title: Optimization on the space of rigid and flexible motions: an alternative manifold optimization approach.
abstract: In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.
authors.affiliation: Dept. of Mechanical Eng. and Division of Systems Eng., Boston University.
authors.forename: Pirooz
authors.initials: P
authors.lastname: Vakili
authors.affiliation: Division of Systems Eng., Boston University.
authors.forename: Hanieh
authors.initials: H
authors.lastname: Mirzaei
authors.affiliation: Dept. of Mechanical Eng., Boston University.
authors.forename: Shahrooz
authors.initials: S
authors.lastname: Zarbafian
authors.affiliation: Dept. of Electrical & Computer Eng., and Division of Systems Eng., Boston University.
authors.forename: Ioannis Ch
authors.initials: IC
authors.lastname: Paschalidis
authors.affiliation: D. Kozakov, and S. Vajda are with the Dept. of Biomedical Eng., Boston University.
authors.forename: Dima
authors.initials: D
authors.lastname: Kozakov
authors.affiliation: D. Kozakov, and S. Vajda are with the Dept. of Biomedical Eng., Boston University.
authors.forename: Sandor
authors.initials: S
authors.lastname: Vajda