To address the overturning stability of a mobile manipulator for nuclear power rebar binding in confined spaces, a dual-boundary parallel tip-over moment method was proposed. By reconstructing the tipping-over axis system to optimize the computational flow, the average calculation time decreases by 18.7% compared to traditional methods, satisfying the millisecond-level real-time control requirements. A statically and dynamically coupled dynamic model was formulated to analyze the influence mechanisms of inertial forces and gyroscopic moments on stability. A fuzzy proportional integral derivative(PID) controller was designed with joint angular accelerations as control variables, establishing a closed-loop feedback loop for the tipping-over moment. Simulation results indicate that under typical continuous operation conditions, the mean steady-state error converges to -0.51 N·m with a standard deviation of 0.26 N·m. Upon introducing an external step load disturbance, the maximum dynamic moment deviation decreases by 34% compared to fixed-gain PID control. Data verifies that this control strategy exhibits characteristics of suppressing moment fluctuations and expanding the system stability margin, providing a safety control reference for dynamic operations of mobile manipulators.