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See detailTowards coordination algorithms on compact Lie groups
Sarlette, Alain ULg

Master of advanced studies dissertation (2007)

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a ... [more ▼]

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so-called consensus state without using any external reference. In the same line of thought, a leader-follower approach where ’follower’ agents would track one ’leader’ agent is excluded, in favor of a fully cooperative strategy. Moreover, the presence of communication links between agents is explicitly restricted, leading to undirected, directed and/or time-varying communication structures. Two levels of complexity are considered for the models of the agents. First, they are modeled as simple integrators on Lie groups. This setting is meaningful in a trajectory-planning context for swarms of mechanical vehicles, or to solve algorithmic problems involving multiple agent coordination. In a second step, the model of Newtonian mechanics is used for Lie group solids, which correspond to the abstraction of the Euler laws for the rotation of a rigid body to general Lie groups. This setting is relevant for the actual control of mechanical vehicles through torques and forces. As a common starting point, the consensus problem is formulated in terms of the extrema of a cost function. This cost function is linked to a specific centroid definition on manifolds, which is referred to in this work as the induced arithmetic mean, that is easily computable in closed form and hence may be of independent interest. Using the integrator model, this naturally leads to efficient gradient algorithms to synchronize (i.e. maximizing the consensus) or balance (i.e. minimizing the consensus) the agents; the latter however can only implement the corresponding control laws if the communication graph is fixed and undirected. For directed and/or varying communication graphs, a convenient adaptation of the gradient algorithms is obtained using auxiliary estimator variables that evolve in an embedding vector space. An extension of these results to homogeneous manifolds is briefly discussed. For the mechanical model, the coordination objective is specialized to coordinated motion (i.e. moving such that the relative positions of the agents are conserved) and synchronization (i.e. having all the agents at the same position on the Lie group). Control laws are derived using two classical approaches of nonlinear control - tracking and energy shaping. They are both based on the ideas developed in the first part. For the sake of easier understanding and given its practical importance as representing orientations of rigid bodies in 3-dimensional space, the group SO(3) (or more generally SO(n)) is used as a running example throughout this report. Other examples are the circle SO(2) and, for the extension to homogeneous manifolds, the Grassmann manifolds Grass(p, n). As this report is written in the middle of research activities, it closes with several future research directions that can be explored in the continuity of the present work. [less ▲]

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See detailCooperative attitude synchronization in satellite swarms: a consensus approach
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

in Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace (2007, June)

The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as ... [more ▼]

The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as particles on SO(3) and drive these particles to a common point in SO(3). Unlike the Euler angle or quaternion descriptions, this model suffers no singularities nor double-points. Our approach is fully cooperative and autonomous: we use no leader nor external reference. We present two types of control laws, in terms of applied control torques, that globally drive the swarm towards attitude synchronization: one that requires tree-like or all-to-all inter-satellite communication (most efficient) and one that works with nearly arbitrary communication (most robust). [less ▲]

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See detailSynchronization and balancing on the N-torus
Scardovi, Luca; Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

in Systems & Control Letters (2007), 56(5), 335-341

In this paper. we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness ... [more ▼]

In this paper. we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. [less ▲]

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See detailRigid body attitude synchronization: a consensus approach
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

Conference (2007, March)

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

in Proceedings of the 17th MTNS Symposium, Kyoto 2006 (2006, August)

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with ... [more ▼]

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous synchronization results that have focused on convergence in the Euclidean space (R^n)^N. We address the question from a control perspective, but make several connections with existing models, including the Hopfield network, the Vicsek model and the (continuous-time) Kuramoto model. We propose two different distributed algorithms. The first one achieves convergence to equilibria in shape space that are the local extrema of a potential U_L built on the graph Laplacian associated to a fixed, undirected interconnection topology; it can be implemented with sensor-based interaction only, since each agent just relies on the relative position of its neighbors. The second one achieves synchronization under varying and/or directed communication topology using local estimates of a consensus variable that are communicated between interacting agents. Both algorithms are based on the notion of centroid and can be interpreted as descent algorithms. The proposed approach can be extended to other embedded compact manifolds. [less ▲]

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

Conference (2006, March)

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See detailCharacterization of the spin and attitude of the ESA Huygens probe during its descent onto Titan using the engineering dataset
Sarlette, Alain ULg

Master's dissertation (2005)

The Huygens probe is the ESA’s main contribution to the Cassini-Huygens mission, carried out jointly by the ESA, the NASA and the ASI. It was designed to descent into the atmosphere of Titan, Saturn’s ... [more ▼]

