In the literature on robotics and multibody dynamics, the concept of average
angular velocity has received considerable attention in recent years. We
address the question of whether the average angular velocity defines an
orientation framethat depends only on the current robot configuration and
provide a simple algebraic condition to check whether this holds. In the
language of geometric mechanics, this condition corresponds to requiring the
flatness of the mechanical connection associated to the robotic system. Here,
however, we provide both a reinterpretation and a proof of this result
accessible to readers with a background in rigid body kinematics and multibody
dynamics but not necessarily acquainted with differential geometry, still
providing precise links to the geometric mechanics literature. This should help
spreading the algebraic condition beyond the scope of geometric
mechanics,contributing to a proper utilization and understanding of the concept
of average angular velocity.Comment: 8 pages, accepted for IEEE Robotics and Automation Letters (RA-L
