  Implementing virtual fixtures in guiding tasks constrains the movement of the
robot's end effector to specific curves within its workspace. However,
incorporating guiding frameworks may encounter discontinuities when optimizing
the reference target position to the nearest point relative to the current
robot position. This article aims to give a geometric interpretation of such
discontinuities, with specific reference to the commonly adopted Gauss-Newton
algorithm. The effect of such discontinuities, defined as Euclidean Distance
Singularities, is experimentally proved. We then propose a solution that is
based on a Linear Quadratic Tracking problem with minimum jerk command, then
compare and validate the performances of the proposed framework in two
different human-robot interaction scenarios.
