Coordinated motion design on lie groups

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3). © 2010 IEEE.

Optimal data fitting on lie groups: A coset approach

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 n 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). © 2010 Springer -Verlag Berlin Heidelberg.

stochastic process algebra based software process simulation modeling

Chinese Acad Sci, ISCAS Lab Internet Software Technologies

Relation algebra operations on formal contexts.

This paper discusses the use of relation algebra operations on formal contexts. These operations are a generalisation of some of the context operations that are described in the standard FCA textbook (Ganter & Wille, 1999). This paper extends previous research in this area with respect to applications and implementations. It also describes a software tool (FcaFlint) which in combination with FcaStone facilitates the application of relation algebra operations to contexts stored in many formats.

Algebra Llinol - Cyflwyniad

Cyfieithiad yw'r llyfr hwn o Linear Algebra - An Introduction a ymddangosodd gyntaf yn 1978 ac a gyhoeddwyd gan y cwmni Van Nostrand Reinhold. Cafwyd Ail Argraffiad yn 1982 a dros y blynyddoedd bu nifer o ail brintiadau. Yn y cyfamser cyfieithwyd y llyfr i'r Groeg a Thwrceg. Er i'r llyfr gael ei ddefnyddio dros y blynyddoedd gan nifer o fyfyrwyr yn Aberystwyth a oedd yn cyflwyno eu gwaith yn Gymraeg, nid oedd ar gael yn y Gymraeg. Dyma, o'r diwedd, ymgais i wneud rhyw fath o iawn am hynny. Er bod y llyfr wedi bod allan o brint yn y Saesneg ers rhai blynyddoedd yn awr, mae'n amlwg ei fod yn dal i gael ei gymeradwyo mewn nifer o brifysgolion. Felly, y gobaith yw y bydd o ddefnydd. Efallai mai'r peth nesaf bydd ei gyfiethu'n ?l i'r Saesneg! Mae nifer o newidiadau yn y fersiwn hwn. Mae'n siwr bod nifer o gamgymeriadau ac efallai gwelliannau posibl i'r cyfieithu - byddwn yn ddiolchgar dderbyn unrhyw awgrymiadau. Gellir eu cyflwyno hefyd drwy Dr Gwion Evans o'r Adran Fathemateg, Prifysgol Aberystwyth.

A Biomechanical Model of Human Oculomotor Plant Kinematics Based Upon Geometric Algebra

A biomechanical model of the human oculomotor plant kinematics in 3-D as a function of muscle length changes is presented. It can represent a range of alternative interpretations of the data as a function of one parameter. The model is free from such deficits as singularities and the nesting of axes found in alternative formulations such as the spherical wrist (Paul, l98l). The equations of motion are defined on a quaternion based representation of eye rotations and are compact atnd computationally efficient.