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Development and testing of model predictive control strategies for spacecraft formation flying
Full text linkSatellite Formation Flying (SFF) is a key technology for several future missions, since, with respect to a single spacecraft, it allows better performances, new capabilities, more flexibility and robustness to failure and cost reduction. Despite these benefits, however, this new concept poses several signicant design challenges and requires new technologies. The Guidance, Navigation and Control (GNC) system is a key element in the SFF concept since it must be reliable in coordinating all the satellites fying in formation during each mission phase, guaranteeing formation integrity and preventing from formation evaporation, and, at the same time, efficient in using the limited on board resources. Model Predictive Control (MPC), also referred to as Receding Horizon Control, is a modern optimal control technique that seems to be suitable for these purposes because of its three main features: model-based control scheme, constraints handling ability and replanning nature.
The final aim of my Ph.D. activities was to develop and test MPC strategies for SFF applications. This task was accomplished by means of both computer simulations and experimental tests conducted on both the MIT Synchronized Position Hold Engage & Reorient Experimental Satellites (SPHERES) testbed and the SFF Hardware Simulator under development at the Center of Studies and Activities for Space "Giuseppe Colombo" (CISAS), University of Padova.
MPC capabilities were first tested in computer simulations in carrying out a formation acquisition maneuver for two space vehicles, taking into account two scenarios: a Leader-Follower (LF) formation and Projected Circular Orbit (PCO) formation. The performances of the MPC-based controller were compared with those of a Linear Quadratic Regulator (LQR) based controller in the presence of active constraints on the maximum control acceleration, evaluating also the effects of the gravitational harmonics J2 and J3 and atmospheric drag perturbations on the proposed maneuvers. Simulation results of both scenarios showed that, with similar performances in tracking the same reference state trajectory in terms of settling time, the MPC controller is more efficient (less delta-v requirement) than the LQR controller also in the perturbed cases, allowing a delta-v requirement reduction by 40% in the LF formation scenario and by 30% in the PCO formation scenario.
The next activity concerned the development of some guidance and control strategies for a Collision-Avoidance scenario in which a free-flying chief spacecraft follows temporary off-nominal conditions and a controlled deputy spacecraft performs a collision avoidance maneuver. The proposed strategy consists on a first Separation Guidance that, using a computationally simple, deterministic and closed-form algorithm, takes charge of avoiding a predicted collision. When some safe conditions on the relative state vector (position and velocity) are met, a subsequent Nominal Guidance takes over. Genetic Algorithms are used to compute a pair of reference state trajectories in order to place the deputy spacecraft in a bounded safe or "parking" trajectory, while minimizing the propellant consumption and avoiding the formation evaporation. The performances of a LQR and a MPC in tracking these reference trajectories were compared, showing how a MPC controller can reduces the total delta-v requirement by 5 - 10% with respect to a LQR controller.
MPC capabilities were then evaluated on the MIT SPHERES testbed in simulating the close-proximity phase of the rendez-vous and capture maneuver for the Mars Orbital Sample Return (MOSR) scenario. Better performances of MPC with respect to PD in executing this maneuver were conrmed both in a Matlab simulator and in the MIT SPHERES software simulator, with a total delta-v requirement reduction by 10-15 %. The proposed MPC control strategy was then tested using the SPHERES Flat Floor facility at the MIT Space System Laboratory.
The last part of my research activities was devoted to the SFF Hardware Simulator of the University of Padova. My contributions to this project dealt with: (a) conclusion of the designing, building and testing of the five main subsystems of the hardware simulator; (b) software development for the hardware simulator and its Matlab software simulator; (c) preparatory experimental activities aimed at characterizing the thrust force performed by the on board thrusters and estimating the hardware simulator inertia properties; and (d) test of attitude control maneuvers with the use of predictive controllers.
In particular, three main tests were carried out with the hardware simulator moving at one degree of freedom about the yaw axis. The first one aimed at tuning a Kalman Filter to properly estimate the yaw axis angular velocity using a double-integrator as dynamic model and angular position measurements provided by the yaw quadrature encoder. With the use of a simple Kalman Filter, the yaw angular position and velocity could be estimated with an error less than 0.1 ° and 0.1°/s, respectively. In the second test, an explicit MPC was used to perform a 170° slew maneuver of the hardware simulator attitude module about the yaw axis. The final target angular position was reached with an error less than 0.5° in 20 s. In the third test, a 3 degrees of freedom attitude reference trajectory was first computed using pseudospectral optimization methods for a repointing maneuver with active constraints on the attitude trajectory. The state trajectory was then projected along the satellite z-Body axis and tracked in the hardware simulator using an explicit MPC. Experimental results showed that with an explicit MPC the reference trajectories can be tracked with an error less that 1.5° for the angular position and less than 1°/s for the angular velocity, both in dynamic conditions. The final target state was reached with an error less than the estimation accuracy.
