ABSTRACTS
| Kyle T. Alfriend (Texas A&M) |
Dynamics and Control of Formation Flying Satellites
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Swarms of satellites flying in formation is a concept being actively pursued
by the U.S. Air Force and NASA. It is hoped that the size and complexity of
large, single spacecraft missions can be replaced by multiple smaller, less
complex satellites. Mission planners will have the flexibility of repositioning
the satellites to perform different tasks. An example is that many satellites
operating cooperatively could emulate a large antenna. Reliability and
survivability of the system would increase because failure of a few satelites
would just result in gradual degradation of the performance of the system.
In addition, development time and hopefully, cost, would be reduced. In order
to achieve this the system needs to operate autonomously.
Such missions will require that the relative motion orbits be nearly periodic.
Potential periodic formation orbits have been classified using Hill's (or
Clohessy Wiltshire) equations. These linearized equations assume a spherically
symmetric Earrth and a circular reference orbit. Unfortunately they are
inadequate for describing long term dynamics and control of the formation.
The one advantage we have in this problem is that the physics are well known
and there is considerable knowledge on optimal maneuvers for satellites, e.g.
the Hohmann transfer. Control of the system will be approached not as a
standard LQG problem, but from an astrodynamics perpective utilizing the
knowledge we have in orbit theory and optimal satellite maneuvers. This
approach leads to some interesting new results.
In order to maximize system lifetime it is necessary to minimize fuel
consumption and to balance fuel consumption among the satellites. In order
to achieve this it is necessary to thoroughly understand and model the
dynamics. This presentation includes:
* A classification of the types of relative motion orbits.
* Present a new control concept called $\dot\alpha$ control that minimizes total
fuel consumption and balances fuel consumption across the constellation.
* Assessment of the nonlinear effects.
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| Apostolos Christou (Armagh Onservatory) |
NEO Rendezvous Opportunities: Targets, Dynamics and Statistics
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In situ investigations of Near Earth Objects (NEOs),
must take into account both scientific and operational concerns.
Usually the most scientifically attractive targets
are not accessible through the resources of scientific/
industrial consortia.
This work attempts to provide guidelines to the accessibility
of NEOs by undertaking an end-to-end study of the statistics
of flight opportunities to actual objects.
Initially, a process involving both physical and dynamical
criteria is used to select those objects, out of the current NEO population,
which could make attractive mission targets.
Then, the characteristics of flight opportunities to those objects
during the next 10 years are tabulated through a rigorous procedure
of constructing single and multi-revolution keplerian transfer trajectories.
This results in several hundred such opportunities, the key properties
of which -- e.g. departure and arrival velocities -- are used as input
to a statistical study. The outcome of this process is quantitative guidelines
pertaining to the frequency of favourable launch windows, times-of-flight,
launch and arrival conditions etc. During this presentation the different
steps in this procedure will be exposed. The resulting statistics will
be presented, analysed and further illustrated through typical mission
scenarios.
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| Michael Dellnitz (Paderborn) |
Set Oriented Numerical Methods in Space Mission Design
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Over the last years so-called `set-oriented' numerical
methods have been developed for the reliable approximation of
invariant objects of dynamical systems. With these
techniques it is possible to approximate, for instance,
invariant manifolds, invariant measures or `almost invariant sets'.
In this talk an overview about the applicability of set oriented
numerical tools in the context of space mission design will be given.
The talk will particularly focus on
* the computation of invariant manifolds in connection with the
NASA/JPL mission Genesis,
* the use of set oriented numerical tools for finding appropriate
locations for formation flights in connection with the ESA
mission Darwin, and
* the computation of transport phenomena in the solar system
via the approximation of almost invariant sets for certain
n-body problems.
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| Yoshi Hashida (Surrey) |
Autonomous Onboard Orbit Determination and UoSat-12
InOrbit Results
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The analytical approach for the satellite orbit determination will be
discussed in this presentation. Our future enhanced microsatellties will
require accurate orbital knowledge and control onboard to support their
payloads. Up until recently, we did not have our own satellite tracking
capability even on the ground segment as this would involve a considerable
cost to maintain and operate. Low cost and low power space GPS (Global
Positioning System) receivers, however, open the way for onboard orbit
determination of our satellites. To overcome the problem that the heavy
computational demand required for executing orbit determination is
unsuitable for the onboard processing environment, we have developed a new
analytical description of orbit by focusing on near circular orbits which is
appropriate for the most of all our LEO (Low Earth Orbit) satellites. Our
onboard orbit estimator by the use of our analytical orbit modelling is
presented and some UoSat-12 orbit determination results are introduced.
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| Wang Sang Koon (Caltech) |
Low Energy Transfer to the Moon
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New space missions are increasingly more complex; demand for exotic
orbits to solve engineering problems has grown beyond the
existing astrodynamic infrastructure based on two-body interactions.
The delicate heteroclinic dynamics used by the
Genesis Mission dramatically illustrate the need for a new paradigm:
dynamical system study of three-body problem.
