Generation of smooth motion trajectories for a rigid body

Abstract

Käesolev töö on pühendatud tahke keha siledate liikumistrajektooride genereerimise kirjeldamisele, arvestades selle algset ja lõplikku asendit ning orientatsiooni ruumis. Selleks tuuakse sisse sileda muutkonna, Riemanni geomeetria, Lie rühmade ning nendega seotud Lie algebrate mõisted. Trajektooride genereerimise ülesanne formuleeritakse seejärel geodeetika ülesandena rühmal SE(3), mis on varustatud vasakpoolselt invariantse Riemanni meetrikaga, tuletatud tahke keha kineetilisest energiast. The following thesis addresses the problem of generating smooth trajectories for a rigid body, considering its initial and final position, as well as its orientation in space. For this purpose, concepts of smooth manifolds, Riemannian geometry, Lie groups and their associated Lie algebras are introduced. The problem of trajectory generation is then formulated as a geodesic problem on SE(3) equipped with a left-invariant Riemannian metric, derived from the kinetic energy of the rigid body.