In this paper, a new guidance problem with the impact time constraint is investigated, which can be applied to salvo attack of anti-ship missiles. The closed form solution based on the linear formulation is derived, suggesting an additional loop for adjusting the impact time in addition to the traditional optimal guidance loop. This solution is a combination of the well-known PNG law and the feedback of the impact time error, which is the difference between the impact time by PNG and the prescribed impact time. The new guidance law called ITCG (Impact-Time-Control Guidance) can be used to guide multiple missiles to hit a stationary target simultaneously at a desirable impact time. Nonlinear simulation of several engagement situations demonstrates the performance and feasibility of ITCG. In addition, the similarity of the closed form solution and APNG is investigated and the switching rule for practical implementation is discussed.

Impact-time-control guidance law for anti-ship missiles

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.

Homing Guidance Law for Cooperative Attack of Multiple Missiles

This paper proposes a new guidance law to control both impact time and impact angle for a flight vehicle's homing problem, which can be applied for an efficient salvo attack of antiship missiles or a cooperative mission of unmanned aerial vehicles (UAVs). The proposed law can lead vehicles to home on a target at a designated impact time with a prescribed impact angle. It comprises a feedback loop and an additional control command, the first to achieve the desired impact angle with zero miss distance, and the second to control the impact time. Numerical simulations demonstrate the performance of the proposed law in the accuracy of impact angle and impact time

Guidance law to control impact time and angle

Missile guidance and pursuit

The analytic solution for the time-to-go of the pure proportional navigation guidance law against a stationary target is derived considering full nonlinear engagement kinematics without near-collision course approximation. The solution is globally exact for all flying directions with respect to the target and is generally exact for all possible values of the guidance gain. The time-to-go solution is used to design an almost-globally asymptotically stable guidance law for intercepting a stationary target with the impact time constraint. The impact-time-control guidance law is designed based on the pure proportional navigation guidance law with a modified nonlinear time-varying guidance gain. The proposed impact-time-control guidance law does not have the drawbacks of the existing impact-time-control guidance laws, such as a narrow capture zone, a limited set of feasible initial conditions, restricted achievable impact time, singularity, and nonzero terminal lateral acceleration command. Numerical simulatio...

Modified Pure Proportional Navigation Guidance Law for Impact Time Control

Two minimum-time trajectories are developed for use as a time-to-go algorithm for a missile controlled by a linear-quadratic guidance law. The first algorithm is based on the minimum normal-acceleration-weighted final time trajectory for a constant speed missile, and the second algorithm is based on the minimum final time trajectory of an accelerating missile with bounded normal acceleration. Because the initial off-boresight angle is fixed, these algorithms are expected to work well for intercepts where large off-boresight angles occur. Both time-to-go algorithms are tested in a six-degree-of-freedom simulation of a bank-to-turn missile attacking a smart target, and their miss distances are compared with those obtained by time-to-go algorithms known as range over closing speed and accelerated range over closing speed. Both algorithms give low miss distances for a wide range of intercept geometries including those with large off-boresight angles. These results are substantially improved relative to those obtained with range over closing speed. However, the accelerated range over closing speed algorithm matches the minimum-time results and is the preferred algorithm because of its simplicity.

Time-to-go prediction for homing missiles based on minimum-time intercepts

The SAEL initiative and workshop series was founded in July 2019 in a collaborative effort from international partners from the aerospace industry that include the University of Nottingham, 328 Support Services GmbH, Crane Aerospace & Electronics and the University of Cambridge. The vision of SAEL is to bring together world-leading experts from the aerospace sector to lead the shift from conventional to sustainable aviation through aircraft electrification solutions and meet the challenging climate objectives. SAEL aims to create a multidisciplinary interactive open-source technology model for designing hybrid electric airplane. It is a powerful tool to identify the critical paths to sustainable aviation, and the needed interactions amongst key stakeholders. SAEL can help policymakers identify the right experts and the critical challenges which could target research investment decisions and provide an analytical decision making framework to support ambitions like Jet Zero.

Solutions for Aircraft Electrification Leadership (SAEL) - Driving zero-net carbon aviation through an open global aircraft electrification technology framework

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Time-to-go prediction for homing missiles based on minimum-time intercepts

Solutions for Aircraft Electrification Leadership (SAEL) - Driving zero-net carbon aviation through an open global aircraft electrification technology framework