Cooperative Guidance Law Research Articles

Distributed Model Predictive Control Cooperative Guidance Law for Multiple UAVs

Aiming at the problem of multiple unmanned aerial vehicles (UAVs) cooperatively intercepting a maneuvering target, this paper proposes a cooperative guidance law with less energy consumption and a newly accurate time-to-go estimation algorithm in the two-dimensional (2D) plane. Firstly, based on the relative motion equations between UAVs and the target on the 2D plane, the line-of-sight (LOS) direction and the LOS normal direction models are established. Then, based on the distributed model predictive control (DMPC) theory, DMPC cooperative guidance laws are designed in two directions. This guidance law can ensure that all UAVs intercept the maneuvering target at the expected LOS angle at the same time and reduce the energy consumption during the guidance process. Then, a new time-to-go estimation algorithm is designed, which can reduce the time-to-go estimation error and improve the cooperative accuracy. Finally, the simulation results show that the DMPC cooperative guidance law reduces energy consumption by more than 50% compared to other guidance laws and the proposed time-to-go estimation algorithm improves the accuracy by 200% compared to traditional methods.

Cooperative Guidance Law Based on Super-Twisting Observer for Target Maneuvering

Cooperative Guidance Law Based on Super-Twisting Observer for Target Maneuvering

Three-dimensional cooperative guidance with impact angle constraints via value-policy decomposed multi-agent reinforcement learning

For a three-dimensional impact angle-constrained time-coordination guidance problem, a value-policy decomposed multi-agent twin delayed deep deterministic (VPD-MATD3) policy gradient algorithm is proposed in this paper, and a temporal-spatial cooperative guidance law is designed consequently. The derived cooperative engagement kinematics is formulated as a value-policy decomposed partially observable Markov decision process. Value decomposition and policy decomposition are correspondingly proposed to address the two bottlenecks of reward coupling and policy coupling in 3D guidance, thus improving the training process. The training environment with multiple uncertainties, such as observation noise, maneuverability perturbation, autopilot time lag, switching communication topology, and random initialization, is subsequently constructed. Time-energy type reward functions are designed, incorporating energy consumption as a direct optimization indicator via a penalty term. A long short-term memory network layer is inserted inside the policy networks to suppress the negative effect of observation noise. The policy training curves verify the significant effect of the proposed algorithm in improving training convergence. The policy testing results illustrate the robustness and generalization of the VPD-MATD3 cooperative guidance law and its ability to cope with randomly switched communication topologies. Moreover, the comparative testing further reveals its time-energy suboptimal property.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Fixed-Time Distributed Event-Triggered Cooperative Guidance Methods for Multiple Vehicles with Limited Communications to Achieve Simultaneous Arrival

Aiming at the salvo-attack problem of multiple missiles, a distributed cooperative guidance law based on the event-triggered mechanism is proposed, which enables missiles with large differences in spatial location and velocity to achieve simultaneous attacks with only a few dozen information exchanges. It effectively reduces the generation of control commands and communication frequency, thereby reducing channel load and improving communication efficiency and reliability. Compared to traditional periodic sampling communication, the number of communications has been reduced by over 90%. The guidance process is divided into two stages. The first stage is the cooperative guidance stage, where missiles achieve consensus of the time-to-go estimates through information exchange. In this stage, each missile is designed with an event-triggered function based on its own state error, and the missile only updates and transmits its information in the communication network when the error meets the set threshold, effectively reducing the occupancy rate of missile-borne resources during the cooperation process. The second stage is the independent guidance stage, where missiles can hit the target simultaneously while keeping the communication network silent. This is achieved by ensuring that the time-to-go estimates of missiles can represent the real time-to-go after achieving consensus. By the design of the two-stage guidance law and the replacement of the event-triggered function, the cooperative guidance system can be ensured to remain stable in scenarios where the leader missile is present and destroyed, and this excludes Zeno behavior. The stability of the cooperative guidance law is rigorously proved by algebraic graph theory, matrix theory, and the Lyapunov method. Finally, the numerical simulation results demonstrate the validity of the algorithm and the correctness of the stability analysis.

