In the realm of missile defense systems, the self-sufficient maneuver capacity of missile swarms is pivotal for their survival. Through the analysis of the missile dynamics model, a time-efficient cooperative attack strategy for missile swarm is proposed. Based on the distribution of the attackers and defenders, the collision avoidance against the defenders is considered during the attack process. By analyzing the geometric relationship between the relative velocity vector and relative position vector of the attackers and defenders, the collision avoidance constrains of attacking swarm are redefined. The key point is on adjusting the relative velocity vectors to fall outside the collision cone. This work facilitates high-precision attack toward the target while keeping safe missing distance between other attackers during collision avoidance process. By leveraging an innovative repulsion artificial function, a time-efficient cooperative attack strategy for missile swarm is obtained. Through rigorous simulation, the effectiveness of this cooperative attack strategy is substantiated. Furthermore, by employing Monte Carlo simulation, the success rate of the cooperative attack strategy is assessesed and the optimal configuration for the missile swarm is deduced.
This paper concentrates on addressing the hypersonic glide vehicle (HGV) tracking problem considering the high maneuverability and non-stationary heavy-tailed measurement noise without prior statistics in complicated flight environments. Since the interacting multiple model (IMM) filtering is famous with its ability to cover the movement property of motion models, the problem is formulated as modeling the non-stationary heavy-tailed measurement noise without any prior statistics in the IMM framework. Firstly, without any prior statistics, the Gaussian-inverse Wishart distribution is embedded in the improved Pearson type-VII (PTV) distribution, which can adaptively adjust the parameters to model the non-stationary heavy-tailed measurement noise. Besides, degree of freedom (DOF) parameters are surrogated by the maximization of evidence lower bound (ELBO) in the variational Bayesian optimization framework instead of fixed value to handle uncertain non-Gaussian degrees. Then, this paper analytically derives fusion forms based on the maximum Versoria fusion criterion instead of the moment matching approach, which can provide a precise approximation for the PTV mixture distribution in the mixing and output steps combined with the weight Kullback-Leibler average theory. Simulation results demonstrate the superiority and robustness of the proposed algorithm in typical HGVs tracking when the measurement noise without priori statistics is non-stationary.
A high precision detection technique is analyzed based on the optical micro electro-mechanical system (MEMS) accelerometer with double gratings for noise suppression and scale factor enhancement. The brief sensing model and modulation detection model are built using the phase sensitive detection, and the relationship between stimulated acceleration and system output is given. The schematics of gap modulation and light intensity modulation are analyzed respectively, and the choice of modulation frequency in the optical MEMS accelerometer system is discussed. According to the experimental results, the scale factor is improved from 15.45 V/g with the gap modulation to 18.78 V/g with the light intensity modulation, and the signal to noise ratio is improved from 42.95 dB to 81.73 dB. The overall noise level in the optical MEMS accelerometer is effectively suppressed.
A three-dimensional path-planning approach has been developed to coordinate multiple fixed-wing unmanned aerial vehicles (UAVs) while avoiding collisions. The hierarchical path-planning architecture that divides the path-planning process into two layers is proposed by designing the velocity-obstacle strategy for satisfying timeliness and effectiveness. The upper-level layer focuses on creating an efficient Dubins initial path considering the dynamic constraints of the fixed wing. Subsequently, the lower-level layer detects potential collisions and adjusts its flight paths to avoid collisions by using the three-dimensional velocity obstacle method, which describes the maneuvering space of collision avoidance as the intersection space of half space. To further handle the dynamic and collision-avoidance constraints, a priority mechanism is designed to ensure that the adjusted path is still feasible for fixed-wing UAVs. Simulation experiments demonstrate the effectiveness of the proposed method.
