Cooperative Guidance Strategy Research Articles

Multiple-stage spatial–temporal cooperative guidance without time-to-go estimation

This paper investigates the spatial–temporal cooperative guidance problem for multiple flight vehicles without relying on time-to-go information. First, a two-stage cooperative guidance strategy, namely the cooperative guidance and the Proportional Navigation Guidance (PNG) stage strategy, is developed to realize the spatial–temporal constraints in two dimensions. At the former stage, two controllers are designed and superimposed to satisfy both impact time consensus and impact angle constraints. Once the convergent conditions are satisfied, the flight vehicles will switch to the PNG stage to ensure zero miss distance. To further extend the results to three dimensions, a planar pursuit guidance stage is additionally imposed at the beginning of guidance. Due to the independence of time-to-go estimation, the proposed guidance strategy possesses great performance in satisfying complex spatial–temporal constraints even under flight speed variation. Finally, several numerical simulations are implemented to verify the effectiveness and advantages of the proposed results under different scenarios.

Adaptive Terminal Time and Impact Angle Constraint Cooperative Guidance Strategy for Multiple Vehicles

This paper addresses the guidance of various flight vehicles under multiple constraints in three-dimensional space. A cooperative guidance strategy that satisfies both time and angle constraints is designed to reach a moving target. The strategy is organized into two parts: modeling and programming calculations. First, a nonlinear motion model for guidance is established and normalized, including both the vehicle and the target. Later, the arrival method is automatically determined according to the strategy and depending on the type of target. The cooperative terminal time is determined based on an augmented proportional navigation method. An improved model predictive static programming (MPSP) algorithm was designed as a means of adjusting the adaptive terminal time. Then, the algorithm was used to update the control quantity iteratively until the off-target quantity and the angle of constraints were satisfied. The simulation results showed that the strategy could enable multiple flight vehicles at different initial positions to reach the target accurately at the same time and with the ideal impact angle. The strategy boasts a high computational efficiency and is capable of being implemented in real time.

Cooperative Guidance Strategy for Active Spacecraft Protection from a Homing Interceptor via Deep Reinforcement Learning

The cooperative active defense guidance problem for a spacecraft with active defense is investigated in this paper. An engagement between a spacecraft, an active defense vehicle, and an interceptor is considered, where the target spacecraft with active defense will attempt to evade the interceptor. Prior knowledge uncertainty and observation noise are taken into account simultaneously, which are vital for traditional guidance strategies such as the differential-game-based guidance method. In this set, we propose an intelligent cooperative active defense (ICAAI) guidance strategy based on deep reinforcement learning. ICAAI effectively coordinates defender and target maneuvers to achieve successful evasion with less prior knowledge and observational noise. Furthermore, we introduce an efficient and stable convergence (ESC) training approach employing reward shaping and curriculum learning to tackle the sparse reward problem in ICAAI training. Numerical experiments are included to demonstrate ICAAI’s real-time performance, convergence, adaptiveness, and robustness through the learning process and Monte Carlo simulations. The learning process showcases improved convergence efficiency with ESC, while simulation results illustrate ICAAI’s enhanced robustness and adaptiveness compared to optimal guidance laws.

Adaptive cooperative guidance with seeker-less followers: A position coordination-based framework

This paper addresses the problem of cooperative guidance for multiple flight vehicles, comprising a leader and seeker-less followers. All the flight vehicles are required to hit the target simultaneously at a desired impact time, even though the target information is unavailable to the followers. To achieve this, a fixed-time convergent guidance law is proposed for the leader, incorporating impact time control. We introduce an adaptive cooperative guidance strategy for the seeker-less followers through coordinated position location relative to the leader. The simulation results validate the effectiveness satisfactorily coinciding with the theoretical analysis.

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.

Impact Time Consensus Cooperative Guidance Against the Maneuvering Target: Theory and Experiment

Cooperative guidance issues with impact time consensus against a maneuvering target are considered in this paper. Different from the existing achievements, the expected impact time does not need to be predesigned, which is coordinated by multiple missiles using the neighboring information. First, the impact time consensus command is generated by using the maximum consensus algorithm of time-to-go for each missile. Second, an analytical cooperative guidance law with bias proportional guidance form is proposed for achieving impact time consensus. In addition, the convergence and the stability of the proposed algorithm and guidance law are analyzed. Third, an equivalent guidance experimental platform is constructed for testing the performance of the proposed cooperative guidance strategy. Finally, the numerical simulation and experimental results are presented to verify the effectiveness of the proposed theoretical cooperative guidance methods.

