  Global redundancy resolution (GRR) roadmap is a novel concept in robotics
that facilitates the mapping from task space paths to configuration space paths
in a legible, predictable, and repeatable way. Such roadmaps could find
widespread utility in applications such as safe teleoperation, consistent path
planning, and factory workcell design. However, the previous methods to compute
GRR roadmaps often necessitate a lengthy computation time and produce
non-smooth paths, limiting their practical efficacy. To address this challenge,
we introduce a novel method Expansion-GRR that leverages efficient
configuration space projections and enables a rapid generation of smooth
roadmaps that satisfy the task constraints. Additionally, we propose a simple
multi-seed strategy that further enhances the final quality. We conducted
experiments in simulation with a 5-link planar manipulator and a Kinova arm. We
were able to generate the GRR roadmaps up to 2 orders of magnitude faster while
achieving higher smoothness. We also demonstrate the utility of the GRR
roadmaps in teleoperation tasks where our method outperformed prior methods and
reactive IK solvers in terms of success rate and solution quality.
