Abstract
An open research question is how to define a useful metric on SE(n) with respect to (1) the choice of coordinate frames and (2) the units used to measure linear and angular distances. We present two techniques for approximating elements of the special Euclidean group SE(n) with elements of the special orthogonal group SO(n+1). These techniques are based on the singular value and polar decompositions (denoted as SVD and PD respectively) of the homogeneous transform representation of the elements of SE(n). The projection of the elements of SE(n) onto SO(n+1) yields hyperdimensional rotations that approximate the rigid-body displacements (hence the term projection metric. A bi-invariant metric on SO(n+1) may then be used to measure the distance between any two spatial displacements. The results are PD and SVD based projection metrics on SE(n). These metrics have applications in motion synthesis, robot calibration. motion interpolation, and hybrid robot control.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
