Analytical solution of three-dimensional realistic true proportional navigation

Yang, Ciann Dong; Yang, Chi Ching

doi:10.2514/3.21659

Cited by 88 publications

(36 citation statements)

References 25 publications

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“…(8) (12) where A is the upper bound of the target maneuver, N 1 > 2 is the coefficient of parallel navigation and it is quite familiar (usually 3 ∼ 5),…”

Section: Guidance Law With Finite-time Convergencementioning

confidence: 99%

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Finite-time convergent guidance law based on integral backstepping control

Golestani

Mohammadzaman

Vali

2014

Aerospace Science and Technology

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“…(8) (12) where A is the upper bound of the target maneuver, N 1 > 2 is the coefficient of parallel navigation and it is quite familiar (usually 3 ∼ 5),…”

Section: Guidance Law With Finite-time Convergencementioning

confidence: 99%

“…2. According to the principles of the kinematics, the three relative acceleration components can be described as follows [12]:…”

Section: Three-dimensional Finite-time Convergent Guidance Lawsmentioning

confidence: 99%

Finite-time convergent guidance law based on integral backstepping control

Golestani

Mohammadzaman

Vali

2014

Aerospace Science and Technology

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“…The other one is pure proportional navigation (PPN), whose commanded acceleration is perpendicular to interceptor's velocity [1,2]. During the several decades after the inception of PN in 1940s, both of TPN and PPN have been researched widely and deeply [3][4][5][6][7][8][9][10][11][12]. According to the analysis of capture region, PPN has an advantage of capture capability over TPN [4,6,8,9].…”

Section: Introductionmentioning

confidence: 99%

Differential geometric modeling of guidance problem for interceptors

Chen

Bai

2011

Sci. China Technol. Sci.

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It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry theory, rather than directly decomposing the motion in the Cartesian coordinates. The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper, based on the classical differential geometry curve theory. Firstly, the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS, the kinematic equations of LOS are established, and the concepts of curvature and torsion of LOS are proposed. Simultaneously, the new relative dynamic equations between interceptor and target are constructed. Secondly, it is found that there is an instantaneous rotation plane of LOS (IRPL) in the space, in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems. The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN. In addition, the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL. After that, the differential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced, and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC. Moreover, the performance of the original guidance laws will be reduced after the differential geometric transformation. At last, an exoatmospheric interception is taken for simulation to demonstrate the differential geometric modeling proposed in this paper. kinematic equations of LOS, instantaneous rotation plane of LOS, proportional navigation, augmented true proportional navigation, LOS angular acceleration guidance law, differential geometric guidance commands Citation:

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“…The vibration disturbances can come from numerous sources including gravity gradients, attitude control reaction wheels, 1 ¡ 3 jet propulsion systems, 4 ¡ 6 thermoelastic deformation, 7,8 uid sloshing, 9 and payload-payloadinteractions. 10 There are a number of possible ways to deal with these corrupting disturbances such as using vibration isolation systems, 11 concurrently designing the structure and controller, 12 and generating vibration-reducingmotion setpoints.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Guidance Law for Landing on a Celestial Object

Liaw

Cheng

Liang

2000

Journal of Guidance, Control, and Dynamics

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IntroductionA S space vehicletechnologydevelops,the rendezvousof a space vehicle with a space station or a celestial object becomes possible and imminent. Many rendezvous guidance strategies for landing on an asteroid or the docking of two vehicles have been studied recently. The rendezvous problems of two space vehicles in two dimensions were presented in Refs. 1 and 2. Under similar dynamical equations, the rendezvous of a space vehicle with an asteroid was discussed in Refs. 3 and 4. However, the existing studies tended to neglect the combined impact of atmosphere and gravity. The Viking Lander descent to Mars through an unknown atmosphere density pro le, winds, and terrain characteristics was described in Ref. 5. Autonomous spacecraft navigation and control for a comet landing with model error and the effects of environmental disturbances was analyzed by Monte Carlo simulation in Ref. 6. The rendezvous with a celestial object usually consists of three successive phases 3 : 1) cruise or transfer to the vicinity of the celestial body, 2) approach, and 3) maneuvers near the celestial body. This Note is concerned with maneuver near the celestial body by using the generalized three-dimensional model with the effects of both gravity and atmospheric drag. Moreover, in this Note, the unmodeled perturbing forces such as solar radiation pressure and nonspherical gravitational effects are treated as disturbances. 7 These perturbing forces usually cause periodic variations 8 and will be formulated as trigonometric functions.The main goal of this Note is, from a theoretic point of view, to propose a new landing guidancelaw for ensuringthe vehiclelanding on the celestial body in a nite time and satisfying the landing constraint in the terminal phase when the space vehicle approachesa celestial body. That is, v ! 0 as r ! r a , where r a denotes the celestial radius. By properly selecting the desired trajectory, the landing process is transformed into a tracking problem. The variable structure control (VSC) technique is then applied to the design of a tracking control law. By the construction of a time-varying boundary layer, the tracking performance is shown to be achieved at an exponential convergence rate. Moreover, the modi ed guidance law attained is continuous and alleviates the classical chattering drawback of the VSC control scheme. An illustrative example is also presented to demonstrate the use of the results. Landing Control ProblemThe rendezvouskinematics model in vectorialform are given by 4Here, r, v, a, f, and d denote the position, velocity, and applied, drag, and disturbance accelerations,respectively, and l is the gravitational constant times the mass of the asteroid. The velocity v in the spherical coordinate system (r, h , u ) can be expressed as 9where r is the distance from the spacecraft to the celestial object, h and u are the azimuth and pitch angles with respect to the celestial body, and e r , e h , and e u are unit vectors along the coordinate vectors. An atmospheric model with varying density wo...

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Analytical solution of three-dimensional realistic true proportional navigation

Cited by 88 publications

References 25 publications

Finite-time convergent guidance law based on integral backstepping control

Finite-time convergent guidance law based on integral backstepping control

Differential geometric modeling of guidance problem for interceptors

Three-Dimensional Guidance Law for Landing on a Celestial Object

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