Research on Cooperative Strategy Guidance Based on Game Theory

Multi-missile cooperative combat refers to the joint execution of the same combat task through the cooperation and cooperation between multiple same missiles or multiple different missiles. As the combat environment of the future battlefield becomes more and more complex, not only the precision guidance performance of the missile itself can be continuously improved, but also the cooperative operation of multiple missiles is needed to maximize the effectiveness of group combat. In this paper, the cooperative guidance strategy of multi-to-one interception problem will be studied again according to the game theory. According to the establishment of multi-to-one missile-target game model, the strategy set of missile and target is determined. Then according to the multi-to-one missile-target game model, the system equation is determined, and the cooperative guidance strategy is obtained by calculating the results. Finally, the simulation results are analyzed to further verify the effectiveness of the cooperative interception guidance law based on this method.

Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target

In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.

Optimal Cooperative Guidance Strategies for Aircraft Defense with Impact Angle Constraints

Given the limitations of escape maneuvers and decoy deployment of combat aircraft under missile attacks; active defense dramatically improves the survival chances by launching active defense missiles to intercept incoming missiles. Different from previous work, this paper implemented impact angle constraints on the defense missile to achieve a better defense effect. The low-cost active defense missile with limited maneuverability is considered to cooperate with the aircraft through three mechanisms, namely two-way cooperation without any predetermined strategy, one-way cooperation with the defense missile employing a linear guidance strategy, and one-way cooperation with independent evasion maneuver for the target. Three optimal cooperative guidance strategies with impact angle constraints were investigated. Finally, a nonlinear two-dimensional model for agents with first-order autopilot dynamics was simulated to verify the performance of the proposed strategies. The simulation results indicated that the cooperative mechanism directly affects the available range of impact angles, and the constraints of a big impact angle can be realized by introducing the nonlinear model parameters and considering the angle variation between the velocity vector and the initial line-of-sight. Furthermore, the two-way cooperative mechanism achieves the best performance and more flexible solutions to accommodate different vehicle maximum overload limits.

Cooperative guidance laws for interception of active maneuvering target under information symmetric and asymmetric conditions

This paper proposes novel cooperative guidance strategies with dynamic game properties for a group of interceptors to intercept an active intelligent maneuvering target under both information symmetric and asymmetric conditions. A novel differential game guidance law is proposed to intercept the target with an active maneuvering strategy based on relative distances, relative velocities, and remaining flight time under information symmetric conditions. In the case where the team of interceptors has information superiority, a reasonable evading strategy is designed for the target, and a cooperative optimal guidance law is proposed for interceptors taking the target's evading strategy into consideration. When neither side has the knowledge of the opponent's maneuvering strategy, a novel robust adaptive interception guidance law is designed based on the reduction of the surrounding area regarding the target's maneuver as unknown disturbances. Numerical simulations are carried out to illustrate the effectiveness and superiority of proposed cooperative guidance laws.

Autonomous Cooperative Guidance Strategies for Unmanned Aerial Vehicles During On-Board Emergency

This paper presents autonomous guidance strategies for both solo and group of unmanned aerial vehicles (UAVs), to be used when emergency conditions are encountered during mission. Fixed-wing UAVs equipped with batteries that serve as on-board power source are considered. They are also equipped with inertial and supervisory satellite-based navigation system. An emergency condition where limited available on-board power along with nonavailability of both ground command link and satellite-based navigation information is considered. We proposed two guidance strategies, look-lock-land and inject-contribute-exit for single- and multiple-UAV missions. An optimization model is developed to arrive at the maximum area that can be covered by spiral trajectory without violating on-board power constraints. In addition, we also proved that spiral trajectory acts like a circular highway for multiple-UAV missions. Algorithms to achieve look-lock-land, inject-contribute-exit and to compute Inertial Navigation Systems (INS) error correction factor are discussed. The performance of the proposed autonomous emergency guidance strategies is demonstrated on a sea-based oil-well-monitoring mission.

