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This paper aims to present the control laws to be used in the control of pendular motion on tethered satellite systems in space during orbiting by using a nonlinear design technique.

This work presents both physical and mathematical models represented in a circular orbit. Euler equation of the rigid body is applied under reasonable assumption so as to form the equations of pendular motion. These equations are then used to develop the control laws using a nonlinear design technique. The control laws are required to drive the in-plane angles and out-of-plane angles of the pendular motion to the required trajectories. Simulations are then conducted to study the control results.

Simulation results show that the control laws in both plane angles of motions considered are able to move the pendular motion to the required trajectory. It was also eminent that a lot of effort is required in the case of the reference trajectory that corresponds to the constant inside-plane. To control the pendular motion of the plane, one requires an extended period of time and it should be controlled within a reasonable range. In the outside-of-plane pendular motion, minimal or no effort is required for the control. The reason is that the trajectory is natural planar.

This research is expected to provide a dynamic control strategy for all tethered satellite space systems.

The research proposes a combined dynamic method for the purpose of improving the control of all types of tether satellites.

The purpose of this paper is to study the dynamic vibrations of the tethered satellite system (TSS).

The energy principle and the variational approach are used to establish the dynamic equations of the TSS. By introducing new generalized coordinates, the equations are transformed into the Hamiltonian system. Then, the symplectic Runge-Kutta (SRK) method is used to solve the canonical equations.

The influence of the tether length on the dynamic behavior of the TSS is very important.

The dynamic responses of the TSS are obtained by using the SRK method.

The purpose of this paper is to develop analytic solutions for a tethered satellite system (TSS) subjected to internal tether tension moment and external aerodynamic torque for spin-up and spin-down manoeuvres.

Analytic solutions for TSS based on the approximation of Euler’s equations of motion via Fresnel integrals and sine and cosine integrals. Test simulation was performed for two cases (spin-up and spin-down manoeuvres). The conclusion is based on graphical interpretation.

The effects of angular velocities on X, Y and Z axes of the TSS under the influence of combined torques from internal tether tension and external aerodynamic drag influenced during spinning manoeuvres are shown graphically.

This research focuses only on a circular orbit, which is one of the simplest orbits without many variables taken into account such as flight path angle and true anomaly. It could get quite complex for other orbit types like elliptic and parabolic orbits.

Practical implications include observing the stability rotational motion of TSS so as to perform a two-way payload exchange via momentum transfer.

In this paper, analytic solutions for a torque motion of a TSS comprising non-linear Euler’s equations of motion are established for spin-up and spin-down manoeuvres.

This paper aims to present the impact analysis of payload rendezvous with tethered satellite system and the design of an adaptive sliding mode controller which can deal with mass parameter uncertainty of targeted payload, so that the proposed cislunar transportation scheme with spinning tether system could be extended to a wider and more practical range.

In this work, dynamical model is first derived based on Langrangian equations to describe the motion of a spinning tether system in an arbitrary Keplerian orbit, which takes the mass of spacecraft, tether and payload into account. Orbital design and optimal open-loop control for the payload tossed by the spinning tether system are then presented. The real payload rendezvous impact around docking point is also analyzed. Based on reference acceleration trajectory given by optimal theories, a sliding mode controller with saturation functions is designed in the close-loop control of payload tossing stage under initial disturbance caused by actual rendezvous error. To alleviate the influence of inaccurate/unknown payload mass parameters, the adaptive law is designed and integrated into sliding mode controller. Finally, the performance of the proposed controller is evaluated using simulations. Simulation results validate that proposed controller is found effective in driving the spinning tether system to carry payload into desired cislunar transfer orbit and in dealing with payload mass parameter uncertainty in a relatively large range.

The results show that unideal rendezvous manoeuvres have significant impact on in-plane motion of spinning tether system, and the proposed adaptive sliding mode controller with saturation functions not only guarantees the stability but also provides good performance and robustness against the parameter and unstructured uncertainties.

This work addresses the analysis of actual impact on spinning tether system motion when payload is docking with system within tolerated docking window, rather than at the particular ideal docking point, and the robust tracking control of deep-space payload tossing missions with the spinning tether system using the adaptive sliding mode controller dealing with parameter uncertainties. This combination has not been proposed before for tracking control of multivariable spinning tether systems.

The purpose of this paper is to present kinetic equations for tether-net system during deorbiting using a novel method differing from the traditional method.

The work presents kinetic equations for tether-net system in which the tether exhibits tensional and tensionless states alternately during deorbiting. Orbital position coordinates of net-capture and abandoned spacecrafts are adopted as generalized coordinates above-mentioned instead of librations and the length of the tether. Geostationary orbit (GEO) and the orbit whose apogee is 300 km above GEO are chosen as the initial and target orbit, respectively. Simulations are conducted to study the deorbiting results considering a variety of parameters and initial conditions.

The distinctive dynamic characteristics of tether-net system can be seen by kinetic equations based on the proposed dynamic modeling strategies. Moreover, the deorbiting results are deeply affected by the initial tension force and librations showed by simulations. The initial tension force and librations should be controlled within a reasonable range.

