Search

Use of a debris-tether-tug (DTT) system has been recognized as one of the most promising techniques for space debris removal. Attitude motion of the debris may give rise to severe disturbances to the debris removal system. In this case, a conventional DTT system with a single tether may no longer be capable of removing the debris in a stable manner. A hierarchical tether architecture is proposed to stabilize the debris with a main tether from the tug branched into multiple sub-tethers attached to the edges of the debris. The primary goal of this paper is to study the dynamics of a DTT system consisting of a tug, a rigid debris and the proposed tether architecture. First, a three-dimensional dynamics model is developed using Kane's method. A simplified model is studied analytically to determine the equilibrium configurations and their stability, and the frequencies of oscillation about the stable equilibrium points. Numerical simulations are then conducted to verify the analytical results with both rigid and elastic tethers. Additionally, the stabilization effect of the branched tether system is investigated considering various debris angular velocities.

Missions to asteroids are now an important component of the space exploration program of major space agencies in the world, with the goal of better understanding the formation of the Solar system and learn about their dynamics to be able to react in case of a possible collision with the Earth. As binary asteroids compose approximately 16% of near Earth asteroids, they are getting more attention from researchers. One mission is currently being planned to binary asteroid system 65803 Didymos. This mission motivates research on the dynamics of a spacecraft near a binary asteroid. Since the primary bodies of these binary systems have small masses, perturbations like the Solar Radiation Pressure (SRP) or the shape of the primary bodies have a great influence on the dynamics of a spacecraft in their vicinity. Studies that already exist on the effect of the SRP on the dynamics of a spacecraft near binary asteroid systems have mostly used low-fidelity SRP acceleration models, such as the cannonball model or simple flat plate model with a purely reflecting spacecraft. This study shows how the choice of the model influences the strength of the SRP acceleration acting on the spacecraft and how it is possible to take advantage of the choice of the nominal attitude of the spacecraft to influence how the SRP affects the spacecraft dynamics when using a more complex SRP acceleration model. Various types of trajectories are studied, with different results and conclusions.

One of the most promising techniques to capture large debris on orbit consists in the use of tether-nets. With this concept currently at a medium technological readiness level only, numerical studies on tether-net removal missions are still needed. This paper presents a versatile simulator developed with the aim of gaining insight into the dynamics of tether-net capture of space debris. Its modular architecture supports multiple modeling choices and allows simulating diverse capture scenarios with different system designs. Simulation results are shown for the capture of a realistic launcher upper stage with the representation of the main components of the system, consisting in chaser, main tether, net, and two possible configurations of a closing mechanism. It is shown that only a closing mechanism with more than one attachment to each side of the net can guarantee containment of this type of debris after capture. It is also observed that a safer capture scenario is one in which the axis of rotation of the target is parallel to the direction of ejection of the net. Additional simulation results suggest that tether-nets could be used to capture not only large debris, but also small asteroids, and that this simulator could enable future studies.

This research addresses the design and testing of a debris containment system for use in a tether-net approach to space debris removal. The tether-net active debris removal involves the ejection of a net from a spacecraft by applying impulses to masses on the net, subsequent expansion of the net, the envelopment and capture of the debris target, and the de-orbiting of the debris via a tether to the chaser spacecraft. To ensure a debris removal mission's success, it is important that the debris be successfully captured and then, secured within the net. To this end, we present a concept for a net closing mechanism, which we believe will permit consistently successful debris capture via a simple and unobtrusive design. This net closing system functions by extending the main tether connecting the chaser spacecraft and the net vertex to the perimeter and around the perimeter of the net, allowing the tether to actuate closure of the net in a manner similar to a cinch cord. A particular embodiment of the design in a laboratory test-bed is described: the test-bed itself is comprised of a scaled-down tether-net, a supporting frame and a mock-up debris. Experiments conducted with the facility demonstrate the practicality of the net closing system. A model of the net closure concept has been integrated into the previously developed dynamics simulator of the chaser/tether-net/debris system. Simulations under tether tensioning conditions demonstrate the effectiveness of the closure concept for debris containment, in the gravity-free environment of space, for a realistic debris target. The on-ground experimental test-bed is also used to showcase its utility for validating the dynamics simulation of the net deployment, and a full-scale automated setup would make possible a range of validation studies of other aspects of a tether-net debris capture mission.

