Generalized Vector Explicit Guidance
01 Mar 2006-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 29, Iss: 2, pp 261-268
TL;DR: In this paper, the authors proposed a new guidance law termed generalized vector explicit guidance (GENEX), which can simultaneously achieve design specifications on miss distance and final missile-target relative orientation.
Abstract: This paper proposes and evaluates a new guidance law termed generalized vector explicit guidance (GENEX). This guidance law can simultaneously achieve design specifications on miss distance and final missile-target relative orientation. The latter may be used to enhance the performance of warheads the effectiveness of which is influenced by the terminal encounter geometry. The GENEX guidance law is parameterized in terms of a design coefficient that determines the degree of curvature in the trajectory. Feasibility of GENEX guidance was demonstrated by its application to two weapon scenarios. The first was an air-to-air missile terminal homing scenario. Assuming ideal sensor information and a single-lag missile response model, the guidance was shown to perform well against an air target performing evasive maneuvers. A specified zero-aspect terminal encounter angle was achieved while simultaneously minimizing miss distance. The second application involved an air-to-surface munition released from an unmanned air vehicle. The GENEX guidance law was able to produce trajectories satisfying a terminal impact angle constraint. In addition, an engagement region of sufficient size was shown to be achievable using guidance gains scheduled with target location and weapon release altitude.
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TL;DR: In this article, the authors proposed a two-stage proportional navigation guidance (PNG) law for achieving all impact angles against stationary targets in surface-to-surface engagements, with an orientation guidance scheme for the initial phase of the interceptor trajectory.
Abstract: G UIDANCE laws with terminal impact angle constraints are widely reported in the literature [1–7]. Proportional navigation guidance (PNG) has been used for deriving impact angle constrained guidance laws for stationary and moving targets. Lu et al. [8] have used PNG in an adaptive guidance law for a hypervelocity impact angle constrained hit at a stationary target. Satisfying impact angle constraint by varying the navigation constant N of the PNG is addressed by Ratnoo and Ghose [9]. In their work [9], a two-stage PNG law is proposed for achieving all impact angles against stationary targets in surface-to-surface engagements. A biased PNG (BPNG) law proposed by Kim et al. [3] has an extra term for annulling the terminal impact angle error together with the conventional line-of-sight rate term for the lateral acceleration command. BPNG law expands the capture region of existing guidance laws against moving targets. However, the performance of BPNG law deteriorates with tail-chase kinds of engagements. The problem of achieving all impact angles against moving targets is addressed here. The idea of a two-stage PNG law, proposed by Ratnoo and Ghose [9], is further investigated and developed for nonstationary nonmaneuvering targets. It should be noted that for different values of N, the PNG law results in a set of impact angles against a moving target. However, studies on classical PNG law [10] reveal that the value of N should be greater than a minimum value for the terminal lateral acceleration demand to be bounded. The achievable set of impact angles is derived for PNG law, with the values of N satisfying the previously mentioned constraint. To achieve the remaining impact angles, an orientation guidance scheme is proposed for the initial phase of the interceptor trajectory. The orientation guidance law is also PNG law, withN being a function of the initial engagement geometry. It is proven that, following the orientation trajectory, the interceptor can switch to N 3 and achieve any desired impact angle in a surface-to-surface engagement scenario.
201 citations
TL;DR: Ohlmeyer and Phillips as discussed by the authors proposed a closed-form solution for energy-optimal impact-angle-constrained guidance laws for a stationary target by using the linear quadratic regulator technique after linearizing the engagement kinematics.
Abstract: IN MANY advanced guidance applications, it is required to intercept the target from a particular direction: that is, to achieve a certain impact angle [1–3]. Closed-form solutions for energyoptimal impact-angle-constrained guidance laws have been proposed for a stationary target by Ryoo et al. [4], who used the linear quadratic regulator technique after linearizing the engagement kinematics. The guidance law proposed by them captures all impact angles from any initial launch angle in a planar engagement scenario. Lu et al. [5] solved the problem of guiding a hypersonic gliding vehicle in its terminal phase to a stationary target using adaptive proportional navigation guidance. Ohlmeyer and Phillips [6] extended the idea of explicit guidance (proposed by Cherry [7]) to include a terminal impact angle constraint. However, the simulations by Ohlmeyer and Phillips [6] are carried out only for a vertical impact against a stationary target, and the impact angle errors encountered are sensitive to the launch altitude.
