Chemical plant inspection robots play a crucial role in industrial production. They can efficiently conduct inspections in hazardous or unsuitable chemical environments for direct human operation, monitor equipment status and environmental parameters in real time, ensure production safety. However, the chemical plant inspection robot is often affected by uncertainties such as external interference and load changes. Due to the influence of these uncertain factors, the expected trajectory tracking cannot be achieved when executing the trajectory tracking task. To address this issue, an adaptive robust control method based on Udwadia Kalaba (U-K) theory is proposed in this study, the constraint problem at the kinematic level is transformed into the trajectory tracking problem at the dynamic level. Firstly, the dynamic model of the chemical plant inspection robot is established. Secondly, an adaptive robust controller is proposed. Thirdly, its stability is verified by the Lyapunov method. Finally, the simulation experiment is carried out to demonstrate it. Compared with the traditional PID control method, the effectiveness and superiority of the proposed control method are verified.