Furthermore, this dynamics has much to say
about the morphology and transport of materials within the Solar System.
The cross-fertilization of ideas between the natural dynamics of the Solar
System and applications to engineering has produced
new techniques for constructing spacecraft trajectories with interesting
characteristics.
Specifically, these techniques are used here
to produce a lunar capture mission which uses less
fuel than a Hohmann transfer. We approximate the Sun-Earth-Moon-Spacecraft
four-body problem as two three-body problems. Using the invariant manifold
structures of the Lagrange points of the three-body systems, we are able to
construct low energy transfer trajectories from the Earth which
exhibit ballistic capture at the Moon.
The techniques used in the design and construction of this trajectory
may be applied in many situations.
This is joint work with Martin W. Lo, Jerrold E. Marsden and Shane D. Ross.
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| Vaios Lappas (Surrey) |
A Control Moment Gyroscope Cluster for Agile
Small Satellites
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The presentation
focuses on the hardware development of a new class of actuators for small
satellites, Control Moment Gyroscopes (CMG). These actuators can provide
unique torque, angular momentum and slew rate capabilities to small
satellites without any increase in power, mass or volume. This will help
small satellites become more agile. Agility considerably increases the
operational envelope and efficiency of spacecraft and substantially
increases the return of earth and science mission data. The presentation
elaborates on the development of a cluster of 4-CMGs in pyramid arrangement
for full 3-axis control for a microsatellite class spacecraft. Preliminary
results are presented on the testing of a CMG tested on SSTL's air bearing
facility. A 2-CMG cluster for rapid pitch axis control was also discussed as
a potential experimental payload for future enhanced microsatellite
missions.
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| Ben Leimkuhler (Leicester) |
Reversible Multiple Time-Scale Integrators
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The efficient simulation of multiple point particle or rigid body systems plays
an important role in many types of modelling ranging from celestial mechanics
and astrodynamics to computer gaming and molecular dynamics. One of the
enduring problems in this area is to find stable integrators which allow
various system components to be evolved with a stepsize appropriate to the
associated characteristic mode. Even when a clear separation exists so
that coupling can, in many places, be seen as adiabatic, the longest timestep
for simulation is generally limited by the presence of resonances to a fraction
of the fastest period.
In this talk, I will exhibit a new type of time-reversible integrator based on
averaging and splitting that allows for efficient multiple-scale
simulations of nonlinear conservative dynamics. I will indicate the extension
of the method to constrained models and demonstrate the effectiveness of the
method in several numerical examples. Time-permitting, I will also describe how
the new approach may be used to facilitate effective decoupling for
parallel dynamics simulations.
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| Seppo Mikkola (Turku Observatory) |
Satellites in Proximity. Theory, Software and Numerical Experiments
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Motion of several satellites in neighboring orbits is discussed in terms of
the state-transition-matrix. Analytical
treatment is complicated if the full force model is used,
but numerical results can be obtained.
Software for computing the relative motion of
satellites flying in formation has been written and numerical
experiments conducted.
If dissipative forces can be neglected, satellites in quasi-circular orbits
can stay in proximity for years, even without control. This requires
accurate adjustment of the energy and angular momentum z-component.
Both linearized and full non-linear computations produce similar results for
the stability of configurations.
If particular geometric configuration is not required,
control is necessary only to adjust initial conditions
and compensate for differences due to dissipative forces.
Joint work with Phil Palmer (Surrey).
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| Phil Palmer (Surrey) |
Optimal Control of Satellite Formations
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This talk will focus upon dynamical modelling of satellite formations and
how to optimise manoeuvres for fuel and time efficiency during formation
reconfiguration. The approach is generic and applies to any tight formation
manouevre in LEO, as long as the timescale for the manoeuvre is sufficently
short compared to evolution from Earth oblateness or drag. The talk will
describe how constraints from the proximity of other satellites as well as
the propulsion system on the satellites can be included. There will be a
discussion of reachability and how to formulate well posed manoeuvre
problems. At the end we shall demonstrate the application to synthesising an
aperture by a ring of satellites around an arbitrary non-nadir direction. By
manoeuvring the orbits of each satellite we then reconstruct a new ring
which points around a second arbitrary direction.
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| Mark Psiaki (Cornell) |
Exploiting Euler Dynamics in Order to Use the Earth's Magnetic Field for
3-Axis Attitude Determination or Control
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The Euler equations for attitude dynamics are exploited in order to develop
attitude determination systems and attitude control systems that work with
reduced sensor or actuator sets. This work is being carried out in support of
efforts to provide standard 3-axis functionality estimation and control when
using only limited sensors or actuators, such as magnetometers or magnetic
torquers. Such systems allow small, inexpensive nanosatellies to attain 3-axis
pointing and attitude determination capabilities with at low costs in terms of
power, weight, and cost. They are also useful for back-up mode operation for
traditional spacecraft.
