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Cooperative Guidance Law for Target Pair to Lure Two Pursuers into Collision
Abstract and Figures
A novel cooperative defensive guidance law is presented for a two-on-two engagement. Instead of classical strategies in which evasive maneuvers are performed or additional agents (e.g., defender missiles) are deployed, the target pair lures the pursuing missiles into collision. The optimal cooperative strategy is solved using state-dependent Riccati equation method. Linearized kinematics and arbitrary-order linear adversaries’ dynamics are assumed in the guidance law derivation. Imperfect information is assumed on the relative states and the guidance laws employed by the missile pair. Guidance strategies that the pursuing missiles may employ are assumed to belong to a finite set of linear guidance laws. In addition to the proposed cooperative defensive strategy, a decentralized estimation scheme based on the multiple-model adaptive estimation approach is also presented. Guidance law and estimation performance are demonstrated using nonlinear simulations. Simulation results show the viability of the proposed guidance law and highlight the sensitivity of the guidance law to range measurement accuracy.
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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.
This letter presents a cooperative target defense strategy using nonlinear model-predictive control (NMPC) framework for a two-target two-attacker (2T2A) problem. Each attacker needs to capture a designated target individually. The objective of the two targets is to cooperate such that they lure the two attackers into a collision. We assume that the targets do not have perfect knowledge of the attacker states, and hence they estimate the attacker states using EKF. The NMPC scheme computes closed-loop optimal control commands for the targets while satisfying state and control constraints. Theoretical analysis is carried out to determine escape regions that will lead to the targets' survival or capture. Numerical simulations are carried out to evaluate the performance of the proposed NMPC-based strategy for different scenarios validating the theoretical results.
The cooperative guidance issues for multiple missiles against a maneuvering target with collision avoidance and obstacle dodging mechanism are considered. Firstly, a fully head-on guidance law is designed by using backstepping control and trajectory shaping techniques, which provides a great reference trajectory for the leader missile. Secondly, based on the modified artificial potential field (MAPF) method, a novel collision avoidance and obstacle dodging strategies in the cooperative guidance process of follower missiles is proposed. The secure time-varying line of sight (LOS) angle formation tracking guidance law is then designed for follower missiles by using backstepping control frameworks and the repulsive force obtained by the MAPF method. Finally, two numerical simulation examples are conducted to illustrate the effectiveness of proposed secure cooperative guidance strategy.
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.
A cooperative interception scenario between a maneuvering target, its defenders, and missiles attacking the said target is considered. The straightforward approach for optimal guidance laws synthesis for the scenario participants is to adopt objectives from the single agent target–missile–defender engagement analysis. This leads to a multiobjective optimization problem in which the cost function consists out of the squared miss distance and the control effort. In this article, we suggest to alter the aforementioned cost function in order to address the need to control the proximity level between the agents, a concept that is usually not accounted for in guidance law development. This approach utilizes the same quadratic framework, making it easy to add/include into traditional systems. Defensive (defenders collision avoidance) and offensive (missiles collision encouragement) cooperative distance control laws are developed for the end game phase using the same information used to implement the guidance law. Simulation results show that the desired distance control behavior can be achieved via the proposed method.
Multiple model adaptive evasion strategies from an incoming homing missile are presented. The problem is formulated in the context of an evading target aircraft having imperfect information on the relative state and on the employed guidance law and guidance parameters of the missile. The missile’s guidance strategy is assumed to belong in a finite set of linear guidance laws and to be fixed throughout the engagement. Arbitrary-order linear missile and target dynamics, bounded target control, and nonlinear kinematics are also assumed. The filter used to identify the missile’s guidance strategy is a nonlinear adaptation of the multiple model adaptive estimator, in which each model represents a possible guidance law and corresponding guidance parameters of the attacking missile. Specific limiting cases are carefully analyzed in which the attacking missile uses proportional navigation, augmented proportional navigation, or an optimal guidance law. Matched optimal evasions from these specific cases are also derived and fit into the framework of the multiple model adaptive control approach. For the limiting cases, an alternative reduced-order approach is proposed to save computational resources. Considering noisy bearing-only measurements, the performance of the proposed evasion concepts is compared through a Monte Carlo simulation campaign to the scenario when the target has full knowledge about the attacking missile and the relative state.
