In this paper, a new impedance-based teleoperation strategy is proposed for assist-as-needed tele-rehabilitation via a multi-DOF telerobotic system having patient–master and therapist–slave interactions. Unlike a regular teleoperation system and as the main contribution of this work to minimize the therapist’s movements, the therapist’s hand only follows the patient’s deviation from the target trajectory. Also it provides a better perception of the patient’s problems in motor control to the therapist The admissible deviation of the patient’s limb from a reference target trajectory is governed by an impedance model responding to both patient’s and therapist’s interaction forces. As the other benefit of this framework, two sources of assistance to the patient are delivered through the master robot: (1) the adjustable impedance model, and (2) the force applied by the therapist to the slave robot. The assistive impedance model is beneficial to reduce magnitudes of the required force from the therapist and decrease his/her intervention. This results in delaying and declining the therapist’s muscle fatigue in time-consuming movement therapies. Bilateral nonlinear control laws with two types of adaptation laws are designed for the nonlinear teleoperation system. The Lyapunov stability proof of the teleoperation system and the stability of the impedance model enhance the patient’s and therapist’s safety even in the presence of modeling uncertainties of the multi-DOF telerobotic system. The performance of the proposed bilateral impedance-based strategy is experimentally investigated using different impedance parameters adjusted based on the patient’s characteristics (e.g., involuntary tremor) and disabilities (e.g., insufficient actuation force). The experiments are performed by a healthy person (as the therapist), a mechanical test bed and a volunteer (simulating the patients’ characteristics). A new force–position mapping from Cartesian to Normal–Tangential (N–T) coordinates is utilized between the master and slave workspaces and compared with typical Cartesian to Cartesian projection.
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