164 citations
TL;DR: In this paper, a sliding-mode approach is used to implement the guidance concept in all aerial interception geometries: namely, head-on, tail-chase, and the novel head-pursuit.
Abstract: interest is aerial interception between a missile and a maneuvering target. The guidance concept is applicable in all aerial interception geometries: namely, head-on, tail-chase, and the novel head-pursuit. Analytical conditions for existence of these different engagement geometries are derived. The guidance concept is implemented using the sliding-modeapproach. Thecommonassumption of flight alonganinitial collisiontriangle isnottaken,andthusthe guidance law is applicable for both midcourse and endgame guidance. The application in the different engagement geometries is studied via simulation. It is shown that the head-on scenario allows the smallest range of intercept angles.Italsoplacesthemostseveremaneuverabilityrequirementsontheinterceptor.Thus,insomecases,tail-chase or head-pursuit engagements should be considered instead. The choice between the two is dependent on the adversary’s speed ratio; for tail-chase, the interceptor must have a speed advantage over its target, while for headpursuit, it must have a speed disadvantage.
148 citations
TL;DR: In this paper, a nonlinear suboptimal guidance law is presented for successful interception of ground targets by air-launched missiles and guided munitions, which accurately satisfies terminal impact angle constraints in both azimuth as well as elevation simultaneously.
Abstract: A nonlinear suboptimal guidance law is presented in this paper for successful interception of ground targets by air-launched missiles and guided munitions. The main feature of this guidance law is that it accurately satisfies terminal impact angle constraints in both azimuth as well as elevation simultaneously. In addition, it is capable of hitting the target with high accuracy as well as minimizing the lateral acceleration demand. The guidance law is synthesized using recently developed model predictive static programming (MPSP). Performance of the proposed MPSP guidance is demonstrated using three-dimensional (3-D) nonlinear engagement dynamics by considering stationary, moving, and maneuvering targets. Effectiveness of the proposed guidance has also been verified by considering first. order autopilot lag as well as assuming inaccurate information about target maneuvers. Multiple munitions engagement results are presented as well. Moreover, comparison studies with respect to an augmented proportional navigation guidance (which does not impose impact angle constraints) as well as an explicit linear optimal guidance (which imposes the same impact angle constraints in 3-D) lead to the conclusion that the proposed MPSP guidance is superior to both. A large number of randomized simulation studies show that it also has a larger capture region.
144 citations
Cites background or methods from "Generalized Vector Explicit Guidanc..."
...Some of the most recent literature on this topic formulates the angle constrained guidance problem as a trajectory -shaping algorithm based on the linear optimal control theory [17,18]....
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...The vector explicit guidance law [17] can be given by the following equation:...
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...Finally, as noted by Ohlmeyer and Phillips [17], detailed analysis of realistic capture capabilities can be revealed by full-scale MonteCarlo statistical analysis, whether it is explicit guidance or nonlinear MPSP-based guidance....
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...This can perhaps be attributed to the nonlinear dynamics of the 3-D angles, m and m, which are not taken into consideration explicitly when shaping the trajectories [17,18]....
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...Vector explicit guidance laws based on the linear optimal control theory have been developed recently for stationary andmaneuvering targets [1,17,18]....
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TL;DR: To derive a state feedback command for the proposed law with terminal constraints on the impact time and angle, a polynomial function of the guidance command with three unknown coefficients is introduced, determined to satisfy the terminal impact angle constraint.
