Abstract: For the wheeled robot swarm systems with external random disturbances, we design a distributed model predictive control (DMPC) method based on event triggering mechanism. Firstly, we introduce a robust constraint to handle external disturbances. Secondly, we design a two-stage differential event triggering mechanism that adaptively adjusts the sampling frequency to balance computational and sensing costs. Thirdly, we develop a dual-mode DMPC algorithm to further reduce computational and communication consumption, and ensure the feasibility of the proposed algorithm, closed-loop system stability and the Zeno-free behaviour through theoretical analysis. Finally, the simulation experiments on wheeled robot systems show that compared to traditional event-triggered DMPC, the proposed algorithm can reduce the controller's computational resource consumption by 85.7% while ensuring the desired control performance.