Metrics on Motion and Deformation of Solid Models

Abstract

Recently, the importance of metrics on the group of rigid body motions has been addressed in a number of works in the kinematics and robotics literature. This paper defines new metrics on motion which are particularly easy to compute. It is shown how these metrics are applicable to path generation for rigid body motions, and also as a means for generating interpolated sequences of deformed solid models. In order to address both problems in a unified framework, general metrics on Lie groups are discussed.