  The paper deals with the well-known problem of teleoperating a robotic arm
along six degrees of freedom. The prevailing and most effective approach to
this problem involves a direct position-to-position mapping, imposing robotic
end-effector movements that mirrors those of the user. In the particular case
where the robot stands near the operator, there are alternatives to this
approach. Drawing inspiration from head pointers utilized in the 1980s,
originally designed to enable drawing with limited head motions for tetraplegic
individuals, we propose a "virtual wand" mapping. It employs a virtual rigid
linkage between the hand and the robot's end-effector. With this approach,
rotations produce amplified translations through a lever arm, creating a
"rotation-to-position" coupling. This approach expands the translation
workspace at the expense of a reduced rotation space.
  We compare the virtual wand approach to the one-to-one position mapping
through the realization of 6-DoF reaching tasks. Results indicate that the two
different mappings perform comparably well, are equally well-received by users,
and exhibit similar motor control behaviors. Nevertheless, the virtual wand
mapping is anticipated to outperform in tasks characterized by large
translations and minimal effector rotations, whereas direct mapping is expected
to demonstrate advantages in large rotations with minimal translations. These
results pave the way for new interactions and interfaces, particularly in
disability assistance utilizing head movements (instead of hands). Leveraging
body parts with substantial rotations could enable the accomplishment of tasks
previously deemed infeasible with standard direct coupling interfaces.