This paper comprehensively explores the impulsive on-orbit inspection game problem utilizing reinforcement learning and game training methods. The purpose of the spacecraft is to inspect the entire surface of a non-cooperative target with active maneuverability in front lighting. First, the impulsive orbital game problem is formulated as a turn-based sequential game problem. Second, several typical relative orbit transfers are encapsulated into modules to construct a parameterized action space containing discrete modules and continuous parameters, and multi-pass deep Q-networks (MPDQN) algorithm is used to implement autonomous decision-making. Then, a curriculum learning method is used to gradually increase the difficulty of the training scenario. The backtracking proportional self-play training framework is used to enhance the agent’s ability to defeat inconsistent strategies by building a pool of opponents. The behavior variations of the agents during training indicate that the intelligent game system gradually evolves towards an equilibrium situation. The restraint relations between the agents show that the agents steadily improve the strategy. The influence of various factors on game results is tested.
In this paper, an online midcourse guidance method for intercepting high-speed maneuvering targets is proposed. Firstly, the affine system is used to build a dynamic model and analyze the state constraints. The midcourse guidance problem is transformed into a continuous time optimization problem. Secondly, the problem is transformed into a discrete convex programming problem by affine control variable relaxation, Gaussian pseudospectral discretization and constraints linearization. Then, the off-line midcourse guidance trajectory is generated before midcourse guidance. It is used as the initial reference trajectory for online correction of midcourse guidance. An online guidance framework is used to eliminate the error caused by calculation of guidance instruction time. And the design of discrete points decreases with flight time to improve the solving efficiency. In addition, it is proposed that the terminal guidance capture is used innovatively space to judge the success of midcourse guidance. Numerical simulation shows the feasibility and effectiveness of the proposed method.
This survey presents a comprehensive review of various methods and algorithms related to passing-through control of multi-robot systems in cluttered environments. Numerous studies have investigated this area, and we identify several avenues for enhancing existing methods. This survey describes some models of robots and commonly considered control objectives, followed by an in-depth analysis of four types of algorithms that can be employed for passing-through control: leader-follower formation control, multi-robot trajectory planning, control-based methods, and virtual tube planning and control. Furthermore, we conduct a comparative analysis of these techniques and provide some subjective and general evaluations.
This paper presents a quadcopter system for navigation in outdoor urban environments. The main contributions include the hardware design, the establishment of global occupancy grid maps based on millimeter-wave radars, the trajectory planning scheme based on optimal virtual tube methods, and the controller structure based on dynamics. The proposed system focuses on utilizing a compact and lightweight quadrotor with sensors to achieve navigation that conforms to the direction of urban roads with high computational efficiency and safety. Our work is an application of millimeter-wave radars and virtual tube planning for obstacle avoidance in navigation. The validness and effectiveness of the proposed system are verified by experiments.
How multi-unmanned aerial vehicles (UAVs) carrying a payload pass an obstacle-dense environment is practically important. Up to now, there have been few results on safe motion planning for the multi-UAVs cooperative transportation system (CTS) to pass through such an environment. The problem is challenging because it is difficult to analyze and explicitly take into account the swing motion of the payload in planning. In this paper, a modeling method of virtual tube is proposed by fusing the advantages of the existing modeling algorithm for regular virtual tube and the expansion environment method. The proposed method can not only generate a safe and smooth tube for UAVs, but also ensure the payload stays away from the dense obstacles. Simulation results show the effectiveness of the method and the safety of the planned tube.
Developing intelligent unmanned swarm systems (IUSSs) is a highly intricate process. Although current simulators and toolchains have made a notable contribution to the development of algorithms for IUSSs, they tend to concentrate on isolated technical elements and are deficient in addressing the full spectrum of critical technologies and development needs in a systematic and integrative manner. Furthermore, the current suite of tools has not adequately addressed the challenge of bridging the gap between simulation and real-world deployment of algorithms. Therefore, a comprehensive solution must be developed that encompasses the entire IUSS development lifecycle. In this study, we present the RflySim ToolChain, which has been developed with the specific aim of facilitating the rapid development and validation of IUSSs. The RflySim ToolChain employs a model-based design (MBD) approach, integrating a modeling and simulation module, a lower reliable control module, and an upper swarm decision-making module. This comprehensive integration encompasses the entire process, from modeling and simulation to testing and deployment, thereby enabling users to rapidly construct and validate IUSSs. The principal advantages of the RflySim ToolChain are as follows: it provides a comprehensive solution that meets the full-stack development needs of IUSSs; the highly modular architecture and comprehensive software development kit (SDK) facilitate the automation of the entire IUSS development process. Furthermore, the high-fidelity model design and reliable architecture solution ensure a seamless transition from simulation to real-world deployment, which is known as the simulation to reality (Sim2Real) process. This paper presents a series of case studies that illustrate the effectiveness of the RflySim ToolChain in supporting the research and application of IUSSs.
