Incomplete Orientation Mapping for Teleoperation With One DoF Master-Slave Asymmetry

Teleoperation systems require a human-centered approach in which the kinematic mapping is intuitive and straightforward for the operators. However, a mismatch in the degrees-of-freedom (DoFs) between master and slave could result in an asymmetrical teleoperation system. That is an obstacle for intuitive kinematic mapping. In particular, it is even more challenging when the missing DoF is a pure rotational DoF, since the rotation group <inline-formula><tex-math notation="LaTeX">$SO(3)$</tex-math></inline-formula> is a nonlinear Riemannian manifold. This letter is concerned with an asymmetric teleoperation system, where the master subsystem can provide 6-DoF pose sensing while the slave subsystem only has 5 DoFs. The rotation along the missing DoF, which is configuration-dependent, is mapped to a geodesic curve in <inline-formula><tex-math notation="LaTeX">$SO(3)$</tex-math></inline-formula>. We define and prove the closed-form solution of the perpendicular curve to the geodesic curve. Based on the perpendicular curve, we develop a novel Incomplete Orientation Mapping (IOM) approach to avoid the motion in the missing DoF. By comparing with two baseline methods, the experimental results demonstrate that the proposed method can discard the rotational motion along the missing DoF for all configurations, while preserving the remaining rotations.