In this study, the problem of time-optimal trans-media maneuver trajectory design for the morphing unmanned aerial-underwater vehicles (MUAUVs) is considered. A the three-degree MUAVU dynamic model to plan the optimal flight and navigation trajectory is established. To solve the trajectory optimization model, the improved Radau pseudospectral method (RPM) is used to transform the optimal control model into a nonlinear programming problem (NLP). A double-layer hybrid solver based on the improved grey wolf algorithm and sequential quadratic programming (IGWO-SQP) is designed to solve the NLP under complex constraints. The outer layer employs an improved grey wolf optimization algorithm based on scouting strategy and the inner layer adopts a gradient-based SQP algorithm, which overcomes the disadvantage of sensitive initial value of traditional algorithm. The simulation results demonstrated that the proposed method is effective and feasible to solve the trajectory optimization of MUAUVs. A comparative study between air-water and water-air trans-media optimal trajectory verifies the proposed method which is usually applied to the aircraft is feasible to solve the underwater navigation trajectory of the MUAUV.

A well-planned dive trajectory is the key for the trans-media maneuver and flight control of morphing unmanned aerial-underwater vehicles (MUAUVs). The main focus of this paper is the application of a watch-based multi-objective grey wolf optimizer (MOGWO) to dive trajectory optimization problems. A multi-objective trajectory optimization model considering the change of sweep angle and static moment is developed and parameterized by the Gauss pseudospectral method, and a multi-objective nonlinear programming problem is constructed. To overcome the defect that, in the MOGWO, the rest wolves blindly follow the best wolves, the watch strategy is introduced, which provides the wolves with the ability of independent exploration. Subsequently, the watch-based MOGWO is employed to generate the Pareto front, which is compared with that obtained through other multi-objective techniques. The simulation results demonstrated that the proposed method is more reliable and can obtain more widely distributed non-dominated solutions, indicating that the watch-based MOGWO is effective and feasible in dealing with multi-objective trajectory optimization problems with complex constraints. In addition, comparative studies on optimal trajectories demonstrated that the maneuverability and gliding ability of the MUAUV are improved through cooperation between the angle-of-attack, bank angle, and sweep angle.

A trans-media aerial underwater vehicle (TMAUV) could break through the single-medium limitation with the abilities to fly in the air, navigate underwater, and cross the air–water surface repeatedly. This paper researches on the air–water trans-media trajectory, including the water entry and exit trajectories, for slender TMAUVs. A longitudinal dynamic model is developed for the air–water trans-media process under low-speed condition. In this condition, the vehicle is assumed to be fully wetted and the water surface is assumed to be kept flat. A novel estimation for the fluid force is proposed for the immersed part of the vehicle, with angular velocity and angle of attack taken into consideration. Added mass and its derivatives are calculated by the cross-sectional method based on the slender body theory. To verify the feasibility and effectiveness of the model, water entry experiments of a slender projectile with a length of 2000 mm are performed with ground and underwater high-speed cameras. Simulations and experimental results show similar trends, as indicated by the comparisons. Furthermore, the proposed model is compared with computational fluid dynamics method simulating water entry and exit processes. Simulation results present good agreement with experimental results. On the basis of the results, the proposed model could be used to predict the water entry and exit trajectories with different initial conditions.

Fuzzy information is generally represented by fuzzy set (FS). Pythagorean fuzzy set (PFS), as a new extension of FS, can represent fuzzy information more effectively. The accuracy of fuzzy information represented by PFS directly affects the result of information processing. Generalized parameter (GP), expressed by Pythagorean fuzzy number, can judge the accuracy of fuzzy information represented by PFS. However, for complex fuzzy application problems, a single GP cannot comprehensively judge the fuzzy information, and the GP may also be wrong. Therefore, the concept of group generalized parameters (GGPs) is proposed. The GGPs can comprehensively judge the accuracy of fuzzy information, and can avoid the influence caused by the error of a certain GP. In order to effectively aggregate the fuzzy information and the GGPs, some new group generalized Pythagorean fuzzy aggregation operators are proposed, including group generalized Pythagorean fuzzy weighted average (GGPFWA) operator and group generalized Pythagorean fuzzy weighted geometric (GGPFWG) operator. The definitions, theorems and properties of GGPFWA operator and GGPFWG operator are given and proved. In this paper, GGPFWA operator and GGPFWG operator are applied to solve decision making problems, and their effectiveness and feasibility have been verified by three cases of pattern recognition, medical diagnosis and multiple criteria decision making.