It is a new design concept to employ control moment gyroscopes (CMGs) as reactionless actuators for space robots. Such actuation has several noticeable advantages such as weak dynamical coupling and low power consumption over traditional joint motor actuation. This paper presents a robust control law for a CMG-actuated space robot in presence of system uncertainties and closed-chain constraints. The control objective is to make the manipulation variables to track the desired trajectories, and reduce the possibility of CMG saturation simultaneously. A reduced-order dynamical equation in terms of independent motion variables is derived using Kane's equations. Desired trajectories of the independent motion variables are derived by minimum-norm trajectory planning algorithm, and an adaptive sliding mode controller with improved adaptation laws is proposed to drive the independent motion variables tracking the desired trajectories. Uniformly ultimate boundedness of the closed loop system is proven using Lyapunov method. The redundancy of the full-order actual control torques is utilized to generate a null torque vector which reduces the possibility of CMG angular momentum saturation while producing no effect on the reduced-order control input. Simulation results demonstrate the effectiveness of the proposed algorithms and the advantage of weak dynamical coupling of the CMG-actuated system.

This study addresses a relative position coordinated control problem for spacecraft formation flying subject to directed communication topology. Two different kinds of communication delay cases, including time-varying delays and arbitrarily bounded delays are investigated. Using the backstepping control technique, two virtual velocity control inputs are firstly designed to achieve coordinated position tracking for the kinematic subsystem. Furthermore, a hyperbolic tangent function is introduced to guarantee the boundedness of the virtual controller. Then, a finite-time control algorithm is designed for the dynamic subsystem. It can guarantee that the virtual velocity can be followed by the real velocity after finite time. It is theoretically proved that the proposed control scheme can asymptotically stabilize the closed-loop system. Numerical simulations are further presented that not only highlight closed-loop performance benefiting from the proposed control scheme, but also illustrate its superiority in comparison with conventional formation control schemes.

This paper investigates the finite time coordinated formation control problem for spacecraft formation flying (SFF) under the assumption of directed communication topology. By using the neighborhood state measurements, a robust finite time coordinated formation controller is firstly designed based on the nonsingular terminal sliding mode surface. To address the special case that the desired trajectory of the formation is only accessible to a subset of spacecraft in the formation, an adaptive finite time coordinated formation controller is also proposed by designing a novel sliding mode surface. In both cases, the external disturbances are explicitly taken into account. Rigorous theoretical analysis proves that the proposed control schemes ensure that the closed-loop system can track the desired time-varying trajectory in finite time. Numerical simulations are presented that not only highlights the closed-loop performance benefits from the proposed control algorithms, but also illustrates the effectiveness in the presence of external disturbances when compared with the existing coordinated formation control schemes.

Dynamic analysis and trajectory tracking of a Tethered Space Robot (TSR) is investigated in this paper. A hybrid controller is used to perform the control task. It consists of two components, the first one deals with librational motion of the tether, while the second one takes care of the manipulator motion. A Nonlinear Model Predictive Control (NMPC) approach is used to control the tether libration; for this purpose, the libration is described by a single degree of freedom and the tether length rate is employed as the input to suppress the librational motion. A modified Computed Torque Method (CTM) is used to control the manipulator motion. The dynamic interaction between the manipulator motion and the librational motion is considered both in the system dynamics and control of the system. Using numerical simulations, performance of the proposed control system is evaluated for end-effector positioning as well as for trajectory tracking for two cases: a Low Earth Orbit (LEO) and the Geostationary Earth Orbit (GEO).

Tether-nets are one of the more promising methods for the active removal of space debris. The aim of this paper is to study the dynamics of this type of systems in space, which is still not well-known and the simulation of which has multiple outstanding issues. In particular, the focus is on the deployment and capture phases of a net-based active debris removal mission, and on the effect of including the bending stiffness of the net threads on the dynamical characteristics of the net and on the computational efficiency. Lumped-parameter modeling of the net in Vortex Dynamics, without bending stiffness representation, is introduced first and validated then, against results obtained with an equivalent model in Matlab, using numerical simulations of the deployment phase. A model able to reproduce the bending stiffness of the net in Vortex Dynamics is proposed, and the outcome of a net deployment simulation is compared to the results of simulation without bending stiffness. A simulation of net-based capture of a derelict spacecraft is analyzed from the point of view of evaluating the effect of modeling the bending stiffness. From comparison of simulations with and without bending stiffness representation, it is found that bending stiffness has a significant influence both on the simulation results and on the computation time. When bending stiffness is included, the net is more resistant to the changes in its shape caused both by the motion of the corner masses (during deployment) and by the contact with the debris (during capture).