Research on a Distributed Cooperative Guidance Law for Obstacle Avoidance and Synchronized Arrival in UAV Swarms

In response to the issue where the original synchronization time becomes inapplicable for UAV swarms after temporal consistency convergence due to obstacle avoidance, a new distributed consultative temporal consistency guidance law that takes into account threat avoidance has been proposed. Firstly, a six-degree-of-freedom dynamic model and a guidance control model for unmanned aerial vehicles (UAVs) are established, and the guidance commands are decomposed into control signals for the pitch and yaw planes. Secondly, based on the theory of dynamic inversion control, a temporal consistency guidance law for a single UAV is constructed. On the other hand, an improved artificial potential field theory is used and integrated with a predictive correction network to generate guidance commands for threat avoidance. A threshold smoothing method is employed to integrate the two guidance systems, and a cluster consultation mechanism is introduced to design a two-layer temporal synchronization architecture, which negotiates to change the synchronization time of the swarm to achieve the convergence of consistency once again. Finally, in typical application scenarios, simulation verification demonstrates the effectiveness of the control method proposed in this paper. The proposed control method achieves the guidance of UAV formations to synchronize their arrival at the target location under complex threat conditions.

Three-dimensional free-will arbitrary time cooperative guidance law against moving target

A novel three-dimensional free-will arbitrary time cooperative guidance law based on biased proportional navigation is proposed for intercepting a high-value moving target. In contrast to existing research, the presented method does not require controlling the interceptors' axial speed or prediction of the interception point. First, the engagement plane is constructed so that a three-dimensional guidance problem can be formulated as a planar problem. Second, a new accurate time-to-go estimation algorithm against the moving target is deduced based on the formulated problem model. Third, a free-will arbitrary time cooperative guidance law is designed utilizing the leader-follower architecture. Multiple missiles can intercept a moving target simultaneously and the intercept time of each missile will converge within a free-will arbitrary time. Fourth, the proposed cooperative guidance law under different communication circumstances is analyzed. When the communication resources are abundant, missiles can reach dynamic average consensus. Meanwhile, the system is robust against the communication imperfection. Finally, numerical simulations are presented to verify the effectiveness of the time-to-go estimation algorithm and proposed cooperative guidance law.

Dynamic Encircling Cooperative Guidance for Intercepting Superior Target with Overload, Impact Angle and Simultaneous Time Constraints

This paper proposes a dynamic encircling cooperative guidance (DECG) law to enable multiple interceptors to cooperatively intercept a superior target, considering low velocity, limited overload, impact angle and simultaneous arrival constraints. First, the feasible escaping area of the target is analyzed and a dynamic encircling strategy for the target is established. This strategy efficiently provides virtual escaping points, allowing interceptors to dynamically encircle the target without excessive energy consumption, ultimately leading to a successful interception. Second, to enhance the physical feasibility of the kinematic equations governing the interaction between interceptors and target at the virtual escaping points, the independent variable is substituted and the kinematic equations are remodeled. Convex optimization is employed to address the multi-constraint optimal guidance problem for each interceptor, thereby facilitating simultaneous interception. Compared with the existing guidance laws, DECG has a more practical and feasible cooperative strategy, is able to handle more constraints including the interceptor’s own constraints and cooperative constraints, and does not rely on the precise calculation of explicit remaining flight time in the guidance law implementation. Lastly, the effectiveness, superiority and robustness of the DECG law are evaluated through a series of numerical simulations, and its performance is compared with that of the cooperative proportional navigation guidance law (CPNG).

Three-dimensional piecewise cooperative guidance with smooth switching topology

To investigate the issue of large-scale multi-missile cooperative attacks on a same target, this paper presents a three-dimensional piecewise cooperative guidance law based on smooth switching topology, realizing time consensus and impact angle constraints. Firstly, to implement the piecewise cooperative guidance law design, we establish the attack surface of the arc profile according to the expected LOS angle and the communication switching point, and obtain the virtual impact point (VIP). Secondly, a switching function is designed to ensure the smooth transition of the communication topology, mitigating the chattering issue in existing communication topology switching, while a time consensus protocol control input is implemented to facilitate the time cooperative attack of the missile in the LOS direction. Meanwhile, a fixed-time terminal sliding mode guidance law is established to guarantee the satisfaction of the impact angle constraint at the VIP. Additionally, an adaptive three-dimensional proportional navigation guidance (PNG) law is designed to guarantee zero miss distance at the real impact point (RIP). Finally, simulations involving four missiles attacking stationary targets simultaneously validate the effectiveness and superiority of the piecewise cooperative guidance law.