As an extension of the intuitionistic fuzzy set, the Pythagorean fuzzy set can depict uncertain information more effectively, so it has been well applied in multiple criteria decision making problems. At present, the multiple criteria decision making methods using the Pythagorean fuzzy set are gene rally ranked based on the aggregation operator or the distance measure, ignoring the important tool of the similarity measure. Therefore, this paper proposes several new similarity measures of the Pythagorean fuzzy set and applies them to multiple criteria decision making problems. Firstly, several new similarity measures of the Pythagorean fuzzy set are proposed, and their properties are discussed. Then, based on the weighted similarity measures, the multiple criteria decision making method is proposed. Finally, the accuracy and reliability of the new similarity measures and the proposed multiple criteria decision making method are verified by the simulation cases.

For a product, how to select the optimal material is a crucial step in the design process. Multiple criteria decision making (MCDM) method has been successfully applied to solve various material selection problems. In the MCDM method, alternative materials are evaluated by processing criteria information. In order to handle the uncertainty and inaccuracy in the criteria information, this paper develops a novel MCDM method based on group generalized Pythagorean fuzzy weighted average (GGPFWA) operator. In the novel method, decision makers are divided into advisers and deciders. The advisers use Pythagorean fuzzy set (PFS) to represent the criteria information of alternative materials. PFS is a new extension of fuzzy set, which can effectively represent fuzzy and uncertain information. The deciders use group generalized parameters (GGPs) to judge the accuracy of criteria information provided by each adviser. The GGPs are expressed by Pythagorean fuzzy numbers. Then, the criteria information and the GGPs are aggregated by GGPFWA operator, and the aggregate value of each material is obtained. By processing the aggregate value, the ranking of alternative materials is determined and the optimal material is selected. The accuracy and reliability of the novel method are verified by two material selection cases.

Abstract The ricochet behaviour of the air–water trans-media vehicle (AWTMV) during water-entry crossing was experimentally investigated. Three types of small-scale AWTMV including cone, ogive, and flat nose were used in the test. The underwater trajectory, velocity, and inclination angle of projectiles during the ricochet process were obtained using a high-speed camera. The angle change of the AWTMV and the ratio of the residual velocity are introduced. Based on this result, the relationship between the ricochet responses and initial conditions was derived. The results of this study show that (1) a small incident angle and great velocity make the occurrence of ricochet behaviour easier, (2) the stability of the trajectory of projectiles with cone, ogive, and flat nose weakened in turn at the same initial conditions, (3) the angle change and the ratio of the residual velocity are linear functions of the incident angle and velocity.

A vehicle able to navigate both in the air and underwater is referred to an unmanned aerial-underwater vehicle (UAUV). Aiming at the attitude and altitude control of UAUVs, an incremental dynamic inverse control (INDI) method with second-order low-pass filters is proposed. Based on the underwater motion model of an UAUV and the incremental attitude control model, the relationship between thrust increment and angular acceleration increment is obtained through Taylor series expansion and angular acceleration feedback. Subsequently, attitude and altitude controllers based on nonlinear dynamic inversion (NDI) and INDI are designed and their robustness is analyzed. By introducing second-order low-pass filters at the part of control and feedback, the accuracy of the angular acceleration estimation is improved and the time synchronization of the control system is ensured. Simulation results demonstrated that when introducing external disturbances and uncertainties, the INDI control with second-order low-pass filters proposed in this article can track the reference signal faster and more accurately than the NDI control.

为避免航行器结构破坏和电子器件失灵,可以利用入水时的跳弹现象减小入水冲击.本文通过实验方法探究了入水条件对航行器入水过程的影响,研究了不同速度和角度下航行器的跳弹/下沉过程,得到了一个可以预测航行器跳弹/下沉的经验公式.撞水瞬间航行器的头部会受到很大的冲击力,利用CFX软件对航行器不同工况入水过程进行了仿真,计算了不同工况下航行器的压力响应曲线,可以为航行器高速入水时减小入水冲击力提供参考.

