S1 File -

An in-depth study on the fixed-time event-triggered obstacle avoidance consensus control in heterogeneous USV-AUV systems with input delay and uncertain disturbances are conducted in this paper. When initial state of the system fails to achieve consensus, the desired heterogeneous USV-AUV formation can be achieved by fixed-time consensus control, within a fixed predetermined time, regardless of the initial states. Besides, an event-triggered communication strategy among the agents is introduced in the system, significantly reducing communication energy consumption. By employing the proposed control strategy, the Zeno behavior also can be avoided. Additionally, an obstacle avoidance control algorithm for the heterogeneous USV-AUV system based on improved artificial potential fields (IAPF) is designed, which helps in avoiding both static and dynamic obstacles. Compared to existing research, this algorithm reduces control input jitter, resulting in smoother obstacle avoidance paths. Through extensive simulation experiments and comparisons with other methods, effectiveness and superiority of the proposed algorithm is validated.