Jin-Ik Lee

Homing Guidance Law for Cooperative Attack of Multiple 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.

Roll-Pitch-Yaw Integrated Robust Autopilot Design for a High Angle-of-Attack Missile

This paper explores the feasibility of roll-pitch-yaw integrated autopilots for a high angle-of-attack missile. Investigation of the aerodynamic characteristics indicates strong cross-coupling effects between the motions in longitudinal and lateral directions. Robust control techniques based on H ∞ synthesis are employed to design roll- pitch-yaw integrated autopilots. The performance of the proposed roll-pitch-yaw integrated controller is tested in high-fidelity nonlinear 5-degree-of-freedom simulations. The proposed controllers are scheduled as a function of total angle of attack in a linear parameter varying framework with proportional navigation guidance laws. The integrated controller demonstrates satisfactory performance that cannot be achieved by the controller designed in a decoupled manner.

Analytic Solutions of Generalized Impact-Angle-Control Guidance Law for First-Order Lag System

To examine the effects of system lag on performance of a generalized impact-angle-control guidance law, analytic solutions of the guidance law for a first-order lag system are investigated. Under the assumptions of a stationary target and a first-order missile system with constant speed and small flight-path angle, the analytic solutions are obtained by solving a third-order linear time-varying ordinary differential equation. The solutions are expressed by combinations of polynomial, logarithmic, and infinite power series functions. The analytic solutions provide an insight into the behavior of the missile near the target: the guidance command, the acceleration of the missile, and the velocity component perpendicular to the collision course tend to diverge as the missile approaches the target. Terminal misses due to the system lag are discussed using the analytic solutions, and effects of guidance coefficients on the terminal misses are examined. Linear and nonlinear simulations are performed to verify th...

Generalized Formulation of Weighted Optimal Guidance Laws with Impact Angle Constraint

The generalized formulation of weighted optimal guidance laws with impact angle constraint is investigated here. From the generalized formulation, we explicitly find the feasible set of weighting functions that lead to analytical forms of weighted optimal guidance laws. This result has potential significance because it can provide additional degrees of freedom in designing a guidance law that accomplishes the specified guidance objective.

Optimality of Proportional Navigation Based on Nonlinear Formulation

The proportional navigation (PN) guidance law is derived for an ideal pursuer with a stationary target, by obtaining an optimal feedback solution minimizing a performance index of the range-weighted control energy. Without any linearization of system equations, the optimal PN with an arbitrary navigation constant is obtained. Thus the exact analyses on optimality of PN based on nonlinear formulation is presented here.

Command-Shaping Guidance Law Based on a Gaussian Weighting Function

In this paper, a new homing guidance law is introduced based on the energy cost weighted by a Gaussian function in order to shape the missiles trajectory and distribute the acceleration command during the engagement. This law can improve guidance performance by alleviating sensitivity with respect to initial heading error and by reducing the possibility of command saturation through distributing acceleration demand properly.

Impact-Time-Control Guidance Law With Constraints on Seeker Look Angle

An impact-time-control guidance (ITCG) law is required for simultaneous attack of multiple missiles. In application of ITCG, the limit of seeker look angle should be regarded as an important factor in homing engagement scenarios. To avoid the loss of target tracking during engagement, the seekers look angle should be confined to the seekers field-of-view limit. This paper suggests a new ITCG law for a realistic situation with constraints on seeker look angle driven by the exact nonlinear equations of motion in plane. The proposed guidance law ensures the seekers look angle to reduce monotonically from the initial value to zero at the intercept point. The resulting solution is presented in the form of proportional navigation guidance law with a time-varying navigation gain. The closed-form navigation gain can be obtained from information on the current missile-to-target range and heading angle.

Sinusoidal function weighted optimal guidance laws

In this paper, new optimal guidance laws for a stationary or a slowly moving target are proposed by solving the optimal control problem with the energy performance index weighted by sinusoidal functions. This weighting function is adopted to shape the specific guidance command: introducing a small acceleration at the initial and final time. This property is desirable for reducing the sensitivity against the initial heading error and improving terminal guidance performance. Numerical simulations are performed to determine the performance of the proposed guidance laws.

Homing Guidance Law for Reducing Sensitivity on Heading Error

In this paper, a new homing guidance is developed to reduce sensitivity to initial heading error at the beginning of the terminal guidance phase. In order to reshape the control input alleviating the sensitivity, a new performance index is proposed by introducing distribution functions to the input weighting. The distribution functions are expressed in terms of second order polynomials of time-to-go, so that it is possible to distribute the input weighting over the ight. Then, a homing guidance law is derived by applying the LQ optimal control theory to the guidance problem with the new performance index. Whilst the navigation gain is constant in the general PN guidance, the proposed guidance laws have time varying gains to ease the sensitivity to the initial heading error. The performance of the proposed guidance algorithms are veried by the mathematical analysis and

Integrated Roll-Pitch-Yaw Autopilot Design for Missiles

An roll-pitch-yaw integrated autopilot for missiles is designed for compensation of dynamics coupling. The proposed autopilot is based on the classical control technique. The gains of the proposed autopilot are optimized by using co-evolutionary augmented Lagrangian method(CEALM). Several cost functions are compared in order to find feasible control gains. For a case that a bank angle of missiles is unknown, multiple models are used in the autopilot optimization. In nonlinear simulations as well as linear simulations, the proposed autopilot provided good performances.