In order to accurately assess the threat of air multi-target in the complicated and changeable air combat environment, an assessment method based on improved group generalized intuitionistic fuzzy soft set (I-GGIFSS) is proposed in this paper. Firstly, considering the characteristics of air target and the influence factors of threat assessment, a reasonable threat assessment system is established, and the appropriate assessment index is determined. Secondly, the generalized parameter matrix provided by many experts is introduced into the generalized intuitionistic fuzzy soft set (GIFSS) to form the group generalized intuitionistic fuzzy soft set (GGIFSS) to compensate for the knowledge limitation and assessment error of a single expert in traditional GIFSS. Finally, subjective weight is determined by group AHP (GAHP) and objective weight is determined by intuitionistic fuzzy entropy (IFE), then subjective weight and objective weight are combined based on relative entropy theory to determine reasonable index weight and expert weight, thus I-GGIFSS is obtained. The validity and superiority of I-GGIFSS are verified by the calculation and comparison of an example.

In the complex and changeable air combat environment, how to accurately assess the threat of incoming targets is the key factor to determine the success or failure of air defense operations. Therefore, a threat assessment method based on dynamic relative entropy ranking method is proposed in this paper. Firstly, the attribute factors of air target are selected, and the target attribute matrix at different times is determined by intuitionistic fuzzy sets. Secondly, the inverse Poisson distribution method is used to determine the weight of time series, and then the time-weighted target attribute matrix is determined, and the target attribute is weighted by intuitionistic fuzzy entropy, so that the attribute-weighted intuitionistic fuzzy decision matrix is obtained. Thirdly, the relative entropy theory is introduced to improve the TOPSIS method, and the relative entropy ranking method is obtained. Then, a threat assessment model based on dynamic relative entropy ranking method is constructed, and the dynamic assessment of incoming targets is completed. Finally, the method is proved to be reasonable and effective by example analysis and comparison.

针对未来军事竞争与对抗呈现多介质空间的体系对抗,而现有航行器平台仍大多局限于单一介质空间运行环境的现状,突破传统航行器定式,提出具有多介质航行能力的水空跨介质航行器概念,介绍了研究背景和发展此类航行器的必要性,分析了规划和发展过程中的关键技术,并对今后的发展思路进行了展望.

In this study, the ricochet behavior of air–water trans-media vehicle (AWTMV) during water-entry crossing was evaluated by both theoretical computations and experiments. First, Logvinovich model was introduced to predict the shape of cavitation. The AWTMV was divided into three areas to deduce hydrodynamic forces based on the relative position of AWTMV and cavitation. Accordingly, a mathematical model of AWTMV during water-entry crossing was established. Then, three types of projectiles including the nose of cone, ogive, and flat were used on an angle-adjustable experimental system to analyze the ricochet behavior under different initial conditions. A comparative analysis was carried out to evaluate the influence on trajectory. The computational and experimental results show a good agreement. Further, the effect of noses on ricochet behavior was evaluated; the experimental and calculation results show that the AWTMV with a cone nose is more likely to change trajectory and behavior under the same initial conditions. Finally, the critical angles of ricochet were derived based on the mathematical model, and an empirical formula is proposed to predict the occurrence of ricochet behavior. These results provide a reference for the design and use of AWTMV.

As the air combat environment becomes more complicated and changeable, accurate threat assessment of air target has a significant impact on air defense operations. This paper proposes an improved generalized intuitionistic fuzzy soft set (GIFSS) method for dynamic assessment of air target threat. Firstly, the threat assessment index is reasonably determined by analyzing the typical characteristics of air targets. Secondly, after the GIFSS at different time is obtained, the index weight is determined by the intuitionistic fuzzy set entropy and the relative entropy theory. Then, the inverse Poisson distribution method is used to determine the weight of time series, and then the time-weighted GIFSS is obtained. Finally, threat assessment of five air targets is carried out by using the improved GIFSS (I-GIFSS) and comparison methods. The validity and superiority of the proposed method are verified by calculation and comparison.

为研究潜-飞两栖导弹和水下兵器在不同入水初始条件下的跳弹行为,利用ANSYS CFX软件构建数值计算模型,分别以入射角度和入水速度为变量,对细长体射弹的入水跳弹行为进行数值模拟.研究结果表明:射弹的入水跳弹行为可分为撞击阶段、侵水阶段和出水阶段等3个阶段;入水初始速度越大,射弹越容易发生跳弹行为,且发生跳弹的速度越快,而较小的初始速度不足以提供使射弹跳出水的动能;射弹的入射角度越小,其轨迹越易向上发生弯曲,越容易出现跳弹行为.

