Bong-Gyun Park

Bias-Shaping Method for Biased Proportional Navigation with Terminal-Angle Constraint

F OR decades, many advanced guidance laws with terminalimpact-angle constraints have been devised to maximize the warhead effect of antiship or antitank missiles and to ensure a high kill probability. The proposed suboptimal guidance with a terminal body-attitude constraint for reentry vehicles in [1] appears to be the first attempt to design an impact-angle-constrained guidance. In [2], an energy-optimal impact-angle control lawwas proposed by solving the linear quadratic optimal control problem with arbitrary missile dynamics. As an extension of this study, the authors also proposed an optimal impact-angle controller that can minimize the time-to-go weighted energy-cost function [3]. Using the Schwartz inequality and differential game theory, terminal-impact-angle-constrained guidance laws for maneuvering targets were developed in [4,5], respectively. To intercept a stationary target with zero terminal acceleration as well as a specified impact angle, the guidance law called the time-to-go polynomial guidance law was suggested in [6], where the acceleration command was assumed initially as a polynomial function of the time-to-go with two unknown coefficients. In [7], a modified proportional navigation (PN) guidancewith a time-varying bias, which is a function of relative range, was proposed using a nonlinear planar engagement and Lyapunov-like function. Although various guidance laws to control the impact angle have been developed so far, most of these laws are difficult to implement, especially for a passive homing missile equipped with an infrared seeker, because an accurate time-to-go estimation or range information is required. The authors of [8–10] proposed two-phase guidance schemes with terminal-angle constraints on the basis of the conventional PN guidance. The guidance scheme suggested in [8] comprises PN guidance with a navigation gainN < 2 for covering all impact angles from 0 to −π and PN with N 2 for intercepting stationary targets with a desired impact angle in surface-to-surface engagements. This guidance scheme was further extended to the case of moving targets in [9]. Using the biased PN (BPN) guidance, the authors of [10] developed a similar two-phase scheme in which the missile follows BPN with a constant bias for the initial homing phase and then switches to PN (i.e., BPN with zero bias) when the integral value of the bias satisfies a certain value calculated from initial engagement conditions and desired impact angle. Because these two-phase guidance schemes only use the line-of-sight (LOS) rate information for the impact-angle control, they can be applied to passive homingmissile systems. However, these guidance schemes have some drawbacks. 1) If the limitation of missile acceleration capability exists, a large miss distance or impact-angle error is generated. 2) A higher look angle, which may result in seeker lock-on failure or instability, is produced in the first-phase guidance. To overcome the drawbacks resulting from the look angle and acceleration limits, we first propose a bias-shaping method based on the two-phase BPNguidance scheme of [10], which can achieve both the terminal-angle constraint and look-angle limitation to maintain the seeker lock-on condition. Next, we investigate analytically the guidance performance of BPN with the proposed bias-shaping method in consideration of the limited acceleration capability. The proposed bias-shaping method consists of two time-varying biases and switching logic similar to the proposed logic of [11] and only requires the LOS rate information to generate the guidance command, thereby easily implementing the proposed law in practical passive homing missiles.

Optimal impact angle control guidance law considering the seeker’s field-of-view limits

A new optimal guidance problem with impact angle constraint and seeker’s field-of-view limits is investigated for a missile with a strapdown seeker. Impact angle control to satisfy the terminal flight path angle constraint causes missile trajectories to be very curved. Since a strapdown seeker has a narrower field-of-view than a gimbaled seeker, a missile with a strapdown seeker using the impact angle control guidance law can miss its target within the field-of-view during the homing phase, leading to the failure of the mission. Therefore, considering the seeker’s field-of-view limits is a key issue for missiles with strapdown seekers when implementing the impact angle control guidance law. To handle the seeker’s field-of-view limits in the homing guidance problem, a look angle, which is defined as the angle between the velocity vector and the line-of-sight, is considered as an inequality constraint. Based on the optimal control theory with a state variable inequality constraint, the optimal impact angle control guidance law with the seeker’s field-of-view limits is designed. The proposed guidance law is made up of three types of optimal acceleration commands: the first command is to reach the maximum look angle of the seeker, the second is to keep the seeker look angle constant on the constraint boundary, and the third is to intercept the target with the desired impact angle. Nonlinear simulations are performed to validate the proposed approach. In addition, comparisons with other guidance laws considering the limitation of the seeker look angle are carried out via nonlinear simulations, and the results show that the proposed guidance law is more efficient in terms of the control energy.

