Aerospace and Electronic Systems Magazine July 2018 - 65

Mehrjardi et al.
Kristiansen et al. described a six degrees of freedom (6DOF)
integral control system and introduced the basis of coupled dynamics fundamentals in their publications. They also introduced
three nonlinear control solutions, namely, the passive-based PD+
controller, the sliding surface controller, and a controller derived
with the integrator backstepping method. Then, they presented
theoretical comparisons of the controllers with using simulation
results [43]. The problem of integrated attitude and orbit dynamics has been treated by Lennox [44]. It is shown that the thrust
direction error leads to the need for an integrated attitude and
orbital control strategy. In this study, an integrated control system
was developed by using a nonlinear Lyapunov attitude controller
and a nonlinear Lyapunov-based orbital controller. It was proved
that the integrated control strategy was able to correct for an initial relative position error between two spacecraft [44]. In Naasz
et al. [45], orbit and attitude control of spacecraft were developed
independently, and then a control system was designed for integrated attitude and orbit. A single integrated dynamic model for
attitude and orbit dynamic of spacecraft was explained in [46]-
[48]. Moreover, in Park et al. [49], a coarse integrated attitude
and orbit estimation algorithm was discussed; however, the attitude estimations had not been input to the controller, and also
the problem of orbit determination was not explained. Then, Park
et al. developed an integrated attitude and orbit control algorithm
for satellite formation flying and tested it by using an integrated
attitude and orbit software-in-the-loop simulator. Their model
was similar to the reconfiguration of an actual satellite. They
concluded that when they used the integrated simulator, errors
and total ΔV were greater in comparison with using only the orbit
simulator. In their research, they concluded that the final error in
the integrated attitude and orbit control algorithm was 0.489 m,
which showed the precision level within 1 m, but, in the simulation without considering the integration terms, the final reconfiguration error was 4.852 m that the precision level decreased
ten times compared to the previous one [50].
In general, integrated translational and rotational dynamics of
a spacecraft within the circular restricted three-body problem is
based on a set of differential equations [51]

(
(
(

 xorb = f x xorb , i q b , iω b , t

 i b
i b i b
 q = f q xorb , q , ω , t
i b
 ω = fω xorb , i q b , iω b , t


)
)
)

(19)

T

where xorb =  x y z x y z is the position and velocity of
the spacecraft center of mass related to the rotating frame, iqb = [q1
q2 q3 q4]T is the spacecraft orientation with respect to the inertial
frame in quaternion term, and iωb = [ω1 ω2 ω3]T is the spacecraft
body angular velocity with respect to the inertial frame. According to equation (17), variation of the attitude states concludes a
variation for the orbital states, and vice versa. This model is a set
of nonlinear differential equations. In comparison to other models,
this model is more complex in terms of mathematical computation;
nevertheless, control accuracy benefits from deeper insight into the
attitude motion.
JULY 2018

During main engine firings, during orbit correction maneuver,
and for spacecraft close to the sun with solar panels, the IOADC
will be required. Due to the nonlinearity terms of the IOADC
mathematical model, it is considered as a complex model and
needs high-precision calculation. To have an agile control system, the IOADC's flight software must perform extremely quickly, must process large quantities of data, and must store and manage the data. Generally, the IOADC agent drives high-accuracy
orbit and attitude data, generates high-precision attitude control
commands, and passes through the executive agent to the flight
software backbone; after a quality assurance by the backbone,
the control actuators produce the desired pointing performance.
The flight computers of the 1990s and 2000s spacecraft utilized
higher level languages (such as C, C++, and Ada) and floatingpoint arithmetic. In the current space technology, powerful onboard computers (e.g., the DF224) enable the designer to utilize
the IOADC mathematical algorithms. A more thorough review of
the technologies needed for developing spacecraft OADC systems, the use of software agents in developing autonomous flight
systems, technology for cooperative space missions, and technology for adding autonomicity to future missions can be found in
the book by Truszkowski [52].
Orbit calculations and attitude control have almost always been
treated as separate problems. It is easier to solve two three-state
problems than one six-state problem. In the usual solutions, small
perturbations are added for cross-coupling between the orbit and
attitude control equations. However, the computation level of integrated attitude and orbit dynamics is a challenging problem. Finding a reasonable approximation of decoupling for the integrated
attitude and orbital dynamics based on the required pointing accuracy of the control system needs to be investigated more in depth.
Moreover, in general, the spacecraft attitude changes much faster
than its orbit. Therefore, for comparable accuracy for the attitude
and orbit estimation, the numerical integrations of attitude require
smaller (more) steps than orbit numerical integrations. One of the
interesting gaps in the IOADC field is "how" to find an optimal
solution for minimizing the computational expenses and, at the
same time, maximizing the control system accuracy based on the
spacecraft hardware constraints. Furthermore, in the future, space
missions will take more advantage of the precise attitude and orbit
models of the IOADC. Hence, developing the IOADC models for
spacecraft with a large structure such as multi-panel solar sails,
electric sails, or tethered systems with different orbits will help
for more accurate missions. Also, the integration between the orbit and attitude of the formation spacecraft makes the formation
relative motion control problem particularly difficult. The 6DOF
integrated translational and rotational dynamics is remarkable for
small spacecraft with thruster that can only generate thrust along
one axis. The major coupling depends on the thrust orientation for
orbit correction on the spacecraft attitude and the thruster installation matrix.

ATTITUDE AND ORBIT CONTROL
The next space missions need more safe control systems, autonomy, optimization, and intelligent controller for different re-

IEEE A&E SYSTEMS MAGAZINE

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