This paper presents a method of multicopter interception control based on visual servo and virtual tube in a cluttered environment. The proposed hybrid heuristic function improves the efficiency of the A* algorithm. The revised objective function makes the virtual tube generating curve not only smooth but also close to the path points generated by the A* algorithm. In six different simulation scenarios, the efficiency of the modified A* algorithm is 6.2% higher than that of the traditional A* algorithm. The efficiency of path planning and virtual tube planning is verified by simulations. The effectiveness of interception control is verified by a software-in-loop (SIL) simulation.
Unmanned aerial vehicles (UAVs) have become one of the key technologies to achieve future data collection due to their high mobility, rapid deployment, low cost, and the ability to establish line-of-sight communication links. However, when UAV swarm perform tasks in narrow spaces, they often encounter various spatial obstacles, building shielding materials, and high-speed node movements, which result in intermittent network communication links and cannot support the smooth completion of tasks. In this paper, a high mobility and dynamic topology of the UAV swarm is particularly considered and the high dynamic mobile topology-based clustering (HDMTC) algorithm is proposed. Simulation and real flight verification results verify that the proposed HDMTC algorithm achieves higher stability of network, longer link expiration time (LET), and longer node lifetime, all of which improve the communication performance for UAV swarm networks.
In order to enhance the dynamic control precision of inertial stabilization platform (ISP), a disturbance sliding mode observer (DSMO) is proposed in this paper suppressing disturbance torques inherent within the system. The control accuracy of ISP is fundamentally circumscribed by various disturbance torques in rotating shaft. Therefore, a dynamic model of ISP incorporating composite perturbations is established with regard to the stabilization of axis in the inertial reference frame. Subsequently, an online estimator for control loop uncertainties based on the sliding mode control algorithm is designed to estimate the aggregate disturbances of various parameters uncertainties and other unmodeled disturbances that cannot be accurately calibrated. Finally, the proposed DSMO is integrated into a classical proportional-integral-derivative (PID) control scheme, utilizing feedforward approach to compensate the composite disturbance in the control loop online. The effectiveness of the proposed disturbance observer is validated through simulation and hardware experimentation, demonstrating a significant improvement in the dynamic control performance and robustness of the classical PID controller extensively utilized in the field of engineering.
This work proposes the application of an iterative learning model predictive control (ILMPC) approach based on an adaptive fault observer (FOBILMPC) for fault-tolerant control and trajectory tracking in air-breathing hypersonic vehicles. In order to increase the control amount, this online control legislation makes use of model predictive control (MPC) that is based on the concept of iterative learning control (ILC). By using offline data to decrease the linearized model’s faults, the strategy may effectively increase the robustness of the control system and guarantee that disturbances can be suppressed. An adaptive fault observer is created based on the suggested ILMPC approach in order to enhance overall fault tolerance by estimating and compensating for actuator disturbance and fault degree. During the derivation process, a linearized model of longitudinal dynamics is established. The suggested ILMPC approach is likely to be used in the design of hypersonic vehicle control systems since numerical simulations have demonstrated that it can decrease tracking error and speed up convergence when compared to the offline controller.
In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration, this paper proposes a system-level calibration method for field condition. Firstly, a 42-dimension Kalman filter is constructed to reduce impact brought by turntable. Then, a biaxial rotation path is designed based on the accelerometer output model, including orthogonal 22 positions and tilt 12 positions, which enhances gravity excitation on nonlinear coefficients of accelerometer. Finally, sampling is carried out for calibration and further experiments. The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method, the proposed method reduces the position error by about 390 m.