Robust nonlinear guidance strategies for survival of cooperating unmanned aerial vehicles against pursuing attackers

In this paper, cooperative guidance strategies for the survival of cooperating team of two unmanned aerial vehicles (UAVs) against two attackers are proposed. The guidance schemes are designed under the assumptions that each UAV is being pursued by one attacker without cooperation with other attacker. The guidance schemes are designed to combat attackers guided either by proportional navigation (PN) or augmented PN guidance methodologies. The attackers are lured onto a collision course with each other such that intra-attacker interception is achieved before the target UAVs are captured. Sliding mode control techniques are employed to satisfy the sufficiency conditions for the survival within a finite time. Due to the nonlinear framework used for guidance design, the proposed strategies remain effective even for the engagements with large heading angle errors. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance strategies under various engagement geometries.

True-proportional-navigation inspired finite-time homing guidance for time constrained interception

This paper addresses the problem of controlling impact time against various types of target – stationary, constant velocity, or maneuvering. Analytical expression of time-to-go, that is exact for non-maneuvering target but approximate for maneuvering ones, is first presented based on true-proportional-navigation guidance concepts. Guidance strategies are then derived, using Lyapunov theory, to meet impact time constraints, without linearizing the engagement dynamics. Hence, the proposed strategies remain effective even for large initial heading errors. Further, a cooperative guidance strategy to achieve simultaneous target interception by multiple interceptors is also proposed. Guidance commands that ensure consensus among the time-to-go values of the interceptors are utilized for this purpose. Using judicious choices of gains, the common time of target interception may be either pre-fixed, or the same may be decided cooperatively during the engagement. Stability analysis of the possible equilibria in heading angle dynamics, for different choices of parameters, is also performed. For both one-to-one and cooperative homing, simulation results are presented for various engagement scenarios to demonstrate the effectiveness of the proposed strategies.

Survival of Unmanned Aerial Vehicles by Luring Pursuers in Angle Constrained Interception

In this paper, a sliding mode control-based cooperative guidance strategy for a team of two unmanned aerial vehicles (aircraft), which ensures their survival against pursuers, is proposed. The pursuing interceptors are assumed to employ augmented proportional navigation guidance. The cooperating aircraft maneuver in a way to lure their respective pursuers to an impact angle constrained collision. The problem of controlling impact angle is first transformed to that of tracking line-of-sight angle and its rate, and then the same is achieved by enforcing sliding mode on appropriate chosen switching surface. Furthermore, the allocation of aircraft’s lateral accelerations is performed in a way to minimize the instantaneous aerodynamic drag acting on both unmanned aerial vehicles. Numerical simulations are presented to validate the effectiveness of the proposed guidance strategy under different engagement geometries.

Three-dimensional consensus algorithm for nonsingular distributed cooperative guidance strategy

This study proposes two nonsingular distributed cooperative guidance strategies to solve the problem of the three-dimensional (3D) cooperative guidance of multiple interceptors attacking a stationary target. The cooperative 3D nonlinear engagement kinematics is first formulated. We then derive guidance commands based on two expressions of the time-to-go estimate by using a combination of the multi-agent consensus algorithm and the nonsingular guidance law, where they are presented without the assumption of a small lead angle. An additional component of the guidance command is investigated to prevent the Lyapunov function from becoming negative semi-definite, and the finite-time stability of the consensus error is guaranteed. Following the convergence of the consensus error, the stability of the lead angle is presented without confining the control parameter. By using the proposed strategies, multiple interceptors can attack the target simultaneously, and the impact time is determined during engagement. A number of simulation scenarios are considered to verify the effectiveness of the proposed control strategies.

