There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Model Predictive Control in Aerospace Systems: Current State and Opportunities

M. MAGGIORE University of Toronto C. MANZIE Univ. of Melbourne A. MARINO University of Salerno P. MHASKAR McMaster Univ. G. NOTARSTEFANO University of Salento P. ODGAARD Vestas Wind Systems M. OISHI University of New Mexico N. OLGAC Univ. of Connecticut T. OOMEN Eindhoven University Y. ORLOV CICESE Mexico Y. PAN National University of Singapore C. PANAYIOTOU Univ. of Cyprus G. PAPAFOTIOU ABB A. PAVLOV NTNU, Norway G. PIN Electrolux S. PIROZZI Università di Napoli H. POTA Univ. of New South Wales at ADFA C. PRIEUR CNRS E. PUNTA National Research Council, Italy N. QUIJANO Universidad de los Andes Colombia D. M. RAIMONDO University of Pavia G. A. ROVITHAKIS Univ. of Thessaloniki K. RUDIE Queen’s Univ.

Ieee transactions on control systems technology

This paper presents a six-degree-of-freedom relative motion control method for autonomous spacecraft rendezvous and proximity operations subject to input saturation, full-state constraint, kinematic coupling, parametric uncertainty, and matched and mismatched disturbances. Relative rotational and relative translational controllers are developed separately based on a unified adaptive backstepping technique. Both element-wise and norm-wise adaptive estimation techniques are used for handling parametric uncertainties, kinematic couplings, and matched and mismatched disturbances, where the bounds of disturbances are unknown. Two auxiliary design systems are employed to deal with input saturation in the relative rotational and relative translational control designs, and the stability of the saturated control solution is verified. Full-state constraint of the relative pose motion is handled by using barrier Lyapunov functions while achieving a satisfactory control performance. All signals in the closed-loop system are guaranteed to be uniformly ultimately bounded, and the relative motion states are all restricted within the known constraints. Compared with the previous control designs of spacecraft rendezvous and proximity operations, the proposed control strategy in this paper can simultaneously deal with input saturation, full-state constraint, kinematic coupling, parametric uncertainty, and matched and mismatched disturbances. Experimental simulation results validate the performance and robustness improvement of the proposed control strategy.

Adaptive Backstepping Control of Spacecraft Rendezvous and Proximity Operations With Input Saturation and Full-State Constraint

The performance of two nonlinear estimators is compared for the localization of a spacecraft. It is assumed that range measurements are not available (as in deep space missions), and the localization problem is tackled on the basis of angles-only measurements. A dynamic model of the spacecraft accounting for several perturbing effects, such as Earth and Moon gravitational field asymmetry and errors associated with the Moon ephemerides, is employed. The measurement process is based on elevation and azimuth of Moon and Earth with respect to the spacecraft reference system. Position and velocity of the spacecraft are estimated using both the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The behavior of the filters is compared on two sample missions: Earth-to-Moon transfer and geostationary orbit raising.

Comparison of EKF and UKF for Spacecraft Localization via Angle Measurements

The key role of autonomous systems in future space missions has made model predictive control a very attractive guidance and control technique. However, the capability of low-power spacecraft processors to handle the real-time computational load of this technique still needs to be fully established, especially for complex control problems. This paper introduces a method to improve the computational efficiency of model predictive control when applied to the problem of autonomous rendezvous and proximity maneuvering using low-thrust propulsion. To ensure safe trajectories in this scenario, a long control horizon is required and the control problem must be solved at a relatively fast sampling rate. The proposed design addresses such requirements by parameterizing the thrust profile with a set of Laguerre functions. In this setting, the number of control variables can be made significantly smaller than the length of the control horizon, as opposed to standard design methods. By exploiting this property, in co...

/pdf/explicit-model-predictive-control-approach-for-low-thrust-bz0ferfvhc.pdf

Explicit Model Predictive Control Approach for Low-Thrust Spacecraft Proximity Operations

Propulsion options for very low Earth orbit microsatellites

is based on an extended Kalman filter, employing gyro, star-tracker, and Global Positioning System measurements. Lyapunov-based and proportional–derivative feedback laws are used for orbit and attitude control, respectively. The performance of the proposed electric propulsion system and guidance, navigation, and control solution is evaluated on a low-Earth-orbit mission.

Autonomous Low-Earth-Orbit Station-Keeping with Electric Propulsion

This letter tackles spacecraft optimal control problems in which the cost function is defined by a sum of vector norms, in order to optimize fuel consumption while achieving sparse actuation. A model predictive control (MPC) strategy is devised for such type of problems, accounting for different spacecraft maneuvering modes. Closed-loop stability is guaranteed by a conic Lyapunov function, which is employed as a terminal cost in the formulation. A systematic method to construct such function is presented. The proposed design is compared to a standard quadratic MPC scheme on a long-range rendez-vous mission.

Sum-of-Norms Model Predictive Control for Spacecraft Maneuvering

Recent technological advances in the development of electric microthrusters pave the way to the successful diffusion of all-electric spacecraft. Since pointing accuracy is a key requirement for space platforms, suitable control systems accounting for the peculiarity of electric on/off actuators have to be devised. In this paper, an attitude control system (ACS) for spacecraft equipped with cold gas and electrothermal xenon microthrusters is presented. The number of thruster firings, which has a key impact on the thruster lifetime, is explicitly taken into account in the control design phase. By adopting a model predictive control (MPC) approach, a cost functional including both fuel consumption and number of firing cycles is minimized at each time step, within a receding horizon scheme. The effectiveness of the proposed ACS is validated on a sample GEO mission and its performance is compared with different control laws involving on/off actuators.

All-Electric Spacecraft Precision Pointing Using Model Predictive Control

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