This is expected to provide dynamic modeling strategies for space tether-net system during deorbiting. Moreover, the preliminary principle of choosing initial conditions and parameters to meet the requirements for deorbiting can be achieved.

The research proposes a novel dynamic modeling method for space tether-net system that differs from traditional tethered system, and also proposes a superior librations expression based on orbital position coordinates of net-capture and abandoned spacecrafts.

The purpose of this paper is to assess the orbital perturbation caused by the gravitational orbit–attitude coupling of spacecraft in the proximity of asteroids.

The gravitational orbit–attitude coupling perturbation (GOACP), which has been neglected before in the close-proximity orbital dynamics about asteroids, is investigated and compared with other orbital perturbations. The GOACP has its origin in the fact that the gravity acting on a non-spherical extended body is actually different from that acting on a point mass located at the body’s center of mass, which is the approximated model in the orbital dynamics. Besides, a case study of a tethered satellite system is given by numerical simulations.

It is found that the ratio of GOACP to the asteroid’s non-spherical gravity is the order of ρ/a_e, where ρ is the spacecraft’s characteristic dimension and a_e is the asteroid’s mean radius. It can also be seen that as ρ increases, GOACP will also increase but the solar radiation pressure (SRP) will decrease due to the decreasing area-to-mass ratio. The GOACP will be more significant than SRP at small orbital radii for a large-sized spacecraft. Based on the results by analyses and simulations, it can be concluded that GOACP needs to be considered in the orbital dynamics for a large-sized spacecraft in the proximity of a small asteroid.

This study is of great importance for the future asteroids missions for scientific explorations and near-Earth objects mitigation.

The GOACP, which has been neglected before, is revealed and studied.

The micro‐satellite clusters have been discussed for several years, however, there is not a common framework about its software, and various researches distributed at different domains. In order to conduct the future work well, the purpose of this paper is to systematically describe micro‐satellite clusters' characteristics, clusters software model, and present a distributed testbed to shorten test process, and minimize the development cost.

The cluster characteristics and model is summarized through analyzing the past satellite cluster programs. Then the ground test system is designed to shorten micro‐satellite's development period, improve its reliability.

The clusters' characteristics are discussed, such as coverage, scalability, fault tolerance, low cost, etc. The clusters' data flow and on‐board software architecture are presented according to properties of clusters. Finally, the distributed testbed that focuses on future on‐board software and hardware technologies that aim to rapid design, build, integration, test, deployment, and operation of the future micro‐satellite is designed.

The presentation of software architecture of cluster member can improve the micro‐satellite's development, and the distributed testbed can improve the ground test efficiency, especially, when the micro‐satellite quantity is big.

The purpose of this paper is to investigate the time optimal trajectory of the multi-tethered robot (MTR) on a large spinning net structures in microgravity environment.

The MTR is a small space robot that uses several tethers attached to the corner-fixed satellites of a spinning net platform. The transition of the MTR from a start point to any arbitrary designated points on the platform surface can be achieved by controlling the tethers’ length and tension simultaneously. Numerical analysis of trajectory optimization problem for the MTR is implemented using the pseudospectral (PS) method.

The globally time optimal trajectory for MTR on a free-end spinning net platform can be obtained through the PS method.

The analysis in this paper is limited to a planar trajectory and the effects caused by attitude of the MTR will be neglected. To make the problem simple and to see the feasibility in the general case, in this paper, it is assumed there are no any limitations of mechanical hardware constraints such as the velocity limitation of the robot and tether length changing constraint, while only geometrical constraints are considered.

The optimal solution derived from numerical analysis can be used for a path planning, guidance and navigation control. This method can be used for more efficient on-orbit autonomous self-assembly system or extravehicular activities supports which using a tether-controlled robot.

This approach for a locomotion mechanism has the capability to solve problems of conventional crawling type robots on a loose net in microgravity.

This paper aims to study the encounter issues of the Tethered-Space Net Robot System (TSNRS) with non-target objects on orbit during the maneuver, including the collision issues with small space debris and the obstacle avoidance from large obstacles.

For the collision of TSNRS with small debris, the available collision model of the tethered net and its limitation is discussed, and the collision detection method is improved. Then the dynamic response of TSNRS is studied and a closed-loop controller is designed. For the obstacle avoidance, the variable enveloping circle of the TSNRS has coupled with the artificial potential field (APF) method. In addition, the APF is improved with a local trajectory correction method to avoid the overbending segment of the trajectory.

The collision model coupled with the improved collision detection method solves the detection failure and speeds up calculation efficiency by 12 times. Collisions of TSNRS with small debris make the local thread stretch and deforms finally making the net a mess. The boundary of the disturbance is obtained by a series of collision tests, and the designed controller not only achieved the tracking control of the TSNRS but also suppressed the disturbance of the net.

This paper fills the gap in the research on the collision of the tethered net with small debris and makes the collision model more general and efficient by improving the collision detection method. And the coupled obstacle avoidance method makes the process of obstacle avoidance safer and smoother.

The work in this paper provides a reference for the on-orbit application of TSNRS in the active space debris removal mission.