Time cooperative guidance law based on neural network

In response to the issue of coordinated guidance for vehicle groups, a neural network-based time-to-go prediction method has been designed. The influence of the motion state of both the vehicle and the target on the prediction results has been considered in this method. Compared with the classical method, the prediction error of the moving target is obviously reduced. A guidance law with a time synergy coefficient is proposed. This method adjusts the flight trajectory of the vehicles by the time-to-go error, ensuring that the cluster of vehicle arrive at the target simultaneously. According to the simulation results, the prediction error of the neural network is less than 0.4 s, and the maximum coordination error is 0.2 s, which achieves the effect of cooperative interception.

Three‐dimensional cooperative guidance for simultaneous attack with specified impact time based on fixed‐time convergence

AbstractIn this paper, distributed three‐dimensional (3D) cooperative guidance laws are designed for leader–follower multiple missiles to achieve simultaneous attack at a specified time. The guidance laws are derived from the biased proportional navigation guidance (PNG) law. Two fixed‐time distributed algorithms with time‐varying coefficients are proposed to track the state of the leader under undirected and directed topologies, respectively. The upper bounds of convergence times for the tracking algorithms are obtained. The biased guidance terms of followers are designed to track the leader with the proposed algorithms and the biased guidance term of the leader is designed to achieve specified impact time. Then, an auxiliary function is included into the biased guidance terms to meet the field‐of‐view (FOV) constraints. The leading angles' properties and convergence times under the proposed guidance laws are further analyzed. Numerical simulations are given to verify the effectiveness of the proposed cooperative guidance laws.

Time-to-go based three-dimensional multi-missile spatio-temporal cooperative guidance law: A novel approach for maneuvering target interception

This research presents a novel approach called 'Time-to-target-based multi-missile spatio-temporal cooperative guidance' This approach enables the simultaneous guidance of multiple missiles, allowing them to intercept a maneuvering target from different terminal intercept angles to maximize damage. The article introduces a finite-time optimal cooperative guidance technique to reduce the load on missile engines in the line-of-sight (LOS) direction. It proposes a time-varying sliding mode guidance scheme, which is parameterized by the remaining flight time, for both longitudinal and lateral LOS directions. The scheme helps prevent excessive initial acceleration in the longitudinal and lateral LOS directions while ensuring intercept angle constraints. The time-varying cooperative guidance law proposed in this study enables the simultaneous interception of a maneuvering target with different terminal intercept angles at the moment of terminal intercept. The numerical simulation results indicate that the multi-missile spatio-temporal cooperative guidance method is effective, superior, and robust. The method enables multiple missiles to achieve the minimum acceptable intercept distance at different terminal intercept angles while optimizing fuel in the LOS direction.

Cooperative guidance law with maneuverability awareness: A decentralized solution

In this paper, we propose a cooperative guidance law aimed to achieve coordinated impact angles with limited observation on target information. The primary challenge lies in establishing an appropriate communication graph among all missiles and devising an algorithm to estimate target acceleration information during engagements. To address this, we propose a specific communication topology and employ a numerical integration-based estimation method. Additionally, a distributed algorithm is introduced to facilitate consensus on target acceleration estimation. Building upon these foundations, we design an optimal-control-based distributed guidance law for each missile. Performance of the proposed guidance law is validated through numerical simulations.

Adaptive Distributed Fixed-Time Cooperative Three-Dimensional Guidance Law for Multimissiles against Manoeuvring Target

The problem of cooperative interception of the manoeuvring target is investigated in this paper. Firstly, in light of fast fixed-time consensus theory, time-to-go, and undirected topologies, adaptive cooperative guidance along the line-of-sight (LOS) direction is proposed to guarantee impact time synchronization. Next, novel nonsingular terminal sliding mode (NTSM) is designed to establish adaptive fixed-time guidance law for steering LOS angular rates to the origin or its small neighbourhood. Without the knowledge of target manoeuvre, the proposed cooperative guidance law can be provided by lateral and longitudinal accelerations of each missile, while more reasonable and rigorous analysis of fixed-time stability is carried out through the Lyapunov theory. Within the specified time, both control tasks of simultaneous attack and the desired impact angles can be completed before the final time of the guidance process. Finally, numerical simulations demonstrate the feasibility and effectiveness of the proposed scheme.

