Tele-rehabilitation with online skill transfer and adaptation in $\mathbb{R}^3 \times \mathit{S}^3$

This paper proposes a tele-teaching framework for the domain of robot-assisted tele-rehabilitation. The system connects two robotic manipulators on therapist and patient side via bilateral teleoperation, enabling a therapist to remotely demonstrate rehabilitation exercises that are executed by the patient-side robot. A 6-DoF Dynamical Movement Primitives formulation is employed to jointly encode translational and rotational motions in $\mathbb{R}^3 \times \mathit{S}^3$ space, ensuring accurate trajectory reproduction. The framework supports smooth transitions between therapist-led guidance and patient passive training, while allowing adaptive adjustment of motion. Experiments with 7-DoF manipulators demonstrate the feasibility of the approach, highlighting its potential for personalized and remotely supervised rehabilitation.