As higher strength to density ratio materials become available, the construction of a space elevator on Earth becomes more plausible. Though many fundamental aspects of the mechanical behaviour of a space elevator have been previously analysed, several details have not been rigorously explored. This paper examines the deformation of the tether from its nominal state when it is loaded with a climber at any altitude. Using an assumed modes numerical approach, the equilibrium conditions governing the static deformation of the elevator tether are derived, taking into account the presence of a climber. These discretised equations are solved numerically to determine the static deformation of the tether. A spectrum of statically deformed tether profiles is presented. Strain, stress and tension profiles are also computed and discussed. In general, when a climber is present below GEO, the extension (and stress) of the portion of tether below it is reduced and that above it is largely unaffected. When a climber is present above GEO, the extension (and stress) of the portion of tether below it is increased (that above it remains largely unaffected). Finally, the absolute displacement of the apex anchor (counterweight) is plotted against climber locations.

With a growing interest in asteroid exploration, combined with the fact that numerous asteroids in nature occur in pairs, it is likely that future missions will include the exploration of binary asteroid systems. Thus, it is useful to study the motion of a spacecraft in the vicinity of such systems, modeled as the three-body problem. In this paper, the circular restricted full three-body problem is considered. The zeroth-order equations of motion near an equilibrium point are similar in form to those in the classical case with point-masses or spherical primaries. For most asteroid pairs found in practice, all five equilibrium points are unstable. However, with selection of appropriate initial conditions, it is possible to obtain bounded solutions to the zeroth-order equations, corresponding to the Lissajous trajectories near collinear points, and bounded trajectories near noncollinear points. Numerical simulations confirm that when including the additional perturbations due to the asphericity of the asteroid pair, the motion of the spacecraft is unbounded. Thus, control laws are developed by utilizing an appropriate Lyapunov function, with the solutions to the zeroth-order equations as reference trajectories. These were found to be sufficient to maintain the spacecraft in bounded trajectories.

This paper presents a new methodology for on-line inertia parameters estimation for a rigid space debris captured by a tethered system, based on a new dynamics model of the system where the base satellite (chaser) and the space debris (target) are modeled as rigid bodies and the attachment points of the tether are offset from the centers of mass of the two bodies. Parameters estimation of unknown debris is critical for subsequent tasks in the space debris remediation mission, in particular, for debris retrieval and de-orbiting. In the proposed algorithm, the chaser and target are modeled as rigid bodies, the latter with unknown inertia parameters. Then, the parameters identification problem is formulated and solved in three phases. First, a coarse estimate of the target mass is obtained during the post-capture phase, while the length of tether is much longer than the offsets of base and target satellite, and the rigid body model is degenerated to a mass point model. Then, with a proper tension control scheme and the coarse estimate used as an initial guess, the debris is retrieved smoothly and a precise mass estimate is achieved during the first half of the retrieval. Finally, when the tether is retrieved relatively short and the rigid body model is used, moments of inertia and the offsets of the space debris will be estimated with a proper tension control scheme for rigid body model.

This paper examines the maintenance of satellite formations using two environmental forces: solar radiation pressure and aerodynamic forces. It is assumed that the satellites are equipped with solar flaps or aerodynamic flaps. Control using aerodynamic flaps is considered for satellite formations in LEO while solar flaps is applied to formations in LEO as well as GEO. The simple control laws based on open-loop and closed-loop control methods are designed for required rotation of the flaps to achieve desired formation keeping. The feasibility of the proposed schemes is proven via stability analyses followed by numerical simulations. A linear flap rotation scheme is found to keep the relative position errors bounded to ±5 m. The proposed control methods show the effectiveness of the use of solar radiation pressure and aerodynamic forces for satellite formation flying.

The space elevator has been proposed as an alternate method for space transportation. A partial elevator is composed of a tether of several hundreds of kilometres, held vertically in tension between two end masses, with its centre of orbit placed at the geosynchronous orbit. A spacecraft can dock at the lower end, and then use the climber on the elevator to ascend to higher altitudes. In this paper, energy calculations are performed, to determine whether a partial elevator can provide sufficient savings in operational costs, compared to the traditional rocket-powered launch. The energy required to launch a spacecraft from a Low Earth Orbit (LEO) to the geostationary orbit (GEO) is calculated for two trajectories. In the first trajectory, the spacecraft travels from LEO to GEO via a Hohmann transfer. In the second trajectory, the spacecraft travels from LEO to the lower end of the partial space elevator with a Hohmann transfer, and then uses the elevator to climb to GEO. The total energy required is compared between the two trajectories. The effects of tether length, spacecraft-to-climber mass ratio, altitude of LEO, and tether material are investigated.

