# Navigation Control and Signal Processing Methods for Multiple Autonomous Unmanned Systems
###### Abstract  
The proposed method for solving the joint problem of multi-agent systems with a  
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From the above analysis, it can be seen that it is easy to be influenced by external disturbances to the nonlinearity characteristics, which brings obvious challenges to the controller design process [39; 40; 41]. To ensure the reliable operation of an AUV, it is crucial to model disturbances accurately and account for their effects. DO has gained widespread popularity in the field of control due to its superior performance in estimating uncertainties [42; 43]. A DO was developed in [44] to assess the influence of disturbances while optimizing communication resource consumption, and intermittent measurement-based uncertainty was also considered, while the converge speed of estimation errors was ignored. In [45], a novel finite-time DO was proposed, but the upper bound of the convergence time is unknown. In [46], a fixed-time DO was proposed to determine the disturbance, and it was shown that the estimation errors can reach the zero domain within the settling time. An observer-based fixed-time sliding mode control (SMC) was proposed in [47], where a weak chattering DO was designed to estimate uncertainties within a fixed time. However, in most previous works, the upper bound of the disturbance is assumed to be known [48], which is not reasonable under specific conditions. By integrating the DO with the formation controller, this paper proposes a novel approach for underactuated AUV formation control. Formation control strategies play a pivotal role in the field of unmanned systems, providing theoretical and practical frameworks for coordination and collaboration among multiple unmanned vehicles. Presently, most existing formation control strategies can be roughly categorized into leader-follower, behavior-based, virtual structure, graph theory-based, artificial potential function, and visually based strategies [49]. Among these, the \"leader-follower\" strategy stands out as one of the most often used and fundamental approaches in formation control. Under this strategy, one or more unmanned vehicles are designated as the leader, whose trajectory serves as a reference for other followers. The leader's movements determine the overall shape and behavior of the formation. Communication and mutual perception between the leader and followers are crucial in maintaining tight coordination within the formation. The primary challenges associated with controlling underactuated AUV systems can be broadly categorized into three groups [50]. Firstly, in the existing literature [51; 52], to simplify the process of controller design, the mass and damping matrices in underactuated AUV models are assumed to be diagonal, while this kind of model cannot reflect the actual conditions due to the inherent lack of symmetry between the bow and stern of the AUV. To overcome this limitation, ref. [53] introduced a coordinate transformation of the design controller. This conventional control design for such models often involves introducing a coordinate transformation which can transform ship dynamics to a \"diagonal form\" before addressing the coupling effects between the position and velocity variables, which can be cumbersome and time-consuming. Secondly, it is observed that the majority of existing formation control schemes, employing the leader-follower method, rely on velocity information from the leader [54; 55]. However, in practical scenarios, measuring the velocity of the leader is challenging for followers due to noise contamination and communication delays. As a result, a more practical and constructive approach for formation control is to rely solely on measurements of positions and orientations, eliminating the need for velocity information [56; 57]. Thirdly, an essential performance criterion for formation control is the converge speed.