Ground potential work robots equipped with dexterous arms can be used to replace manual overhead power distribution operations, but there are still many challenges in the load and control stability of the dexterous arms of ground potential work robots. In order to solve the problems of control stability of the dexterous arm of the geopotential work robot, an adaptive PD control method of the dexterous arm equipped with a gravity balance mechanism is proposed. Firstly, by establishing and analysing the dexterous arm model, the gravity compensation device is set in the first two sections of the dexterous arm. Secondly, the controller model is designed and a Lyapunov function is defined to prove the asymptotic stability of the closed-loop system. Thirdly, the adaptive control architecture of the dexterous arm of the ground potential energisation robot is constructed in MATLAB to test the ability of the controller to suppress the load perturbation, and finally, the effectiveness of the methodology of this paper is verified by integrating and analysing the data of the PD control step-signal response velocity and the gravity-balance-based adaptive PD control step-signal response velocity.