A Gaussian Mixture Framework for Co-Operative Rehabilitation Therapy in Assistive Impedance-Based Tasks

Rehabilitation robots can aid patients to practice activities of daily living in order to enhance muscle strength and recover motor functions. In this paper, we focus on robot-assisted rehabilitation for co-operative therapy tasks that elicit impedance-based behaviors from the patient. For instance, if the rehabilitation robot is controlled to behave as a self-closing door and if pulling this simulated door open is the therapy task the patient needs to complete, the patient's hand should display a minimum required impedance to complete the task. When a patient is unable to complete the task, determining the minimum assistance to be provided to the patient by the rehabilitation robot such that the task can be accomplished is of interest. In this paper, we compare the impedance behavior of a therapist in multiple trials of the task with that of the patient using a learning from demonstration (LfD) technique that utilizes Gaussian mixture models. First and during the demonstration phase, the therapist performs the tasks individually so that the robot gains insight into how a healthy person would perform the task. Next and during the reproduction phase, the robot will co-operate with the patient in the therapist's absence and provide him/her with adaptive external assistance on a patient-specific and as-needed basis so that the task can be completed. To encourage active participation, provision of assistance to the patient is coupled to the variability observed in the therapist's behavior across various trials of the task. Therefore, the presented framework transfers the constraints and underlying characteristics of a given impedance-based task to the rehabilitation robot leading to co-operative interaction between the robot and the patient where the robot provides just-enough assistance. Experimental results involving 1-D and 2-D impedance-based tasks show that the proposed framework effectively provides the patient with assistance as needed during co-operative therapy.