The orbital motion of a spacecraft in the vicinity of a binary asteroid system can be modelled as the full three-body problem. The circular restricted case is considered here. Taking into account the shape, size, and mass distribution of arbitrarily shaped primary bodies, the locations of the equilibrium points are computed and are found to be offset from those of the classical CR3BP with point-masses. Through numerical computations, it was found that in cases with highly aspherical primaries, additional collinear and noncollinear equilibrium points exist. Examples include systems with pear-shaped and peanut-shaped bodies.

Minimum Sliding Mode Error Feedback Control (MSMEFC) is proposed to improve the control precision of spacecraft formations based on the conventional sliding mode control theory. This paper proposes a new approach to estimate and offset the system model errors, which include various kinds of uncertainties and disturbances, as well as smoothes out the effect of nonlinear switching control terms. To facilitate the analysis, the concept of equivalent control error is introduced, which is the key to the utilization of MSMEFC. A cost function is formulated on the basis of the principle of minimum sliding mode error; then the equivalent control error is estimated and fed back to the conventional sliding mode control. It is shown that the sliding mode after the MSMEFC will approximate to the ideal sliding mode, resulting in improved control performance and quality. The new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative tracking error in the presence of J2 perturbations. In addition, some fault tolerant situations such as thruster failure for a period of time, thruster degradation and so on, are also considered to verify the effectiveness of MSMEFC. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the satellite formation with the existence of initial offsets and J2 perturbation effects, even in the fault-tolerant cases.

In this paper, a novel hybrid actuation system for satellite attitude stabilization is proposed along with its feasibility analysis. The system considered consists of two magnetic torque rods and one fluid ring to produce the control torque required in the direction in which magnetic torque rods cannot produce torque. A mathematical model of the system dynamics is derived first. Then a controller is developed to stabilize the attitude angles of a satellite equipped with the abovementioned set of actuators. The effect of failure of the fluid ring or a magnetic torque rod is examined as well. It is noted that the case of failure of the magnetic torque rod whose torque is along the pitch axis is the most critical, since the coupling between the roll or yaw motion and the pitch motion is quite weak. The simulation results show that the control system proposed is quite fault tolerant.

A space elevator has been proposed as an alternate method for launching satellites; however, the materials available now are not strong enough to support the stress generated in the structure. On the other hand, with the existing technology, a partial elevator is feasible. In this paper, the mechanics of a very long tethered system that functions as a partial elevator is studied. For such a system, the center of mass, center of gravity, and center of orbit are not coincident; disregarding this distinction can lead to erroneous results. A relation between these three points is presented in this paper. A consistent stress distribution along the tether is obtained by taking into account the distinction between these points. Dynamics of the system consisting of two end bodies, the tether (with mass), and a climber is examined. The equations of motion are derived using the Lagrangian formulation and analyzed numerically.

The space elevator offers an alternate and efficient method for space travel. It will have two main components. The first component is the tether (or the ribbon), which extends from the Earth to an equatorial satellite at an altitude beyond the geostationary orbit, and is fixed to a base on the surface of the Earth at its lower end. The second component is the climber, which scales the ribbon, transporting payloads to space. An important issue for effective operation of the space elevator will be to understand its dynamics. This paper attempts to develop a realistic and yet simple planar model for this purpose. The basic response of the ribbon to climber transit is determined. Both analytical and numerical results are presented. Specific climbing procedures are devised based on these results so as to minimize the adverse effects of climber transit on the ribbon.

The dynamics of certain multi-tethered satellite formations containing a parent (or central) body are examined in this paper. Some simplifications are made prior to the analysis: the satellites are point-masses, the tethers are massless and straight, and the motion of the parent body of the formations is prescribed. First, planar formations are investigated: these are termed “hub-and-spoke”—which comprises a parent body located at the center (hub) of the formation, from which stem tethers (spokes), each having a satellite at its end—and “closed-hub-and-spoke” (which has the same description but also has, in addition, tethers joining successive satellites). These formations are placed in the orbital plane, or in the Earth-facing plane normal to the orbit, and are given an initial spin rate about an axis orthogonal to their nominal plane. The ensuing motion is studied in order to ascertain the conditions under which the formations remain in dynamic stability. Later, the motion of three-dimensional configurations, whose initial spin vector is along the radial direction, is examined. These formations are deployed along the local vertical. They are a “closed-hub-and-spoke” formation, which is found to be unstable and a “double-pyramid” configuration, which is found to be stable.

Dynamics and control of two-body and n -body tethered satellites are considered. At first, nonlinear roll and pitch motions of two-body systems are examined. Then the effects of aerodynamic and electrodynamic forces on the stability of a tethered satellite are discussed. Various control schemes to stabilize the dynamics during retrieval of the subsatellite are described. Finally, some dynamics and stability results for n -body tethered satellites are presented.