Gianmarco Radice

Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

BACKSTEPPING is a popular nonlinear control design technique [1,2]. It hinges on using a part of the system states as virtual controls to control the other states. Generating a family of globally asymptotically stabilizing control laws is the main advantage of this method that can be exploited for addressing robustness issues and solving adaptive problems. The term backstepping refers to the recursive nature of the control design procedure in which a control law and a control Lyapunov function are recursively constructed to guarantee stability. Backstepping has been considered for the spacecraft slew maneuvers [3,4]. The cascaded structure of spacecraft kinematics and dynamics makes the integrator backstepping a preferred approach for the spacecraft attitude maneuver problem, resulting in smooth feedback controls [5]. However, the typical control actuators used for this problem (such as reaction wheels, control moment gyros, or thrusters) have an upper bound on the control torque they can exert onto the system and the simple or conventional backstepping control method may result in excessive control input beyond that saturation bound. The issue has been addressed in the literature using other control methodologies such as nonlinear proportional–integral–derivative control [6], Lyapunovoptimal control [7] and variable structure control [8–11]. In this work, we design a nonlinear backstepping attitude controller using the inverse tangent-based tracking function [4] and a family of augmented Lyapunov functions [12]. Using this control law, we derive an analytical upper bound of the control torque norm. The bound is effectively used to tune the control parameters so that, for the given settling time specification, the upper bound of the control input is minimized. The performance of the proposed controller has shown improvements in minimizing the peak control torque and the settling time. The rest of the Note is organized as follows: First, the kinematics and dynamics of rigid spacecraft are summarized. Second, the details of the design procedure for the proposed controller and the analytical bounds for the control torque components are given. Third, the efficacy of the proposed scheme is demonstrated by the numerical simulations for the cases of attitude stabilization and tracking both. Finally, the conclusions are presented.

Multicriteria comparison among several mitigation strategies for dangerous near-Earth objects

In this paper a comparative assessment of the effectiveness of different deviation methods for Near Earth Objects is presented. Specifically, solar collector, nuclear interceptor, kinetic impactor, low-thrust propulsion, mass driver and gravity tug are modelled and compared. For each method, a mathematical model is developed in order to compute the achievable deviation. A multi-criteria optmization method is then used to construct the set of Pareto optimal solutions, minimizing the mass of the spacecraft at departure from the Earth and the warning time, i.e., the time from launch to the foreseen impact of the asteroid with the Earth, while at the same time maximizing the deviation. A dominance criterion is defined and used to compare all the Pareto sets for all the various mitigation strategies. Finally a Technology Readiness Level factor is associated to each strategy in order to estimate the required technological development.

Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earths orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.

Comparison of single and multi-spacecraft configurations for NEA deflection by solar sublimation

Since the first Near Earth Object (NEO) defence system, Project Icarus, was published in 1967, where the driving factor was a very short anticipating time (i.e. time available to act on the asteroid), the Near Earth Asteroid (NEA) hazard outlook has changed drastically. In the current state of NEO research, long-term missions are becoming more realistic and as such, the options for low thrust systems are being investigated as a viable option for deviating the asteroid path. Surface ablation approaches have been previously proposed using several techniques such as lasers and nuclear explosives. The method presented here hinges on directing solar energy using mirrors onto a small area on the surface of the asteroid. This concentrated heat then sublimates the surface matter creating narrow but expanding jets of gas and dust that produce a low continuous thrust. This low thrust would then alter the orbit of the NEA by producing a change in velocity, similar to the effect of the ‘tail’ on a comet. This paper adds a new important trade-off to the problem: a comparison between a single structure and a multi-mirror system. The systems analysed include both single and dual mirror configurations, for both a single spacecraft and multiple spacecraft in formation. The criteria include ease of launch, reliability, flexibility in achieving the mission objective, in-space mass and a basic cost analysis. The concept, and potential benefits, of formation flying have long been known. The barrier however, has been the high level of complexity involved in the control of the individual spacecraft within the formation. Advances in control algorithms and associated technologies have opened the door to using spacecraft formations for specialized missions, such as small-body missions which operate in highly perturbed environments. This paper compares the complexities of deploying and operating a large rigid structure around asteroids, with the control of a swarm of smaller structures. Configurations are presented for different NEAs, time-in-advance, and achieved deflections.

