The mathematics that were originally developed for the N-localizer apply to three N-localizers that produce three sets of fiducials in a tomographic image. Some applications of the Nlocalizer use four N-localizers; however, the mathematics that apply to three N-localizers do not apply to four N-localizers. One solution to this problem is to ignore one of the four Nlocalizers in order that the m...

In the present paper, we study surfaces invariant under the 1-parameter subgroup in Sol space $rm Sol_3$. Also, we characterize the surfaces in $rm Sol_3$ whose coordinate functions of an immersion of the surface are eigenfunctions of the Laplacian $Delta$ of the surface.

This work addresses the problem of resolving kinematic redundancy in legged robots, with the dual goals of maintaining a large reachable workspace and of achieving fast end effector motions in task space. In particular, for robots with four or more legs, gait planning allows for considerable flexibility in the orientation of a stance limb with respect to both body orientation and the ground. By...