Two-Dimensional Trajectory Optimization for Soft Lunar Landing Considering a Landing Site

This paper addresses minimum-fuel, two-dimensional trajectory optimization for a soft lunar landing from a parking orbit to a desired landing site. The landing site is usually not considered when performing trajectory optimization so that the landing problem can be handled. However, for precise trajectories for landing at a desired site to be designed, the landing site has to be considered as the terminal constraint. To convert the trajectory optimization problem into a parameter optimization problem, a pseudospectral method was used, and C code for feasible sequential quadratic programming was used as a numerical solver. To check the reliability of the results obtained, a feasibility check was performed.

Time-delay control for integrated missile guidance and control

In this paper, integrated missile guidance and control systems using time-delay control (TDC) are developed. The next generation missile requires that an interceptor hits the target, maneuvering with small miss-distances, and has lower weight to reduce costs. This is possible if the synergism existing between the guidance and control subsystems is exploited by the integrated controller. The TDC law is a robust control technique for nonlinear systems, and it has a very simple structure. The feature of TDC is to directly estimate the unknown dynamics and the unexpected disturbance using one-step time-delay. To investigate the performance of the integrated controller, numerical simulations are performed as the maneuver of the target. The results show that the integrated guidance and control system has a good performance.

Composite Guidance Scheme for Impact Angle Control Against a Nonmaneuvering Moving Target

I N ADVANCED guidance law designs, impact angle control has been widely required to maximize the effect of thewarhead and to achieve a high kill probability. Since the first paper for impact angle control [1] was published, to the best of our knowledge, many guidance laws with impact angle constraint have been studied. Ryoo et al. [2] proposed a pure energy optimal guidance law with impact angle constraint. As an extension of this work, Ryoo et al. [3] proposed an optimal impact angle control guidance law minimizing the time-to-go weighted energy cost function. Lu et al. [4] developed three-dimensional guidance laws, which were based on proportional navigation (PN) with adaptive guidance parameters, to achieve impact angle requirements. Ratnoo and Ghose proposed a two-phase guidance law for capturing all possible impact angles against a stationary target [5] and a nonstationary nonmaneuvering target [6]. The proposed guidance law used PN with N < 2 for the initial phase to cover impact angles from zero to −π through an orientation trajectory and PNwithN ≥ 2 for the final phase to intercept the target with the desired impact angle. Erer andMerttopcuoglu [7] proposed a similar two-phase guidance law switching from biased PN to PN when the integral value of the bias met a certain value determined by engagement conditions. Most of research mentioned has focused on the impact angle as well as a zero terminal miss distance. The impact angle control, however, made the missile trajectory highly curved, which might have then missed the target within the seeker’s lookangle limit. Since this leads to the mission failure, it is very important to consider the missile’s physical constraints, such as the seeker’s look-angle and maximum acceleration limits. Recently, studies considering the look-angle limits as well as the impact angle have been carried out. Park et al. [8] proposed a composite guidance law comprising PN with N 1 to maintain the constant look angle and PNwithN ≥ 2 to intercept the target with the desired impact angle. In [9], the error feedback loop of the look angle was included in PN with N 1 for robustness and converging from the arbitrary look angle to the desired one. In [10], a pure energy optimal guidance lawwith an impact angle constraint and the seeker’s look-angle limit was developed using optimal control theory with state variable inequality constraint. Kim et al. [11] proposed a biasshaping method, based on the work in [7], to consider the look-angle and acceleration limits. Tekin and Erer [12] presented a two-phase guidance law with a numerical process for calculating navigation gains to handle the look-angle limits and acceleration constraints. Also, Erer et al. [13] proposed another two-phase guidance scheme to address the look-angle constraint problem, which can select an initial phase guidance lawbetween PNandbiasedPN.Ratnoo [14] dealt with a similar problem to [8] and showed analytic guarantees for achieving all impact angles with any finite field-of-view (FOV) limit. These works have been studied against stationary targets, so the impact angle errors may appear at the instant of interception if the guidance laws presented in [8–14] are applied to the case of moving targets. In this Note, a composite guidance scheme, studied in [8,9], is extended to the case of a nonmaneuvering moving target. The proposed guidance scheme is composed of modified deviated pure pursuit (DPP) with the error feedback loop of the look angle for the initial guidance phase and PN with N ≥ 3 for the final guidance phase: the first phase is to maintain the constant look angle of the seeker, and the second is to intercept themoving targetwith a terminal angle constraint. The switching of guidance phases occurs when satisfying a specific line-of-sight (LOS) angle determined by engagement conditions. Guidelines on the gain tuning of modified DPP and calculation of themaximumachievable impact angle, which is calculated by taking into account the seeker’s look-angle and maximum acceleration limits, are also investigated for guidance designers.

