References of "Lageman, Christian"
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See detailOptimal Data Fitting on Lie Groups: a Coset Approach
Lageman, Christian; Sepulchre, Rodolphe ULg

in Diehl, M. (Ed.) Recent Advances in Optimization and its Applications in Engineering (2010)

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in Rn to data which can ... [more ▼]

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in Rn to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n). [less ▲]

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See detailSynchronization with partial state feedback on SO(n),
Lageman, Christian; Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

in Proceedings of the 48th IEEE Conference on Decision and Control (2009, December)

This paper considers the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state ... [more ▼]

This paper considers the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in Rn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. [less ▲]

Detailed reference viewed: 35 (6 ULg)