Aiming to address the challenges of high labor intensity and significant labor costs in feed delivery within recirculating aquaculture systems, an automatic feeding robot was designed. Furthermore, a physics-informed neural network based model predictive control (PINN-MPC) method was proposed to tackle the autonomous path tracking problem under variable payloads and slippery road conditions. Firstly, the overall robot architecture and path planning control scheme were designed. Secondly, a control model was established for the robot under variable payloads and complex environment. Subsequently, building upon the traditional MPC framework, the proposed method treated key physical parameters as time-varying factors, and a multi-layer feedforward neural network was employed to predict these parameters online, enhancing control precision. Finally, the effectiveness of the control algorithm was validated through simulations and field experiments. In the single-tank feeding experiment, the average tracking errors of the PINN-MPC at two key observation points were 0.12m and 0.18m, representing a 50% reduction compared with MPC. The longitudinal velocity fluctuation was half of that of MPC, and the standard deviation of lateral deviation was decreased by 58.3%. In the multi-tank feeding experiment, PINN-MPC maintained the average path error between the nine target points within 0.050~0.055m, reduced lateral tire force fluctuation by 58.9%.