Range-to-go weighted optimal guidance with impact angle constraint and seeker's look angle limits

In this paper, an impact angle control guidance law, which considers simultaneously the impact angle and seekers look angle constraints, is proposed for a constant speed missile against a stationary target. An optimal control theory with state variable inequality constraint is used to design the guidance law, for which a control energy performance index with the weighting function of the range-to-go is minimized. Various forms of guidance and trajectory shaping are possible by selecting a proper gain of the weighting function. To handle the seekers look angle limits when the missile trajectory is highly curved by controlling the impact angle, the proposed guidance law generates three types of acceleration commands as the guidance phases: the first acceleration command for an initial guidance phase makes an initial seekers look angle reach the maximum look angle; the second one for a midguidance phase maintains the maximum look angle; the final one for a terminal guidance phase intercepts the target with the desired impact angle. The performance of the proposed guidance law was investigated with nonlinear simulations for various engagement conditions.

Composite Guidance Law for Impact Angle Control of Passive Homing Missiles

In this paper, based on the characteristics of proportional navigation, a composite guidance law is proposed for impact angle control of passive homing missiles maintaining the lock-on condition of the seeker. The proposed law is composed of two guidance commands: the first command is to keep the look angle constant after converging to the specific look angle of the seeker, and the second is to impact the target with terminal angle constraint and is implemented after satisfying the specific line of sight(LOS) angle. Because the proposed law considers the seeker`s filed-of-view(FOV) and acceleration limits simultaneously and requires neither time-to-go estimation nor relative range information, it can be easily applied to passive homing missiles. The performance and characteristics of the proposed law are investigated through nonlinear simulations with various engagement conditions.

Two-dimensional Trajectory Optimization of a Soft Lunar Landing from a Parking Orbit Considering a Landing Site

Abstract In this paper, minimum-fuel, two-dimensional trajectory optimization from a parking orbit to the desired landing site is presented. The landing site is usually not considered when performing the trajectory optimization. However, to design the precise trajectories to land at the desired site, the landing site has to be considered as the terminal constraint. To convert the trajectory optimization problem into a parameter optimization problem, a pseudospcetral (PS) method is used, and CFSQP is used as a numerical solver. To check that the results obtained are good solutions, the feasibility check is performed.

Biased PNG With Terminal-Angle Constraint for Intercepting Nonmaneuvering Targets Under Physical Constraints

A biased proportional navigation guidance law, considering the seekers look angle and acceleration capability limits, for impact-angle-control against nonmaneuvering targets is proposed. The proposed law consists of two time-varying biases: One is to achieve the desired impact angle within the command limit; the other is to keep the look angle constant for not exceeding the boundary value. Under physical constraints, the maximum achievable impact angle is obtained for practical implementation. The performance of the proposed law is demonstrated through nonlinear simulations.

Optimal Midcourse Guidance Law with Flight Path Angle and Lead Angle Constraints to Reach Circular Target Area

Abstract An optimal midcourse guidance law with flight path angle and lead angle constraints to reach a circular target area is proposed here. In this paper, the circular target area is defined as a circle which center is a target to intercept and radius becomes a seekers detection range. This guidance law is especially useful for a missile which has a strap-down type seeker with limited F.O.V. (Field Of View) because a missiles lock-on condition can be satisfied by imposing a final lead angle constraint with consideration of a seekers F.O.V. limit. In addition, through a final flight path angle constraint, a missile can occupy an advantageous homing point. This guidance law is derived from an optimal control theory which minimizes a range weighted control energy and its characteristics are studied further. Finally, performance of this guidance law is verified by a numerical simulation.