The Huygens probe is the ESA’s main contribution to the Cassini-Huygens mission, carried out jointly by the ESA, the NASA and the ASI. It was designed to descent into the atmosphere of Titan, Saturn’s largest moon, on January 14, 2005, providing surface images of the farthest object a man-made probe has ever landed on. Its main purpose was to study Titan’s atmosphere during the descent phase. Of course, priority has been given to the scientific instruments for data recovery but a small engineering dataset was also sent back to Earth. The goal of the present work was, using these engineering data, to characterize the instantaneous orientation of the Huygens probe during its descent, in order to allow correct analysis of the scientific data. The methods used concern evaluation of reduced accelerometer data, analysis of the telecommunication link’s power level using the accurately known antenna gain pattern and a comparison between the Huygens mission and the more fully instrumented SM2 test probe which was dropped in the Earth’s atmosphere in 1995. Some basic dynamic modelization has also been done to investigate likely behaviours and try to identify consistent approximations. In addition to this report, the results of my work include Excel r files containing probe orientation (support) data as well as a MATLAB r routine which allows to compute a probe’s azimuth from the (manually pre-processed) telemetry link gain and the positioning dataset. A user-friendly program for the visualization of the evolution of all involved variables - including a 3D probe orientation display - was also planned, but could not be finished since a complete characterization of the probe’s attitude (tilt-related motions) was not achieved yet before writing the present report. As a whole bunch of people spread over the world were working on the subject of the probe’s orientation using different information, the conclusions of all teams had to be compared. This was continually done by e-mail while working on the subject; a final meeting on April 22 & 23, 2005 was meant to clarify the situation before publishing first official results. [less ▲]

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See detailComparison of the Huygens mission and the SM2 test flight for Huygens attitude reconstruction
Sarlette, Alain ULg; Perez-Ayucar, Miguel; Witasse, Olivier et al

Conference (2005, June)

The Huygens probe is the ESA’s main contribution to the Cassini/Huygens mission, carried out jointly by NASA, ESA and ASI. It was designed to descend into the atmosphere of Titan on January 14, 2005 ... [more ▼]

The Huygens probe is the ESA’s main contribution to the Cassini/Huygens mission, carried out jointly by NASA, ESA and ASI. It was designed to descend into the atmosphere of Titan on January 14, 2005, providing surface images and scientific data to study the ground and the atmosphere of Saturn’s largest moon. In the framework of the reconstruction of the probe’s motions during the descent based on the engineering data, additional information was needed to investigate the attitude and an anomaly in the spin direction. Two years before the launch of the Cassini/Huygens spacecraft, in May 1995, a test probe called SM2 (Special Model 2) was dropped in the Earth’s atmosphere from the balloon launch site of Kiruna, Sweden, to verify proper operation during the descent and especially the parachute deployment sequence. It featured a flight standard structure and DCSS (Descent Control SubSystem) and, unlike the Huygens probe, was fully instrumented to monitor the orientation of the descent module (3-axes accelerometers and gyroscopes). We describe how a comparison between the SM2 test flight and the Huygens mission provides some useful information about the Huygens probe’s behavior. After discussing the spin direction, we focus on the tip and tilt. The final conclusions of this comparison at the time of writing are still of qualitative nature, but the results are a starting point for better interpretation of the engineering data in terms of attitude to derive the probe’s orientation. [less ▲]

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See detailHuygens attitude reconstruction based on flight engineering parameters
Perez-Ayucar, Miguel; Sarlette, Alain ULg; Couzin, Patrice et al

Conference (2005, June)

Huygens is ESA’s main contribution to the joint NASA/ESA/ASI Cassini/Huygens mission to Saturn and its largest moon Titan. The Probe, delivered to the interface altitude of 1270 km above the surface by ... [more ▼]

Huygens is ESA’s main contribution to the joint NASA/ESA/ASI Cassini/Huygens mission to Saturn and its largest moon Titan. The Probe, delivered to the interface altitude of 1270 km above the surface by NASA/JPL Cassini orbiter, entered the dense atmosphere of Titan on 14 January 2005 and landed on the surface after a descent under parachute of slightly less than 2.5 hours. Huygens continued to function after landing for more than 3 hours. Data was transmitted and successfully recovered by Cassini continuously during the parachute descent and for 72 minutes on the surface. Although the Huygens attitude reconstruction based on the flight engineering parameters was not foreseen during the development phase (no gyros were included), a rough descent under parachute and indications of an anomaly in the probe spin direction make the engineering dataset valuable in the frame of the ADRS (Huygens Attitude Determination and Reconstruction Subgroup) as a complement to the scientific measurements. In addition, several scientific teams have a strong interest in understanding the orientation of the probe for interpreting their data, as DISR (Descent Imager and Spectral Radiometer) and HASI-PWA (Huygens Atmospheric Structure Instrument-Permeability, Wave and Altimetry). In this paper we describe the engineering parameters used for the Probe attitude reconstruction (Clausen et al., 2002), namely the radio link AGC (Automatic Gain Control), RASU and CASU (Radial and Central Accelerometer Sensor Units) and RAU (Radar Altimeter Unit). We explain the methodology applied to indirectly infer the attitude information from the measurements of these sensors. We also discuss and present the reconstructed information related to attitude: spin rate and azimuthal position (during the atmospheric descent), and landing orientation. Tip and tilt implications are still being worked at the time of writing. Preliminary data on their behavior is presented. [less ▲]

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