This paper presents a robust position tracking control scheme for underwater vehicles moving in a vertical plane. The idea comes from the demand of underwater position tracking control for the newly borne Trans-media Aerial Underwater Vehicle (TMAUV). Although position control of a TMAUV is still within the scope of autonomous underwater vehicles (AUVs) control, it has new features. An underwater reference path for the TMAUV could be characterized by a strong maneuver that many assumptions in the conventional AUV controller design could not be employed. In this paper, a Lyapunov-based backstepping controller is developed for a nonlinear coupled input system releasing all constraints on the pitch angle, heave velocity, and angular velocity. Furthermore, neural networks and parameter estimation are employed to develop a robust controller in the presence of model uncertainties, parameter uncertainties, and external disturbances. This paper also solves the problem of adaptive estimation for the system parameters under the coupled input condition. Simulations are presented to demonstrate the feasibility and effectiveness.

Similarity measure, as a tool to measure the similarity degree between two objects, is an important research content in fuzzy set theory. Pythagorean fuzzy set, as a new extension of fuzzy set theory, has been widely used in various fields. It is very necessary to study the similarity measure of the Pythagorean Fuzzy set. Considering that the existing similarity measures cannot distinguish the highly similar but inconsistent Pythagorean fuzzy sets and the calculation results are error-prone in application, this paper introduces the exponential function to propose several new similarity measures of the Pythagorean fuzzy set. Firstly, on the premise of introducing the existing similarity measures, several new similarity measures are defined and their properties are discussed, and then the weighted similarity measures are defined. Then, the new similarity measures and the existing similarity measures are compared by an example, and it is verified that the new similarity measures can effectively distinguish highly similar but inconsistent Pythagorean fuzzy sets. Finally, through three simulation cases, it is verified that the new similarity measures can deal with different practical application problems more accurately and reliable than the existing similarity measures.

In this paper, in order to solve the optimization problem of UAV path, an UAV path evaluation method based on RE-ITOPSIS is proposed. First, based on the various threats in the process of UAV flight, the evaluation index is established. Then, the ITPOSIS is improved by using relative entropy to measure the distance between the interval numbers, so that the RE-ITOPSIS is obtained. And the weight of the evaluation indexes is obtained by using information entropy. Finally, the eight path of UAV is evaluated and the optimal path is selected. The comparison of the evaluation results shows that the proposed method can be more accurate and effective to evaluate the path of UAV.

In this paper, we address the problem of altitude and velocity controllers design for variable-sweep aircraft with model uncertainties. The object is to maintain altitude and velocity during the wing transition process where mass distribution and aerodynamic parameters change significantly. Based on the functional decomposition, the longitudinal dynamics of the aircraft can be divided into altitude subsystem in non-affine pure feedback form and velocity subsystem. And then nonlinear robust adaptive NN velocity controller and altitude controller are designed with backstepping method to relax the prior requirements of aerodynamic parameters accuracy in linear LPV controller design. The method of filtered signal is used to circumvent the algebraic loop problem caused by the dynamics of non-affine pure feedback form. Dynamic surface control (DSC) and minimal learning parameters (MLP) techniques are employed to solve the problems of ‘explosion of complexity’ in the back-stepping method and the online updated parameters being too much. The robust terms have been introduced to eliminate the influences of approximation errors. According to the Lyapunov-LaSalle invariant set theorem, the semi-global boundedness and convergence of all the signals of the closed-loop system are proved. Simulation results are presented to illustrate the control algorithm with good performance.

The water-exit process is a key step in connecting underwater navigation and air flight of a submersible aerial vehicle. In order to study motion law and density influence of the vehicle in the water-exit process, and taking into account the limitations of the experiment and numerical simulation in the study of the whole water-exit process, a theoretical modeling method is proposed. First, the vehicle's shape is presented, and the water-exit dynamic model is established by mechanics and motion analysis. Then, numerical simulation and theoretical modeling are used to calculate the water-exit motion under same conditions, and the validity of the water-exit model is verified by the calculation results. Finally, on basis of the established model, the water-exit motion of the vehicle with three different densities is calculated under different initial water-exit angles, axial velocities and thrusts, and the water-exit motion law and vehicle's density influence on the water-exit motion are obtained. The proposed method and obtained results can be used as effective guidance for the vehicle finishes the water-exit motion successfully.