Visual inertial odometry (VIO) problems have been extensively investigated in recent years. Existing VIO methods usually consider the localization or navigation issues of robots or autonomous vehicles in relatively small areas. This paper considers the problem of vision-aided inertial navigation (VIN) for aircrafts equipped with a strapdown inertial navigation system (SINS) and a downward-viewing camera. This is different from the traditional VIO problems in a larger working area with more precise inertial sensors. The goal is to utilize visual information to aid SINS to improve the navigation performance. In the multi-state constraint Kalman filter (MSCKF) framework, we introduce an anchor frame to construct necessary models and derive corresponding Jacobians to implement a VIN filter to directly update the position in the Earth-centered Earth-fixed (ECEF) frame and the velocity and attitude in the local level frame by feature measurements. Due to its filtering-based property, the proposed method is naturally low computational demanding and is suitable for applications with high real-time requirements. Simulation and real-world data experiments demonstrate that the proposed method can considerably improve the navigation performance relative to the SINS.
To solve the problem of providing the best initial situation for terminal guidance when multiple missiles intercept multiple targets, a group cooperative midcourse guidance law (GCMGL) considering time-to-go is proposed. Firstly, a three-dimensional (3D) guidance model is established and a cooperative trajectory shaping guidance law is given. Secondly, for estimating the unknown target maneuvering acceleration, an adaptive disturbance observer (ADO) is designed, combining finite-time theory with a radial basis function (RBF) neural network, and the convergence of the estimation error is proven using Lyapunov stability theory. Then, to ensure time-to-go cooperation among missiles within the same group and across different groups, the group consensus protocols of virtual collision point mean and the inter-group cooperative consensus protocol are designed respectively. Based on the group consensus protocols, the virtual collision point cooperative guidance law is given, and the finite-time convergence is proved by Lyapunov stability theory. Simultaneously, combined with trajectory shaping guidance law, virtual collision point cooperative guidance law and the inter-group cooperative consensus protocol, the design of GCMGL considering time-to-go is given. Finally, numerical simulation results show the effectiveness and the superiority of the proposed GCMGL.
The influence of ocean environment on navigation of autonomous underwater vehicle (AUV) cannot be ignored. In the marine environment, ocean currents, internal waves, and obstacles are usually considered in AUV path planning. In this paper, an improved particle swarm optimization (PSO) is proposed to solve three problems, traditional PSO algorithm is prone to fall into local optimization, path smoothing is always carried out after all the path planning steps, and the path fitness function is so simple that it cannot adapt to complex marine environment. The adaptive inertia weight and the “active” particle of the fish swarm algorithm are established to improve the global search and local search ability of the algorithm. The cubic spline interpolation method is combined with PSO to smooth the path in real time. The fitness function of the algorithm is optimized. Five evaluation indexes are comprehensively considered to solve the three-demensional (3D) path planning problem of AUV in the ocean currents and internal wave environment. The proposed method improves the safety of the path planning and saves energy.
As the core component of inertial navigation systems, fiber optic gyroscope (FOG), with technical advantages such as low power consumption, long lifespan, fast startup speed, and flexible structural design, are widely used in aerospace, unmanned driving, and other fields. However, due to the temperature sensitivity of optical devices, the influence of environmental temperature causes errors in FOG, thereby greatly limiting their output accuracy. This work researches on machine-learning based temperature error compensation techniques for FOG. Specifically, it focuses on compensating for the bias errors generated in the fiber ring due to the Shupe effect. This work proposes a composite model based on k-means clustering, support vector regression, and particle swarm optimization algorithms. And it significantly reduced redundancy within the samples by adopting the interval sequence sample. Moreover, metrics such as root mean square error (RMSE), mean absolute error (MAE), bias stability, and Allan variance, are selected to evaluate the model’s performance and compensation effectiveness. This work effectively enhances the consistency between data and models across different temperature ranges and temperature gradients, improving the bias stability of the FOG from 0.022 °/h to 0.006 °/h. Compared to the existing methods utilizing a single machine learning model, the proposed method increases the bias stability of the compensated FOG from 57.11% to 71.98%, and enhances the suppression of rate ramp noise coefficient from 2.29% to 14.83%. This work improves the accuracy of FOG after compensation, providing theoretical guidance and technical references for sensors error compensation work in other fields.