Distributed cooperative tracking and cooperative guidance against maneuvering aerial target

This paper designs finite-time distributed state estimation algorithm and cooperative guidance law for high-maneuvering target salvo attack. Considering the maneuvering property of the target, a novel maneuvering model is proposed, which can adjust the maneuvering parameter adaptively. Based on the maneuvering target model, the interactive multiple models (IMM)-based distributed cubature information filtering (DCIF) algorithm is designed by two phases, named local filtering phase and consensus fusion phase. The final estimate results can be obtained by fusing the parallel local estimate results effectively with finite consensus fusion steps, which are used to design the cooperative guidance law for maneuvering target salvo attack. Besides, with necessary mild conditions, the lower bound and upper bound of the information matrix are proved to exist, and the stability of the proposed distributed algorithm is analyzed by Lyapunov stability theory and stochastic stability theory. Besides, the cooperative attack simulation example is given to validate the effectiveness of the proposed algorithm.

Considering the Cooperative Guidance Law of Multiple Vehicles in Detection Configuration

Considering the Cooperative Guidance Law of Multiple Vehicles in Detection Configuration

Three-Dimensional Cooperative Guidance Law Against Maneuvering Target with Time-Varying Communication Delays

Three-Dimensional Cooperative Guidance Law Against Maneuvering Target with Time-Varying Communication Delays

An integrated cooperative guidance design for target assignment and simultaneous attack on multiple targets

This paper proposes an integrated cooperative guidance strategy for multiple unmanned aerial vehicles to simultaneously attack multiple targets. To solve the challenging cooperative attack problem coupled with the target assignment problem simultaneously in a unified one-phase framework, a novel auxiliary index denoted as the integrated relative distance is designed and analysed from two opposite perspectives. Because of its special properties, the proposed integrated relative distance plays a crucial role in evaluating dynamic engagement situations between attackers and targets, and it further provides a criterion for whether the cooperative attack mission is completed. Then all integrated relative distances are minimised to directly derive a cooperative guidance law for attackers based on optimal control theory. The simultaneous minimisation of integrated relative distances from both forward and backward perspectives ensures that each target is destroyed by at least one attacker and all attackers are fully exploited to obtain optimal attack performance. By this means, the target assignment problem is automatically solved and the cooperative simultaneous attack is achieved. Several simulation cases are presented to illustrate the effectiveness of the proposed integrated cooperative guidance strategy.

Three dimensional cooperative guidance for intercepting a manoeuvering target

AbstractIn this paper, an optimal distributed guidance law is proposed for cooperatively intercepting a manoeuvering target in three dimensional (3D) framework. Based on the 3D kinematic model of interceptors and the target, the kinematic engagement equations in line‐of‐sight (LOS) coordinate can be obtained. Along the LOS direction, a finite‐time consensus based on directed communication topology is applied to guarantee arrival‐time coordination of multiple interceptors, and sliding mode control is adopted to compensate target manoeuver. In the plane perpendicular to LOS, optimal control is used to design guidance law such that closed‐loop LOS angular rates converge to a tunable small neighbourhood of zero. The proposed cooperative guidance law is proved in theory, and its effectiveness is verified by simulations.

Distributed adaptive cooperative guidance against maneuvering targets with time-varying terminal angle constraint and overload saturation

Distributed adaptive cooperative guidance problem for multiple missiles intercepting a maneuvering target with time-varying terminal angle constraint and overload saturation is investigated in this paper. First of all, an extended state observer (ESO) is designed for each missile which can estimate the line-of-sight (LOS) rate and unknown external disturbances simultaneously. Secondly, a sliding manifold is proposed for each missile which consists of states of the ESO and neighbor terminal angle formation error. Then, a distributed cooperative guidance law is presented which can achieve the terminal angle constrained cooperative guidance. Furthermore, in order to deal with overload saturation, an auxiliary state is designed for the stability of the whole guidance system. Thirdly, the design process of cooperative guidance law is summarized as a guidance algorithm and the stability of the guidance error dynamics is proved via Lyapunov theories. Finally, the validity of the presented cooperative guidance algorithm is demonstrated by a numerical example.