Three-Dimensional Guidance Law for Landing on a Celestial Object

Abstract

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...

Finite-time guidance laws for landing process of a spacecraft subjected to disturbances

“…Based on two-dimensional landing geometry [2,3], dynamical equations related to rendezvous problem of a spacecraft with an astronomical body are given by (5). This model has considered gravity effects, atmospheric drag, and disturbances.…”

“…The latest stage is deeply affected by many challenges including complicated dynamics, parameter uncertainties, combinatorial impacts of gravity and air drag, solar radiations, non-spherical astronomical body, environmental disturbances, and so on [2]. By considering the aforementioned motivation, numerous guidance strategies [1][2][3][4][5][6] have been introduced to study the discussed landing process. Most of these strategies suffer from various deficiencies reviewed in the following paragraph briefly.…”

“…As the second shortcoming, some researches [1-3, 5, 6] have neglected the influences of atmospheric drag and gravity. Finally, as the third disadvantage, many researches [1][2][3][4][5][6] have not considered the environmental disturbances and uncertainties in the model of the landing process.…”

Robust tracking of guidance trajectory for probe pinpoint soft landing on small bodies

“…Many scholars have made a large number of contributions to the study of orbital motion, guidance and control around asteroids, including translation, descent and land near asteroids. Threedimensional guidance laws have been proposed and the landing process are transformed into a tracking problem by properly selecting the desired trajectory, and the VSC technique has been used to design the tracking control law in [4]. A method for descent using feedback control on altitude and thrust modulation has been developed in [5].…”

“…The nominal acceleration of the probe along with an axis is planned as the function: are the parameters to be determined, and they can be computed when the initial and end condition are and t v denote the initial velocity and terminal velocity, and go t is the descent time. Then the planned descent curve and descent velocity curve can be shown in(4).…”