This paper investigates the sliding-mode-based fixed-time distributed average tracking (DAT) problem for multiple Euler-Lagrange systems in the presence of external disturbances. The primary objective is to devise controllers for each agent, enabling them to precisely track the average of multiple time-varying reference signals. By averaging these signals, we can mitigate the influence of errors and uncertainties arising during measurements, thereby enhancing the robustness and stability of the system. A distributed fixed-time average estimator is proposed to estimate the average value of global reference signals utilizing local information and communication with neighbors. Subsequently, a fixed-time sliding mode controller is introduced incorporating a state-dependent sliding mode function coupled with a variable exponent coefficient to achieve distributed average tracking of reference signals, and rigorous analytical methods are employed to substantiate the fixed-time stability. Finally, numerical simulation results are provided to validate the effectiveness of the proposed methodology, offering insights into its practical application and robust performance.
For air-to-air missiles, the terminal guidance’s precision is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneuvering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast convergence. The system’s state is more swiftly converged to the sliding mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detector for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions.
In the existing impact time control guidance (ITCG) laws for moving-targets, the effects of time-varying velocity caused by aerodynamics and gravity cannot be effectively considered. Therefore, an ITCG with field-of-view (FOV) constraints based on biased proportional navigation guidance (PNG) is developed in this paper. The remaining flight time (time-to-go) estimation method is derived considering aerodynamic force and gravity. The number of differential equations is reduced and the integration step is increased by changing the integral variable, which makes it possible to obtain time-to-go through integration. An impact time controller with FOV constraints is proposed by analyzing the influence of the biased term on time-to-go and FOV constraint. Then, numerical simulations are performed to verify the correctness and superiority of the method.
This paper presents a fixed-time cooperative guidance method with impact angle constraints for multiple flight vehicles (MFV) to address the challenges of intercepting large maneuvering targets with difficulty and low precision. A cooperative guidance model is proposed, transforming the cooperative interception problem into a consensus problem based on the remaining flight time of the flight vehicles. First, the impact angle constraint is converted into the line of sight (LOS) angle constraint, and a new fixed-time convergent non-singular terminal sliding surface is introduced, which resolves the singularity issue of the traditional sliding surfaces. With this approach, LOS angle rate and normal overloads can converge in fixed time, ensuring that the upper bound of the system convergence time is not affected by the initial value of the system. Furthermore, the maneuvering movement of the target is considered as a system disturbance, and an extended state observer is employed to estimate and compensate for it in the guidance law. Lastly, by applying consensus theory and distributed communication topology, the remaining flight time of each flight vehicle is synchronized to ensure that they intercept the target simultaneously with different impact angles. Simulation experiments are conducted to validate the effectiveness of the proposed cooperative interception and guidance method.
The process of ground vehicle dynamic gravimetry is inevitably affected by the carrier’s maneuvering acceleration, which makes the result contain a large amount of dynamic error. In this paper, we propose a dynamic error suppression method of gravimetry based on the high-precision acquisition of external velocity for compensating the horizontal error of the inertial platform. On the basis of platform gravity measurement, firstly, the dynamic performance of the system is enhanced by optimizing the horizontal damping network of the inertial platform and selecting its parameter. Secondly, an improved federal Kalman filtering algorithm and a fault diagnosis method are designed using strapdown inertial navigation system (SINS), odometer (OD), and laser Doppler velocimeter (LDV). Simulation validates that these methods can improve the accuracy and robustness of the external velocity acquisition. Three survey lines are selected in Tianjin, China, for the gravimetry experiments with different maneuvering levels, and the results demonstrate that after dynamic error suppression, the internal coincidence accuracies of smooth and uniform operation, obvious acceleration and deceleration operation, and high-dynamic operation are improved by 70.2%, 73.6%, and 77.9% to reach 0.81 mGal, 1.30 mGal, and 1.94 mGal, respectively, and the external coincidence accuracies during smooth and uniform operation are improved by 48.6% up to 1.66 mGal. It is shown that the proposed method can effectively suppress the dynamic error, and that the accuracy improvement increases with carrier maneuverability. However, the amount of residual error that can not be entirely eliminated increases as well, so the ground vehicle dynamic gravimetry should be maintained in the carrier for smooth and uniform operation.
