing with the parameter perturbation systems under the premise of ensuring the stability motion. The field experiment has further confirmed the engineering practicability.