Distributed adaptive cooperative time-varying formation tracking guidance for multiple aerial vehicles system

Distributed adaptive cooperative time-varying formation tracking guidance problems of multiple aerial vehicles system against a maneuvering target are investigated. Different from the former results, the proposed cooperative guidance strategies are based on distributed time-varying formation tracking theories. Firstly, the leader aerial vehicle is designed to achieve interception with desired terminal attack angle, which provides a reference trajectory. The uncertain dynamic items and target's uncertain maneuver have been compensated. For the follower aerial vehicles, the distributed cooperative time-varying formation tracking guidance laws are raised. Adaptive distributed extended state observers are introduced to estimate the leader vehicle's states and input information. Then, an algorithm is shown for determining guidance parameters of cooperative guidance laws. Thirdly, the properties and the stabilities of the algorithm are discussed in detail. Finally, a simulation experiment is performed for showing the feasibility and effectiveness of achieved results.

Autonomous cooperative guidance based on distributed consensus and self-management

As for the time-space cooperative guidance under complex offense–defense game conditions, this article proposes a distributed time-space cooperative guidance strategy based on consensus theory and missile group (MG) self-management. The strategy consists of a three-layer cooperative guidance system: the lower layer is the impact time and angle control guidance (ITACG) based on optimal control with minimum energy consumption. The middle layer is the time-space cooperative control strategy via distributed consistency with the time-to-go as the coordination variable. The upper layer is the MG self-management strategy considering the complex attack–defense conditions. The simulation results show that the cooperative strategy can achieve simultaneous attack at different directions and improve the penetration probability and the ability to respond to the attack–defense situation effectively.

Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target

Cooperative interception of the target with strong maneuverability by multiple missiles with weak maneuverability in the three-dimensional nonlinear model is studied. Firstly, the three-dimensional nonlinear model of cooperative guidance is established. The three-dimensional reachable region is represented composed of lateral acceleration and longitudinal acceleration in the two-dimensional coordinate system. Secondly, the problem of the multiple missile's reachable coverage area is transformed into the problem of cooperative coverage. A cooperative coverage strategy is proposed and an algorithm for quickly calculating the number of required missiles is designed. Then, the guidance law based on the cooperative coverage strategy is proposed, and it is proved that cooperative interception of the target can be achieved under the acceleration limit. Moreover, the relations among the number of missiles, the initial array position of terminal guidance and the coverage area of the target’s large maneuver are analyzed. The dynamic adjustment strategy of guidance parameters is proposed to reduce the guidance error. Finally, simulation results show that multiple missiles with low maneuverability can achieve effective interception of target with strong maneuverability through the proposed cooperative strategy and cooperative guidance method.

Finite-Time Cooperative Guidance Strategy for Impact Angle and Time Control

In this article, two cooperative guidance schemes with impact angle and time constraints are proposed for multiple missiles cooperatively intercepting a maneuvering target in the presence or absence of a leader missile. First, cooperative interception with impact angle constraint is formulated based on the relative motion equation between the interceptors. Subsequently, the design of the guidance law is divided into two stages. In the first stage, based on finite-time consensus theory and the super-twisting control algorithm, the cooperative guidance law in the direction of the line of sight (LOS) is derived to control the impact time so that all missiles can simultaneously intercept the target in finite time. Then, based on finite-time sliding mode control and the super-twisting control algorithm, a finite-time convergence cooperative guidance law in the normal direction to the LOS is developed to control the intercept angle and the LOS angle rate so that each missile can accurately hit the target at a desired angle. Finally, by controlling the consensus error of flight time in the presence of a leader missile, a finite-time cooperative guidance method in the “leader–follower” scenario is derived for simultaneous arrival at the target. The proposed methods can effectively suppress chattering and ensure fast convergence in finite time. Simulation experiments are conducted to verify the effectiveness of the proposed cooperative guidance schemes.

Cooperative Salvo Based Active Aircraft Defense Using Impact Time Guidance

This letter proposes fixed-time convergent cooperative guidance strategy for target-defender team against the incoming threat of an attacker. The target lures the attacker on a collision course by nullifying its line-of-sight rate with respect to the attacker, thereby presenting itself as a bait. At each instant, the target also sends the information of estimated time-to-go of attacker-target engagement to a single defender (swarm leader), which further shares this information with a subset of other defenders. On the collision course, the attacker is likely to become non-maneuvering. The defenders thus simultaneously capture the attacker with reduced maneuverability, before attacker reaches within a vicinity of the target. Efficacy and applicability of the proposed cooperative scheme is demonstrated via numerical simulations.