Vibration-induced bias deviation, which is generated by intensity fluctuations and additional phase differences, is one of the vital errors for fiber optic gyroscopes (FOGs) operating in vibration environment and has severely restricted the applications of high-precision FOGs. The conventional methods for suppressing vibration-induced errors mostly concentrate on reinforcing the mechanical structure and optical path as well as the compensation under some specific operation parameters, which have very limited effects for high-precision FOGs maintaining performances under vibration. In this work, a technique of suppressing the vibration-induced bias deviation through removing the part related to the varying gain from the rotation-rate output is put forward. Particularly, the loop gain is extracted out by adding a gain-monitoring wave. By demodulating the loop gain and the rotation rate simultaneously under distinct frequencies and investigating their quantitative relationship, the vibration-induced bias error is compensated without limiting the operating parameters or environments, like the applied modulation depth. The experimental results show that the proposed method has achieved the reduction of bias error from about 0.149°/h to 0.014°/h during the random vibration with frequencies from 20 Hz to 2000 Hz. This technique provides a feasible route for enhancing the performances of high-precision FOGs heading towards high environmental adaptability.
When the maneuverability of a pursuer is not significantly higher than that of an evader, it will be difficult to intercept the evader with only one pursuer. Therefore, this article adopts a two-to-one differential game strategy, the game of kind is generally considered to be angle-optimized, which allows unlimited turns, but these practices do not take into account the effect of acceleration, which does not correspond to the actual situation, thus, based on the angle-optimized, the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration. A two-to-one differential game problem is proposed in the three-dimensional space, and an improved multi-objective grey wolf optimization (IMOGWO) algorithm is proposed to solve the optimal game point of this problem. With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space, a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game. Then the optimal game point is solved by using the IMOGWO algorithm. It is proved based on Markov chains that with the IMOGWO, the Pareto solution set is the solution of the differential game. Finally, it is verified through simulations that the pursuers can capture the escapee, and via comparative experiments, it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
This paper addresses the time-varying formation-containment (FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired trajectory. Input the fixed time-varying formation template to the leader and start executing, this process also needs to track the desired trajectory, and the follower needs to converge to the convex hull that the leader crosses. Firstly, the dynamic models of nonholonomic systems are linearized to second-order dynamics. Then, based on the desired trajectory and formation template, the FC control protocols are proposed. Sufficient conditions to achieve FC are introduced and an algorithm is proposed to resolve the control parameters by solving an algebraic Riccati equation. The system is demonstrated to achieve FC, with the average position and velocity of the leaders converging asymptotically to the desired trajectory. Finally, the theoretical achievements are verified in simulations by a multi-agent system composed of virtual human individuals.
Enhancing the stability and performance of practical control systems in the presence of nonlinearity, time delay, and uncertainty remains a significant challenge. Particularly, a class of strict-feedback nonlinear uncertain systems characterized by unknown control directions and time-varying input delay lacks comprehensive solutions. In this paper, we propose an observer-based adaptive tracking controller to address this gap. Neural networks are utilized to handle uncertainty, and a unique coordinate transformation is employed to untangle the coupling between input delay and unknown control directions. Subsequently, a new auxiliary signal counters the impact of time-varying input delay, while a Nussbaum function is introduced to solve the problem of unknown control directions. The leverage of an advanced dynamic surface control technique avoids the “complexity explosion” and reduces boundary layer errors. Synthesizing these techniques ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small region around the origin by selecting suitable parameters. Simulation examples are provided to demonstrate the feasibility of the proposed approach.
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model. Therefore, the modeling idea of the mixture of experts (MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis (PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.
In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios, the limitations of existing research, including real-time calculation, accuracy efficiency trade-off, and the absence of the three-dimensional attack area model, restrict their practical applications. To address these issues, an improved backtracking algorithm is proposed to improve calculation efficiency. A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm. Furthermore, the age-layered population structure genetic programming (ALPS-GP ) algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area, considering real-time requirements. The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm. The study reveals a remarkable combination of high accuracy and efficient real-time computation, with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10?4 s, thus meeting the requirements of real-time combat scenarios.
