This paper presents a synthesis procedure for a robot that guides an end-effector as close as possible to a user-specified trajectory. The technique maps the goal workspace from the group of spatial displacements, SE(3), to the group of 4 × 4 rotations, SO(4), in order to obtain a bi-invariant metric for the design procedure. Double quaternions are used to provide a convenient parameterization for SO(4). An example is presented that compares designs obtained using dual quaternions to those for double quaternions, for varying locations of the fixed frame, in order to demonstrate the technique.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.