Observability in engagements with bearings-only measurements is a crucial factor in a homing loop. Under collision course conditions, one does not have information on range, which may result in poor performance when employing guidance laws that require estimation of the target maneuver, such as augmented proportional navigation. Maneuvering away from the collision triangle can improve the performance of the engagement because, by altering the line of sight, the bearing measurement will return some insights on the range. This work is focused on the design criteria of the maneuver. Rather than trying to optimize the maneuver with respect to some cost function, one can start by analyzing the eigenvalues of the error covariance matrix of the Kalman filter in the homing loop, properly normalized. They give, in fact, a measure of the observability of the system. A new guidance strategy is proposed, which exploits the information from the eigenvalues in the framework of a pursuit evasion differential game. A comparison of the new strategy with the classic solution of the differential game on a set of Monte Carlo samples, indicates that the proposed solution improves the performance of the engagement in terms of miss distance.
This paper presents nonlinear guidance strategies for scenarios where an aircraft launches a defender missile as a countermeasure against an incoming attacking missile. The guidance system offers an additional degree of freedom due totwo available controls, the lateral accelerations of defender and aircraft. This extra degree of freedom is used in various ways to design guidance strategies. These guidance strategies, in addition to each ensuring interception of missile, also individually allow: 1) to reduce sensitivity of guidance law to erroneous time-to-go estimates, 2) the aircraft to perform optimal evasive maneuvers, and 3) either of the aircraft or the defender to maneuver independently with their maximum limit small as compared to that of missile. The design of guidance strategies is performed in a nonlinear framework, using sliding-mode control technique, with relevant zero-effort miss variables as switching surfaces. For reduction of sensitivity against time-to-go, an additional zero-effort velocity switching surface is proposed. Simulations are presented to validate the efficacy of the proposed guidance strategies and their superior performance compared to existing classical guidance laws. The protection envelopes, which depict the variations of minimum aircraft-missile distance with respect to heading angle of missile, to ensure successful interception, are also obtained.
A three-body interception scenario is considered, where an aircraft launches a defending missile as a counterweapon against an incoming, attacking missile. Line-of-sight guidance is investigated as a prospective strategy for the defender missile, with the aircraft being the moving launch platform. Kinematic results on line-of-sight guidance with a moving/maneuvering platform are derived, showing defender-attacker interception for all attack geometries and attacker maneuvers. The speed and maximum terminal acceleration requirements are shown to be considerably lower when compared with a proportional navigation guided defender missile. It is also shown that the attacker pays maximum penalty for an evasive maneuver from the defender if the defender uses line-of-sight guidance. A cooperative guidance law is proposed for the aircraft to maximize the attacker-to-defender lateral acceleration ratio. Simulations are carried out for various attack geometries, with and without the cooperative strategy, showing better relative control effort performance for the former.
Optimal-control-based cooperative evasion and pursuit strategies are derived for an aircraft and its defending missile. The aircraft-defending missile team cooperates in actively protecting the aircraft from a homing missile. The cooperative strategies are derived assuming that the incoming homing missile is using a known linear guidance law. Linearized kinematics, arbitrary-order linear adversaries' dynamics, and perfect information are also assumed. Specific limiting cases are analyzed in which the attacking missile uses proportional navigation, augmented proportional navigation, or optimal guidance. The optimal one-on-one, noncooperative, aircraft evasion strategies from a missile using such guidance laws are also derived. For adversaries with first-order dynamics it is shown that depending on the initial conditions, and in contrast to the optimal one-on-one evasion strategy, the optimal cooperative target maneuver is either constant or arbitrary. These types of maneuvers are also the optimal ones for the defender missile. Simulation results confirm the usefulness and advantages of cooperation. Specifically, it is shown how the target can lure in the attacker, allowing its defender to intercept the attacking missile even in scenarios in which the defender's maneuverability is at a disadvantage compared with the attacking missile.
A cooperative guidance law is presented for a defender missile protecting an aerial target from an incoming homing missile The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile Fusion of measurements from both the defender missile and protected aircraft is performed A matched defender's missile guidance law is optimized to the identified homing missile guidance law It uses cooperation between the aerial target and the defender missile The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender The estimator and guidance law are combined in a multiple model adaptive control configuration Simulation results show that combining the estimations with the proposed optimal guidance law, which uses cooperation between the defending missile and protected target, yields hit to kill closed loop performance with very low control effort This facilitates the use of relatively small defending missiles to protect aircraft from homing missiles
: The problem of evading a constant speed proportional navigation pursuer is considered. Both the evader and the pursuer are assumed to have limited lateral acceleration capabilities. A time lag is included in the pursuer's guidance system. The problem of evasion is formulated as an optimal control problem with the performance criterion being the range at the point of closest approach. The type of evasive maneuver is shown to be dependent upon the initial relative positions of the target and pursuer. Typical trajectories for the target and evader are illustrated. (Author)