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OVER the past few years, there have been significant efforts devoted to the research and development of cooperative unmannedsystems 1–3.The formationflyingofmultipleunmanned aerial vehicles (UAVs) has been studied for radar deception, reconnaissance, surveillance, and surface-to-air-missile jamming in military operations. An example of a cooperative operational scenario of multiple vehicles is that of a small UAV flying over an urban area, dispensingmultiplemicro aerial vehicles to examinepointsof interest fromclosedistances 4.Agroupofwell-organized low-costmultiple vehicles can be far superior to a single high-technology and high-cost UAV in effectiveness. Tactical missile systems as well as UAVs provide more capabilities when they are organized as a coordinated group than when they are operated independently. Modern antiship missiles need to be able to penetrate the formidable defensive systems of battleships such as antiair defense missile systems and close-in weapon system (CIWS). CIWS is a naval shipboard weapon system for detecting and destroying incoming antiship missiles and enemy aircraft at short range. These defensive weapons with powerful fire capability and various strategies seriously intimidate the survivability of the conventional antiship missiles. Hence, antiship missile developers have made great efforts to develop a high-performance missile system with ultimate sea-skimming flight and terminal evasive maneuvering capabilities despite a huge cost. On the other hand, cooperative attack strategies have been studied to enhance survivability of the conventional ones. Here, a cooperative attack means that multiple missiles attack a single target or multiple targets cooperatively or, in a specific case, simultaneously 5,6. Clearly, it is difficult to defend a group of attackers bursting into sight at the same time, even though each member is the conventional one in performance. So the simultaneous attack ofmultiple missiles is a cost-effective and efficient cooperative attack strategy. A simultaneous attack of a group of missiles against a single common target can be achieved by two ways. The first approach is individual homing, inwhich a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. The second is cooperative homing, inwhich themissiles communicate among themselves to synchronize the arrival times. In other words, the missiles with larger times-to-go try to take shortcuts, whereas others with shorter times-to-go take detours to delay the arrival times. The first concept requires determination of a suitable common impact time before homing, but the second needs online data links throughout the engagement. Despite a number of studies on guidance problems related to timeto-go 7–10, studies on guidance laws to control impact time for a simultaneous attack are rare, except a few recent works by the authors. An impact-time-control guidance law (ITCG) for antiship missiles was developed in 5 and, as an extension of this study, a guidance law to control both impact time and angle (ITACG) was presented in 11. These individual homing methods are based on optimal control theory, providing analytical closed-loop guidance laws. Herein, the desired impact time is assumed to be prescribed before the homing phase starts. Alternatively, this Note is concerned with a new guidance law based on the second approach, cooperative homing, for a simultaneous attack of multiple missiles. Proportional navigation (PN) is a well-known homing guidance method in which the rate of turn of the interceptor is made proportional with a navigation ratio N to the rate of turn of the line of sight (LOS) between the interceptor and the target. The navigation constant N is a unitless gain chosen in the range from 3 to 5 12. Although PNwithN 3 is known to be energy-optimal, an arbitrary N > 3 is also optimal if a time-varying weighting function is included into the cost function of the linear quadratic energy-optimal problem 13,14. In general, the navigation ratio is held fixed. In some cases, however, it can be considered as a control parameter to achieve a desired terminal heading angle 15.Although PN results in successful intercepts under a wide range of engagement conditions, its control-efficiency is not optimal, in general, especially for the case of maneuvering targets 16. Augmented proportional navigation, a variant of PN, is useful in cases in which target maneuvers are significant 12. Biased proportional navigation is also commonly used to compensate for target accelerations and sensor noises or to achieve a desired attitude angle at impact 17. Even if PN and its variants are alreadywell known andwidely used, they are not directly applicable to many-to-one engagements. This Note proposes a homing guidance law called cooperative proportional navigation (CPN) for many-to-one engagements: CPN has the same structure as conventional PN except that it has a time-varying navigation gain that is adjusted based on the onboard time-to-go and the times-to-go of the other missiles. CPN uses the time-varying navigation gain as a control parameter for reducing the variance of times-on-target of multiple missiles. This Note begins with the formulation of the homing problem of multiple missiles against a single target, subject to constraints on the impact time. Next, preliminary concepts such as the relative time-togo error and the variance of times-to-go of multiple missiles are introduced and a new guidance law is proposed. Then the major property of the law is investigated and the characteristics of the law for the case of twomissiles are examined in detail. Finally, numerical simulation results illustrate the performances of the proposed law.
Jeon et al. (Thu,) studied this question.