Robust Finite-Time Control for Flexible Spacecraft Attitude Maneuver

The robust finite-time control for a flexible spacecraft attitude maneuver in the absence and presence of inertia uncertainties and external disturbances is investigated in this paper. The finite-time controllers, based on the Lagrange-like model and nonsingular terminal sliding mode technique, which guarantee the convergence of attitude maneuver errors in finite time rather than in the asymptotic sense, are proposed to perform an attitude maneuver. By constructing a particular Lyapunov function, the convergences of the proposed controllers for the closed-loop systems are proven theoretically. The robustness problem associated with inertia uncertainties and bounded disturbances is addressed. Numerical simulations are finally provided to illustrate the performance of the proposed controller by comparing it with the conventional sliding mode control. The finite-time controller demonstrates superior performance, such as fast convergence performance, ideal robustness, and effectiveness in suppressing vibration.

Locating Large Solar Power Satellites in the Geosynchronous Laplace Plane

Designs for geostationary solar power satellites are extremely large in scale, more than an order of magnitude larger than the International Space Station. A detailed study of solar power satellites’ orbit dynamics is performed, obtaining a comprehensive understanding of the effect of perturbations on orbits of large solar power satellite structures over a time frame commensurate with proposed solar power satellites’ lifetimes (30–40 years). Analytical equations derived by the process of averaging of the solar power satellites’ equations of motion are used to determine the long-term orbital behavior. Previous solar power satellite studies have simply assumed geostationary Earth orbit, then designed control systems for maintaining it thus. It is found that an alternative solar power satellite orbital location, known as the geosynchronous Laplace plane, is superior to geostationary in many aspects. A solar power satellite in the geosynchronous Laplace plane requires virtually no fuel to maintain its orbit, ...

Consequences of asteroid fragmentation during impact hazard mitigation

The consequences of the fragmentation of an Earth-threatening asteroid due to an attempted deflection are examined in this paper. The minimum required energy for a successful impulsive deflection of a threatening object is computed and compared to the energy required to break up a small size asteroid. The results show that the fragmentation of an asteroid that underwent an impulsive deflection, such as a kinetic impact or a nuclear explosion, is a very plausible event.Astatistical model is used to approximate the number and size of the fragments as well as the distribution of velocities at the instant after the deflection attempt takes place. This distribution of velocities is a function of the energy provided by the deflection attempt, whereas the number and size of the asteroidal fragments is a function of the size of the largest fragment. The model also takes into account the gravity forces that could lead to a reaggregation of the asteroid after fragmentation. The probability distribution of the pieces after the deflection is then propagated forward in time until the encounter with Earth. A probability damage factor (i.e., expected damage caused by a given size fragment multiplied by its impact probability) is then computed and analyzed for different plausible scenarios, characterized by different levels of deflection energies and lead times.

Mirror formation control in the vicinity of an asteroid

Two strategies are presented for the positioning and control of a spacecraft formation designed to focus sunlight onto a point on the surface of asteroid, thereby sublimating the material and ejecting debris creating thrust. In the flrst approach, the formation is located at artiflcial equilibrium points around the asteroid and controlled using the force from the solar radiation pressure. The second approach determines the optimal periodic formation orbits, subject to the gravitational perturbations from the asteroid, the solar radiation pressure and the control acceleration derived from a control law.

Constrained on-board attitude control using gas jet thrusters

This paper analyses a new approach utilising potential functions to autonomously control constrained attitude slew manoeuvres using gas jet thrusters. The method hinges on defining a potential function from the geometric configuration of the satellites current attitude, the final target attitude and any pointing constraint which may be present. It will be demonstrated that complex path shaping and planning can be achieved using little computational effort. The method is mathematically validated using Lyapunovs theorem, and so can be considered for safety critical applications.

Attitude Dynamics of Large Geosynchronous Solar Power Satellites

The solar power satellite (SPS) is an extremely large satellite designed to collect solar energy in space and transmit it to Earth via microwaves. A direct comparison between the attitude dynamics of SPS in the geosynchronous Laplace plane (GLP) orbit and in geostationary Earth orbit (GEO) is made. Initially, the Abacus SPS oriented perpendicular to the orbit plane (POP) is considered. It is found that by locating the Abacus SPS in GLP, attitude control is more costly. However, when both attitude and orbit control are considered, fuel savings of 17, 000 kg/year are achievable compared to in GEO. The benefits of modifying both the mass distribution and the attitude orientation of the Abacus SPS are analyzed. For Abacus type SPSs oriented in the orbital plane (IOP) which employ two dimensional inertia balancing (2-DIB), GLP offers more significant fuel savings of ∼ 73, 000kg/year. Orbit and attitude control for a SPS-IOP with 2-DIB in GLP requires 2.3% of the overall mass in fuel over a 30 year lifetime compared to 10.1% for the original Abacus SPS-POP in GEO. However, a system of solar reflectors is required for the IOP orientation, adding complexity to the design.