Computational Intelligence - November 2013 - 40
in [9] with considerable success to solve the
numerically difficult parameter optimization
problems in the reconfiguration problem. In
[10], an analytical fuel-optimal impulsive formation reconfiguration strategy in terms of
relative orbital elements was presented, where
the relative motion and orbit transfer conditions is re-parameterized in the form of relative orbit elements. Other control methods
have been studied in [11]-[15].
Swarm intelligence refers to the collective
behavior of decentralized, self-organized natural or artificial
systems [16]-[19], and has been attracting more and more
attentions from researchers in both theory fields and application fields [20]-[24]. During the past two decades, a lot of
swarm intelligence algorithms, which are inspired by swarm
intelligence of objects such as birds, ants, bees, etc., have been
proposed and studied, among which are PSO proposed by
Eberhart and Kennedy [25]-[28]and improved by Shi [29]-
[30], ant colony optimization (ACO) [31]-[32], and the artificial bee colony (ABC) algorithm [33]-[34]. However, these
swarm intelligence algorithms are based on the collective
behavior of simple objects. A novel swarm intelligence algorithm, brain storm optimization (BSO), was developed by Shi
in [35]-[36], which mimics the creative problem solving process in human beings by following such intelligent behaviors:
when human beings are faced with difficult problems that a
single person is incapable of solving, a group of persons from
different backgrounds are gathered together to brainstorm in
light of the four general rules outlined by Osborn [37]. A
modified BSO was studied in [38], where two novel designs
were proposed to improve the performance of the conventional BSO.
To enhance the existing technologies of optimal formation
reconfiguration of multiple satellites, this paper proposes a
novel closed-loop brain storm optimization (CLBSO) algorithm by incorporating feedback information into the creating
operator of the basic BSO algorithm. As the only swarm intelligence algorithm mimicking the creative problem solving process of human beings, BSO possesses great potential to be a
powerful and promising tool for solving optimization problems
in real world applications. However, the weighting coefficient
in the creating operator uses a fixed function and does not
make use of any feedback information, which may not guarantee a perfect balance between population exploration and
exploitation, thus providing room for development of a modified BSO algorithm. The objective of the current paper is first
to show the effectiveness and feasibility of the proposed
CLBSO algorithm in solving the optimization problem related
to multiple satellite formation reconfiguration with the constraints of overall fuel cost minimization, final geometry
requirement and collision avoidance, and second to compare its
performance with the PSO algorithm and the basic BSO algorithm. Simulations are carried out using three and five satellites
for different reconfiguration missions and results show that
In view of the limited lifetime of a satellite, the
range of spatial separation between satellites when
they move in space during reconfiguration, and the
geometry requirement of the space mission, it is
important to consider the problem with the three
constraints of overall fuel cost minimization, collision
avoidance and the final configuration.
gains the best overall performance, which is inspired by the
updating rule in PSO that each particle tends to move
towards the individual with the best fitness.
S
I. Introduction
atellite formation flying (SFF) is to place multiple satellites into nearby orbits forming a satellite cluster to
achieve a common mission and has been identified as an
enabling technology for many future missions of NASA
and U.S. Air Force [1]-[2]. In recent years, it has become an
increasingly significant research topic for both the astronomy
and earth science communities due to its well-known merits
compared with a single monolithic spacecraft system for the
same mission. By using a fleet of smaller satellites, SFF can
reduce the total mission costs, provide greater launch flexibility,
and offer a higher degree of system reliability and expandability
in case of a single vehicle failure or mission changes.
This paper addresses the optimal trajectory planning in
cooperative satellite formation reconfiguration, which refers to
the problem of simultaneously determining optimal maneuvers
for each satellite to reach a newly desired formation when an
old formation needs to be modified due to different formation
geometry requirements of different space missions. In view of
the limited lifetime of a satellite, the range of spatial separation
between satellites when they move in space during reconfiguration, and the geometry requirement of the space mission, it is
important to consider the problem with the three constraints
of overall fuel cost minimization, collision avoidance and the
final configuration [3]. This problem has been handled from the
perspective of convex optimization and several techniques have
been applied to obtain optimal control strategies for reconfiguration in the presence of other vehicles in literature. The
mixed-integer linear programming was applied to design fueloptimal trajectories considering collision avoidance and plume
impingement avoidance constraints in [4]. A direct optimization approach based on nonlinear programming was studied in
[5] for the path planning of a projected circular orbit configuration of multiple satellites. A general framework based on the
auction algorithm was developed in [6] to address the problem
of determining the optimal assignment for transferring onorbit satellites between different constellations such that the
total DV for the reconfiguration is minimized. A novel stochastic solver, particle swarm optimization (PSO) [7]-[8],
inspired by the random motion of bird's food seeking, is used
40
IEEE ComputatIonal IntEllIgEnCE magazInE | noVEmBER 2013
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