In this paper, an approach to physical collaboration between a patient and a therapist is proposed using a bilateral impedance control strategy developed for delayed tele-robotic systems. The patient performs a tele-rehabilitation task in a resistive virtual environment with the help of online assistive forces from the therapist being provided through teleoperation. Using this strategy, the patient's involuntary hand tremors can be filtered out and the effort of severely impaired patients can be amplified in order to facilitate their early engagement in physical tasks. The response of the first desired impedance model is tracked by the master robot (interacting with the patient), and the master trajectory plus a deviation as the response of the second impedance model is tracked by the slave robot (interacting with the therapist). Note that the first impedance model is a virtual mass-damper-spring system that has a response trajectory to the combination of patient and therapist forces. Similarly, the second impedance model is a virtual mass-damper-spring system that generates the desired slave–master deviation trajectory as its response to the therapist force. Transmitted signals through the communication channels are subjected to time delays, which exist in home-based rehabilitation (i.e., tele-rehabilitation). Tracking of the impedance models responses in the presence of modeling uncertainties is achieved by employing a nonlinear bilateral adaptive controller and proven using a Lyapunov analysis. The stability of delayed teleoperation system is also proven using the absolute stability criterion. The proposed control method is experimentally evaluated for patient–therapist collaboration in resistive/assistive tasks. In these experiments, a healthy human operator simulates a poststroke patient behavior during the interaction with the master robot.

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