The SFF Hardware Simulator is a ground-based testbed for the development and verification of GNC algorithms that in the present configuration allows the development and testing of advanced controls for attitude motion and in its final form will enable the derivation of control strategies for
Formation Flight and Automated Rendezvous and Docking
Guidance and Control Strategies for the Collision-Avoidance Mode of a Satellite Pair Flying in Formation
No full textAbstract. In this paper we present a study on the
Collision-Avoidance mode of a formation flying
satellite pair in which a free-flying chief
spacecraft follows temporary off-nominal
conditions and a controlled deputy spacecraft
performs collision avoidance maneuvers.
The Collision-Avoidance strategy consists in a
Separation Guidance and a Nominal Guidance.
The Separation Guidance is in charge of the
avoidance of a predicted collision soon to
occur, and it is based on a computationally
simple, deterministic and closed-form
algorithm, so that a valid solution is always
available without delay. The Nominal Guidance
uses Genetic Algorithms and it takes charge of
placing the deputy spacecraft in a bounded safe
or “parking” trajectory, while minimizing the
propellant consumption and avoiding the
evaporation of the formation.
The performances of a Linear Quadratic
Regulator and a Model Predictive Control are
also compared in tracking the reference
trajectories provided by the Collision-
Avoidance strategy
360-deg FOV Scanning LiDAR versus Non-Repetitive Scanning LiDAR: A Rover Navigation Experiment
No full textModel Predictive Control Strategies for Spacecraft Formation Flying Applications
No full textAbstract. Formation flying missions require high
performance orbital control strategies, which
are based on the accurate analysis of the
spacecraft relative dynamics and on efficient
control techniques.
Model Predictive Control (MPC) is a modern
optimal control strategy that is very attractive
for formation flying and rendezvous missions,
mainly because of its ability to cope with
constraints on control actions and dynamic
state of the system. Every real space mission
indeed imposes constraints, as for example the
maximum control force a thruster system can
apply, or the relative positions and/or velocities
that satellites flying in formation should have to
guarantee formation safety. MPC can take into
account both control and state constraints
directly in the optimal control action
computation, resulting in a more efficient
control system than other control strategies.
In this paper we present a study on the MPC
application to a formation acquisition maneuver
for two space vehicles, taking into account two
scenarios: a Leader-Follower formation and a
Projected Circular Orbit formation. The
performances of an MPC controller are
compared with those of a LQR controller in
carrying out the same maneuver, evaluating
also the effects of the gravitational harmonics
J2 , J3 and drag perturbations on the proposed
maneuvers
Determination of the accelerometer metrological characteristics on board the METRIC mission
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Fast and Accurate Numerical Integration of Relative Motion in Spacecraft Formation Flying
No full textAbstract - The special perturbation method DROMO developed
by Peláez in 2006 for the perturbed two-body problem
is employed to propagate the relative motion in spacecraft
formation flying, and the performance of the new
method, named DROMO-FF, is analyzed. DROMO
is a very fast and accurate regularized method which
involves a set of seven integrals of the pure Keplerian
motion whose physical meaning is described
in the paper. We propose to propagate the absolute
motion of N spacecraft simultaneously by using
DROMO with the introduction of new dependent variables,
necessary for the synchronization, and to determine
the relative dynamics by differentiating the
absolute states. After investigating the influence on
the performance due to the numerical integration of
the new variables, we show that DROMO-FF is significantly
more accurate than Cowell’s method for the
same computing time, or equivalently, faster for the
same accuracy. A second approach to propagate relative
motion wherein linearization is performed with
respect to the formation baricenter is presented and
compared to DROMO-FF. It is shown that for closed
formations round-off does not affect the accuracy of
DROMO-FF
Two-bar model for free vibrations damping of space tethers by means of spring-dashpot devices
No full textAbstract Present guidelines indicate the need to deorbit
new satellites launched into low Earth orbit (LEO) within
25 years from their end of life. Our research task is to
develop a new technology suitable to deorbit a satellite at
the end of life with as small an impact as possible on the
mass budget of the mission. An alternative to the traditional
chemical rockets consists in using an electrodynamic
tether that, through its interaction with the Earth ionosphere
and magnetic field, can take advantage of Lorentz
forces for deorbiting purposes. However, Lorentz forces
produce a low and yet continuous injection of energy into
the system that, in the long run, can bring the tether to
instability. This paper addresses this issue through the
analysis of the benefits provided by an elastic-viscous
damping device installed at the attachment point of the
tether to the spacecraft. The analysis carried out by means
of linearization of dynamics equations and numerical
simulations show that a well-tuned damper can efficiently
absorb the kinetic energy from the tether thus providing
system stability during deorbiting. @ CEAS 201
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