The Lie group, SE(3), made up of all rigid-body motions is called the
special Euclidean group in three dimensions, on which mathematical
notions are set up for robotic manipulation or trajectory planning.
This thesis deals with a systematic study of metrics and connections
on SE(3). Three connections, called (-)-,(+)- and (0)-connections
after Cartan and Schouten, are introduced, and further two metric
connections are defined through two types of left-invariant metrics.
The Cartesian stiffness matrices are computed with respect to the
connections introduced, which will play a significant role in the
stability analysisn for multifingered grasp.