Abstract: In this paper, a new impact time and impact angle control guidance law for homing missiles against a stationary target is proposed. To derive a state feedback command for the proposed law with terminal constraints on the impact time and angle, we introduce a polynomial function of the guidance command with three unknown coefficients, one of which is determined to achieve the impact time requirement. The others are determined to satisfy the terminal impact angle constraint, as well as the zero miss distance. Because the proposed guidance law has arbitrary guidance gains, it is possible to shape the intercept trajectory and acceleration command profile by choosing proper gains in relation to the missile's capability, operational conditions, and so on.
143 citations
Cites methods from "Generalized Vector Explicit Guidanc..."
...As an extension of this study, another type of optimal impact angle control law was developed in [4], [16] by solving a linear quadratic optimal control problem with a time-to-go weighted energy cost function....
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References
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TL;DR: In this paper, a new homing guidance law is proposed to impact a target with a desired attitude angle, which is a variation of the conventional proportional navigation guidance (PNG) law which includes a supplementary time varying bias.
Abstract: A new homing guidance law is proposed to impact a target with a desired attitude angle. It is a variation of the conventional proportional navigation guidance (PNG) law which includes a supplementary time-varying bias. The proposed guidance law does not require a time-to-go estimation and has a simpler form. Analytic conditions for fulfilling the guidance goal are also provided. Simulation results demonstrate that the proposed guidance law has wider launch envelopes than the previous one and shows a good performance even against a maneuvering target.
425 citations
TL;DR: In this article, the design of a suboptimal terminal guidance system for reentry vehicles with a constraint on the body attitude angle at impact is studied, and the problem is formulated as a linear quadratic control problem.
Abstract: The design of a suboptimal terminal guidance system for reentry vehicles with a constraint on the body attitude angle at impact is studied. Permissible range of the miss distance and the body attitude angle at impact is specified. The problem is formulated as a linear quadratic control problem. The Riccati equation is derived to provide time-varying feedback gains. The desired scheme is suboptimal. The region of initial states for which the system meets the specifications becomes smaller as the initial height of the reentry vehicle at initial time is decreased.
388 citations
TL;DR: In this paper, a new and practical terminal guidance law is presented for impact angle control for two-dimensional active homing engagement scenarios, which is used to cope with missile velocity reduction due to aerodynamic drag and target maneuver.
Abstract: A new and practical terminal guidance law is presented for impact angle control for two-dimensional active homing engagement scenarios. Impact angle control is required to enhance terminal effectiveness of antitank and antiship missile systems in particular. The proposed guidance law is developed to cope with missile velocity reduction due to aerodynamic drag and target maneuver. In actual applications, the proposed guidance law is combined in cascade with a target tracking filter under the certainty equivalence principle. The proposed guidance law in conjunction with the target tracking filter is shown to be effective in antiship active homing engagement scenarios by a series of Monte Carlo simulation runs.
181 citations
10 Dec 2002
TL;DR: In this paper, the authors presented a precision guidance law with impact angle constraint for a two-dimensional planar intercept, based on the principle of following a circular arc to the target, hence the name "circular navigation guidance".
Abstract: Presents a precision guidance law with impact angle constraint for a two-dimensional planar intercept. It is based on the principle of following a circular arc to the target, hence the name "circular navigation guidance" (CNG). This law is shown mathematically to be successful over a wide range of initial conditions. Computer simulations show that CNG performs much better than an equivalent law from the literature, and that it outperforms the standard proportional navigation guidance law in terms of miss distance. A simplified law is presented that can be used without range-to-target information.
102 citations
TL;DR: In this article, a simple numerical solution for a time-optimal control law is suggested in the case of constrained missile maneuverability and impact angle for a first-order-lag autopilot.
Abstract: As a part of trajectory modulation to increase terminal effectiveness, impact angle control is required in the terminal phase of tactical missile systems Moreover, the missile systems are allowed to have only low altitude and minimum flight time to reduce the probability of detection by sensors of missile defence systems and thus to increase survivability In this paper, a simple numerical solution for a time-optimal control law is suggested in the case of constrained missile maneuverability and impact angle for a first-order-lag autopilot The numerical solution utilizes an analytic solution of a simplified problem with a zero-lag autopilot assumption to determine optimal switching instants Performance of the proposed control law is tested by a simulation study
77 citations