• A nonlinear disturbance observer (NDO) is designed to estimate disturbing forces and torques from caster wheels in P-AGVs, enhancing robustness.
• The proposed NDO-NTSM controller improves trajectory tracking stability by 42–68% compared to traditional NTSM, as validated experimentally.
• Kinematic and dynamic models of P-AGVs with mecanum wheels are developed, explicitly considering disturbance influences.
• Stability of the NDO and NDO-NTSM control systems is theoretically proven via Lyapunov functions, ensuring reliable performance.
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