Aerospace and Electronic Systems Magazine July 2018 - 60

Feature Article:

DOI. No. 10.1109/MAES.2018.160207

Integrated Attitude-Orbit Dynamics and Control of
Spacecraft Systems: State of the Art and Future Trends
Mohamad Fakhari Mehrjardi, Hilmi Sanusi, Mohd. Alauddin Mohd. Ali, Mardina
Abdullah, Universiti Kebangsaan Malaysia (UKM), Bangi, Malaysia

INTRODUCTION
Spacecraft orbit and attitude determination and control (OADC)
is described as the methodology of determining and controlling
the motion and orientation (i.e., the state vector, ephemeris, or
state) of an orbiting object such as a spacecraft relative to the Sun,
the Earth, or the stars [1]. The motion and orientation of a spacecraft are estimated by a set of equations with the state adjusted
in response to a set of discrete sensor's data and subject to both
random and systematic errors [2]. In the context of this article,
the integrated orbit and attitude determination and control (IOADC) problem is generally described by introducing statistical
estimation techniques of determining the state of a spacecraft as
a function of time using the set of observations. The spacecraft
is supposed to be influenced by a variety of external forces and
torques, such as gravity, aerodynamic drag, solar radiation, thirdbody disturbances, and Earth tidal effects [3]. The complex description of these forces and torques results in a highly nonlinear
set of dynamical equations. Since the OADC equations and observational data are inherently nonlinear, linearization technique
is often performed in which linear estimation methods are used to
resolve the OADC problem [4].
Due to the complexity of the OADC problem, the review does
not describe the subject in depth. However, there are a number
of brilliant textbooks and papers that cover the technical details
on the principles and applications of the OADC issue [5], [6].
For example, King-Hele provided an excellent review of aerodynamic drag research on satellites before the launch of Sputnik
1 [7]. They developed and applied a significant effort in practice
to yield a rich harvest of knowledge about the Earth and air at a
very modest cost. They assumed a circular Earth orbit, and the
Earth and its atmosphere supposed as a spherical shape. Besides,
their research was independent of the size, mass, and shape of
the satellite. They concluded that from heights below 200 km the
Authors' current address: Space Science Centre (ANGKASA),
Institute of Climate Change, Level 3, Research Complex,
Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor,
Malaysia, E-mail: (mohamad.fakhari.m@gmail.com).
Manuscript received September 26, 2016, revised January 19,
2017, June 9, 2017, August 27, 2017, and ready for publication
September 3, 2017.
Review handled by H. Liu.
0885/8985/18/$26.00 © 2018 IEEE
60

altitude of the satellite descended in a spiral orbit by the same
speed of the circular orbital velocity at its current orbit altitude.
In other words, the heights of the satellite descend about 7.8 km/s
at a height of 200 km. Also, they showed that while the satellite
descended, the air drag did not slow it, and the speed of the satellite slightly increased.
A context diagram for an IOADC solution is illustrated in
Figure 1. Based on this diagram, there are three requirements
for the IOADC system to work effectively: developing the fundamental physics and mathematical equations of the theory, satisfying observability features of the system in space and time
using measurements data, and computational procedures employed by the computer hardware and software. It is important to
mention that due to the complexity of the IOADC mathematical
model and additional time constants existing in the spacecraft
hardware, there is a time delay in the control system that must be
taken into consideration in the final design stage. There are several types of research on the control systems time delay. Pyragas conducted a brief review of time-delayed feedback control,
its practical implementations, its applications for theoretical
models, and its most important modifications [8]. The paper by
Yamashita et al. presented two disturbance compensator models
that were developed in the attitude control system for a satellite with flexible body. The proposed methods were verified by
the attitude control system of the Japanese Very Long Baseline
Interferometry satellite, "HALCA", launched on February 12,
1997. In the models, the total time delay consists of the rate/
angle sensors delay, the local control loop of the actuator delay,
and the computational delay with the sample/zero-order-hold.
Moreover, the models used proportional-integral-differential
(PID) controller, the worst time delay was considered 200 ms,
and the control sampling frequency was 50 ms. In this study, the
performance of the proposed controller improved over the classical PID controller for satellite attitude maneuvers involving,
e.g., slew, scan, and raster scan [9].
Batch filtering and recursive filtering are two commonly used
algorithms for orbit and attitude determination. Batch filtering
techniques apply all measurements data to update the states and
recursive state filters using only the current and previous set of observations. Recursive filters are more sensitive to individual data
points; however, they are proper for real-time estimation [6].
Kalman filter is a type of recursive filter that provides an
optimal estimation of current states. Kalman filter was used in

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