Traditional designs include enough sensors or
actuators to make the system design relatively easy. A traditional attitude
determination system might include two vector sensors, such as a sun sensor
and a horizon sensor, to make the 3-axis attitude instantaneously determinable
and rate gyros to eliminate the need to use Euler's equations in a Kalman
filter's dynamic propagation. A traditional attitude controller includes
wheels, either 3 wheels for active stabilization of all 3 axes or one wheel
for active stabilization of pitch and passive stabilization of roll and yaw.
New estimation algorithms have been developed that use only magnetometer to
estimate attitude, attitude rate, or both about all 3 axes. It is a challenge
to estimate the attitude and rate about the magnetic field, but this can be
done by exploiting the Euler dynamics. The procedure requires specially
designed Kalman filtering algorithms and initialization procedures that
ensure global convergence. It is also necessary to estimate dynamics
parameters, such as the moment-of-inertia matrix. Example results for
these new estimation algorithms will be presented using data from the
Hubble Space Telescope and from a sounding rocket that was in an unstable spin.
New control algorithms are being developed that use only magnetic torquers
to achieve quasi 3-axis control for nadir-pointing spacecraft. Local
stability and fine pointing can be achieved by using full state feedback with
asymptotic low-bandwidth solutions to a periodic linear quadratic problem.
An alternate controller achieves global stabilization using magnetic torquers
by exploiting the principles of conservation of angular momentum and energy.
As in the case of attitude estimation, proper use of the Euler attitude
dynamics model is the key to the development of satisfactory controller
designs. The performance of these controllers will be demonstrated using
simulation studies.
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| Shane Ross (Caltech) |
The Lunar L1 Gateway: Portal to the Planets
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Our solar system is interconnected by a vast system of tunnels winding
around the sun generated by the Lagrange points of all the planets and
their moons. These passageways are identified by portals around L1 and L2,
membranes in the phase space which control the transport between regions.
This natural Interplanetary Superhighway System (IPS) provides ultra-low
energy transport throughout the Earth's neighborhood, the region between
Earth's L1 and L2. This is enabled by a coincidence: the current energy
levels of the Earth L1 and L2 Lagrange points differ from that of the
Earth-Moon by only about 50 m/s (as measured by Delta-V). The significance
of this coincidence to the development of space cannot be overstated. For
example, this implies that lunar L1 halo orbits are connected to halo
orbits around Earth's L1 or L2 via low energy pathways. Many of NASA's
future space observatories located around the Earth's L1 or L2 may be
built in a lunar L1 orbit and conveyed to the final destination via IPS
with minimal propulsion requirements. Similarly, when the spacecraft or
instruments require servicing, they may be returned from Earth libration
orbits to the lunar L1 orbit where human servicing may be performed. Since
the lunar L1 orbit may be reached from Earth in less than a week, the
infrastructure and complexity of long-term space travel is greatly
mitigated. The same orbit could reach any point on the surface of the Moon
within hours, thus this portal is also a perfect location for the return
of human presence on the Moon. The lunar L1 orbit is also an excellent
point of departure for interplanetary flight where several lunar and Earth
encounters may be added to further reduce the launch cost and open up the
launch period. The lunar L1 is a versatile hub for a space transportation
system of the future and should be seriously considered as a possible
location for a future space station.
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| Bong Wie (Arizona) |
Dynamic Modeling and Attitude/Orbit Control of Solar
Sail Spacecraft
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Study results for developing dynamic models and
attitude/orbit control
systems of solar sail spacecraft are presented. The study
objective was to advance
sailcraft attitude and flight control technology so that a sail
spaceflight experiment for
validating sail attitude stability & controllability and thrust
vector pointing & steering
performance can be conducted within the next 5 years. Various dynamic
models and conceptual
control design options are developed for a sail attitude control system
employing spin stabilization, reaction wheels, a two-axis gimbaled
control boom, control vanes,
and/or sail panel translation & rotation.
Particular emphasis is placed on various control design options for
accommodating or countering the significant solar pressure
disturbance torque caused by an uncertain offset between the center
of mass (cm) and the center of pressure (cp). A 40 x 40 m, 160-kg
sailcraft with a nominal solar pressure force of 0.01 N, an
uncertain cm/cp offset of 0.1
m, and moments of inertia of (6000, 3000, 3000) kg-m^2 is chosen
as a baseline sailcraft to illustrate the various concepts and
principles involved in dynamic modeling and attitude control design.
A solar pressure disturbance torque of 0.001 N-m of such a
baseline sailcraft is about 100 times larger than that of typical
geosynchronous communications satellites. A conventional
three-axis attitude control system employing reaction wheels and/or
thrusters will require large reaction wheels and/or a
prohibitively huge amount
of propellant for proper momentum management, especially for
extended sailing voyages.
Consequently, a sailcraft consisting of a small bus/payload and
large flexible sail booms
& films will be either spin stabilized or three-axis stabilized
using propellantless
attitude control techniques.
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