In this article, a multi-underwater unmanned vehicle (UUV) maneuvering decision-making algorithm is proposed for a counter-game with a dynamic target scenario. The game is modeled with interval-valued intuitionistic fuzzy rules, and an optimal maneuvering strategy is realized using a fractional-order recurrent neural network (RNN). First, underwater environments with weak connectivity, underwater noise, and dynamic uncertainties are analyzed and incorporated into the interval-valued intuitionistic fuzzy set. Then, the maneuvering decision-making model and the expected return of the multi-UUV countermeasure are designed based on the interval-valued intuitionistic fuzzy rules. Subsequently, to optimize the counter-game maneuvering strategy, a fractional-order RNN is formulated based on the Karush–Kuhn–Tucker optimality conditions. In addition, the existence and uniqueness of the optimal maneuvering solutions as well as the stability of the equilibrium point are discussed. Finally, simulation and experimental results are compared to determine the effectiveness of the proposed algorithm. The influence of the fractional order on the convergence rate and optimization error of the proposed algorithm is also minutely examined.

In this work, we propose a method for AUV to reconstruct the docking ring autonomously under the guidance of visual information. The proposed method is based on the knowledge of self-reconfiguration of two AUVs in underwater environment. In order to enable long distance performance, we make use of blue-green light beacons. The light beacons are detected by using YOLO V3 algorithm. In addition, P4P algorithm is applied to resolve the problem of relative poses of AUVs. In case of short distances, we use Aruco marker to precisely guide the AUV towards the docking ring. In addition, we use KCF algorithm to shorten the recognition time, and Kalman filter method to eliminate the interference of occlusions and jitters. The feasibility of the proposed method is verified by performing multiple experiments. Under the reasonable control flow and visual algorithm, the proposed solution avoids the situation where the accuracy of long-distance monocular recognition is low and is easy to be misjudged. The underwater multi-target integrated guidance method based on monocular vision is convenient for the recovery of underwater AUV, and can effectively take into account the advantages of wide effective guidance range and high precision of close range guidance.

The instability of the underwater environment and underwater communication brings great challenges to the coordination and cooperation of the multi-Autonomous Underwater Vehicle (AUV). In this paper, a multi-AUV dynamic maneuver countermeasure algorithm is proposed based on the interval information game theory and fractional-order Differential Evolution (DE), in order to highlight the features of the underwater countermeasure. Firstly, an advantage function comprising the situation and energy efficiency advantages is proposed on account of the multi-AUV maneuver strategies. Then, the payoff matrix with interval information is established and the payment interval ranking is achieved based on relative entropy. Subsequently, the maneuver countermeasure model is presented along with the Nash equilibrium condition satisfying the interval information game. The fractional-order DE algorithm is applied for solving the established problem to determine the optimal strategy. Finally, the superiority of the proposed multi-AUV maneuver countermeasure algorithm is verified through an example.

Cooperative localization (CL) is considered a promising method for underwater localization with respect to multiple autonomous underwater vehicles (multi-AUVs). In this paper, we proposed a CL algorithm based on information entropy theory and the probability hypothesis density (PHD) filter, aiming to enhance the global localization accuracy of the follower. In the proposed framework, the follower carries lower cost navigation systems, whereas the leaders carry better ones. Meanwhile, the leaders acquire the followers’ observations, including both measurements and clutter. Then, the PHD filters are utilized on the leaders and the results are communicated to the followers. The followers then perform weighted summation based on all received messages and obtain a final positioning result. Based on the information entropy theory and the PHD filter, the follower is able to acquire a precise knowledge of its position.

To reduce the cooperative positioning error and improve the navigation accuracy, a single master–slave AUV cooperative navigation method is proposed in this paper, which mainly focuses on planning the optimal path of the master AUV by the time difference (TD) method, under the premise that the path of the slave AUV has been planned. First, the model of multi-AUV cooperative navigation is established, and the observable problem of the system is analyzed. Second, for the single master–slave AUV cooperative navigation system, a Markov decision process (MDP)-based multi-AUV cooperative navigation model is established, and the master AUV path planning method is designed based on the TD method. Finally, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) nonlinear filtering algorithms are applied to simulate and verify the algorithm that is proposed in this paper. The results show that the theoretical positioning error of the slave AUV can be controlled to about 3.2m by planning the path of the master AUV using the TD method. This method can not only reduce the observation error and positioning error of the slave AUV during the whole cooperative navigation process, but also keep the relative measurement distance between the master AUV and the slave AUV within an appropriate range.

In this paper, a trajectory tracking control algorithm is proposed based on the fractional-order PD (FOPD) controller for a Wheeled Mobile Robot (WMR). Firstly, an improved flat phase property is put forward as a robust controller tuning specification. This specification is capable of guaranteeing the flatness of the phase curve in a frequency interval, so the controlled system robustness can be improved. Then, the stabilization process is discussed with respect to the parameters of the FOPD controller through a visualized 3-dimensional surface, so both the stability and robustness of the controlled system can be guaranteed under the proposed controller. Furthermore, the implementation of the proposed robust FOPD controller is presented, which makes the control algorithm easy to be realized. At last, the effectiveness of the proposed trajectory tracking control algorithm is verified by the simulation and experiment results.