Search Results (9)

This article presents a compact tip-tilting platform designed for hardware-in-the-loop emulation of spacecraft relative dynamics and a physical setup for testing tethered systems. The architecture consists of a granite slab supported by a universal joint and two linear actuators to control its orientation. This configuration allows a Floating Spacecraft Simulator to move on the surface in a quasi-frictionless environment under the effect of gravitational acceleration. The architecture includes a dedicated setup to emulate tethered satellite dynamics, providing continuous feedback on the tension along the tether through a mono-axial load cell. By adopting the Buckingham “$\pi$” theorem, the dynamic similarity is introduced for the ground-based experiment to reproduce the orbital dynamics. Proof-of-concept results demonstrate the testbed’s capability to accurately reproduce the Hill–Clohessy–Wiltshire equations. Moreover, the results of the deployed tethered system dynamics are presented. This paper also details the system architecture of the testbed and the methodologies employed during the experimental campaign. Full article

A satellite formation operating in low-altitude orbits is subject to perturbations associated to the higher-order harmonics of the gravitational field, which cause a degradation of the formation configurations designed based on the unperturbed model of the Hill–Clohessy–Wiltshire equations. To compensate for these effects, periodic reconfiguration maneuvers are necessary, requiring the prior allocation of a propellant mass budget and, eventually, the use of resources from the ground segment, having a non-negligible impact on the complexity and cost of the mission. Using the Hamiltonian formalism and canonical transformations, a model is developed that allows designing configurations for formation flying invariant with respect to the zonal harmonic perturbation. $J_n$ invariant configurations can be characterized, selecting the drift rate (or boundedness condition) and the amplitude of the oscillations, based on four parameters which can be easily converted in position and velocity components for the satellites of the formation. From this model, a guidance strategy is developed to inject a satellite approaching another spacecraft into a bounded relative trajectory about it and the optimal time for the maneuver, minimizing the total $\mathrm{\Delta }V$, is identified. The effectiveness of the model and of the guidance strategy is verified on some scenarios of interest for formations operating in a sun-synchronous and a medium-inclination low Earth orbit and a medium-inclination lunar orbit. Full article

In this paper, we consider the relative motion of a follower spacecraft orbiting the Earth in a near circular orbit with respect to a leader spacecraft. The relative orbital motion-control problem of the follower spacecraft is studied here. In order to allow the follower spacecraft to succeed in its target orbital motion maneuver, we proposed a multi-objective optimization method to solve the relative orbital motion-control problem. Firstly, a Hill–Clohessy–Wiltshire equation was used to describe the continuous relative orbital motion-control system. Then, the system was discretized into a discrete system using numerical methods. Next, a multi-objective optimization model of the relative orbital motion-control problem was formulated. In the model, two objectives, i.e., the orbital motion error and the energy consumption, were minimized simultaneously. Furthermore, the ε-constraint method was used to solve the multi-objective optimization problem and the Pareto front, which demonstrates that the trade-off between the two objectives can be achieved. Finally, numerical experiments were carried out to validate the effectiveness of the proposed multi-objective optimization approach. Full article

The plasma brake is a propellantless device conceived for de-orbiting purposes. It consists of an electrically charged thin tether that generates a Coulomb drag by interacting with the ionosphere. In essence, a plasma brake may be used to decelerate an out-of-service satellite and to ensure its atmospheric re-entry within the time limits established by the Inter-Agency Space Debris Coordination Committee. Moreover, since it only needs a small amount of electric power to work properly, the plasma brake is one of the most cost-effective systems for space debris mitigation. This paper exploits a recent plasma brake acceleration model to construct an iterative algorithm for the rapid evaluation of the decay time of a plasma-braked CubeSat, which initially traced a circular low Earth orbit. The altitude loss at the end of each iterative step was calculated using the linearized Hill–Clohessy–Wiltshire equations. It showed that the proposed algorithm, which was validated by comparing the approximate solution with the results from numerically integrating the nonlinear equations of motion, reduced computational time by up to four orders of magnitude with negligible errors in CubeSat position. Full article

In a formation-flying mission where multiple spacecraft must cooperate and maintain a prescribed relative separation, the early detection of possible anomalies is a primary requirement. This is possible, for example, by employing an inspector spacecraft whose aim is to monitor the condition of the formation members with an on-orbit inspection. This paper analyzes a rest-to-rest multiple-impulse transfer that the inspector spacecraft must accomplish to visit all of the formation members. The problem is studied using the linearized Hill–Clohessy–Wiltshire equations and is solved in an optimal framework by minimizing the total velocity variation along the transfer trajectory. The solution algorithm implements a two-step procedure that combines differential evolution algorithms and Nelder–Mead simplex method-based routines. A case study is thoroughly investigated where a formation of six satellites covers a circular orbit of altitude $300\mathrm{km}$ over Earth. The proposed algorithm could efficiently find a solution and with reduced computational times. Full article

This survey deals with the problem of the group motion of spacecraft, which is rapidly developing and relevant for many applications, in terms of developing the onboard control algorithms to ensure the fulfillment of a given mission. The paper provides a comprehensive overview of spacecraft formation flight control. The bibliography is divided into three main sections: the multiple-input–multiple-output approach, in which the formation is treated as a single entity with multiple inputs and multiple outputs; the leader–follower formation, in which individual spacecraft controllers are linked hierarchically; and a virtual structure formation, in which spacecraft are treated as rigid bodies embedded in a common virtual rigid body. This survey expands a 2004 survey and updates it with recent results. Full article

Missions finalized at measuring the space-time variations of the Earth gravity field have become of high relevance in recent years. These missions are indeed of interest for scientific purposes and applications in several fields. Precise observations of the Earth gravity field can be accomplished by measuring the distance between two satellites flying in suitable orbits. Several mission concepts foresee an active formation control to maintain the distance variations between the two satellites within given bounds. In this paper, we first present an original constellation model, called the Triangle Dynamics (TD) model, which is particularly suitable to describe the orbital dynamics of satellite pairs. Open-loop simulations are performed, where the TD model is compared with a standard model, derived from the well-known Hill–Clohessy–Wiltshire (HCW) equations. The simulation results show that the TD model provides more accurate predictions than the HCW model. Then, we propose a formation control approach based on a new Model Predictive Control (MPC) algorithm. The core of this algorithm is the TD model, which is used in real-time to predict the behavior of the satellite pair, allowing the computation of an optimal formation control command. A case study concerned with the Next Generation Gravity Mission (NGGM) is presented to demonstrate the effectiveness of the proposed MPC-TD algorithm. Full article

Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes. Full article

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters. Full article