1 Robotic rehabilitation and assistance for individuals with movement disorders based on a kinematic model of the upper limb Carlos Rossa, Mohammad Najafi, Mahdi Tavakoli, and Kim Adams Abstract—Design and development of robotic-assistance must consider the abilities of individuals with disabilities. In this paper, a 8-DOF kinematic model of the upper limb complex is derived to evaluate the reachable workspace of the arm during interaction with a planar robot and to serve as the basis for rehabilitation strategies and assistive robotics. Through inverse differential kinematics and by taking account the physical limits of each arm joint, the model determines workspaces where the individual is able to perform tasks and those regions where robotic assistance is required. Next, a learning-from-demonstration strategy via a nonparametric potential field function is derived to teach the robot the required assistance based on demonstrations of functional tasks. The paper investigates two applications. First, in the context of rehabilitation, robotic assistance is only provided if the individual is required to move her arm in regions that are not reachable via voluntary motion. Second, in the context of assistive robotics, the demonstrated trajectory is scaled down to match the individual’s voluntary range of motion through a nonlinear workspace mapping. Assistance is provided within that workspace only. Experimental results in 5 different experimental scenarios with a person with cerebral palsy confirm the suitability of the proposed framework. I. I NTRODUCTION S PASTIC movement disorders are prominent features of impaired function of the motor system frequently as- sociated with stroke and cerebral palsy [1]. They are best characterised by changes in reflex excitability, muscle tone, and restricted range of motion, all leading to difficulties in per- forming voluntary movements [2], [3]. About 460,000 people are living with the effects of stroke in Canada and 770,000 people have one or more symptoms of cerebral palsy in the United States [4], [5]. The limitations in performing voluntary movements restricts people in their daily living activities, but robotics can be used to help build skills (rehabilitation) or to be a tool for people with disabilities to do daily activities (assistive). Rehabilitation robots help therapists facilitate functional motor recovery of individuals with physical disability [6], This research was supported by the Canada Foundation for Innovation (CFI) under grant LOF 28241, the Alberta Innovation and Advanced Education Ministry under Small Equipment Grant RCP-12-021, the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canadian Institutes of Health Research (CIHR), and Quanser, Inc. C. Rossa, M. Najafi, and M. Tavakoli are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. E-mail: rossa@ualberta.ca; najafi@ualberta.ca; mahdi.tavakoli@ualberta.ca. K. Adams is with the Faculty of Rehabilitation Medicine at the University of Alberta, and with the Glenrose Rehabilitation Hospital, Edmonton, Canada. E-mail: kdadams@ualberta.ca. [7]. Rehabilitation robots are typically designed for thera- peutic exercise, relearning, and reactivating residual motor function while preventing secondary complications such as muscle atrophy [8]. Progressive resistance exercise is a method of increasing the ability of muscles to generate force [9]. Although some symptoms of spasticity are permanent, studies have documented positive effects of robotic-assisted training in improving motor function of individuals living with cerebral palsy [10], and post-stroke movement impairments [11]. For post-stroke therapy, robot-assisted therapy appears to cause more short-term reduction in motor impairment, e.g., muscle activation and speed of movement, than conventional rehabil- itation therapy [12]. Different planar robots have been used in recent studies for human upper-limb rehabilitation. The Quanser rehabilitation robot was employed in [13] to evaluate intelligent haptic effectiveness for post-stroke rehabilitation. Using the 2-DOF CASIA-ARM robot, a subject’s functional capability was learnt using a Gaussian RBF network and the robot provided assistance according to the subject’s perfor- mance and condition [14]. The InMotion Arm robot has also been used, and the reliability of measured kinematic variables used in patients’ neurorehabilitation after stroke was evaluated [15]. A 2-DOF planar robot detected the correct movements in order to increase the effectiveness of the rehabilitation process [16]. Assistive robots compensate for disability due to a given pathological condition [17]. These technologies are intended to allow individuals to accomplish daily life activities that would otherwise be difficult or impossible to perform, using for example a manipulator arm to interact with a variety of environments and objects [18], [19], [20]. Typically individ- uals control the manipulator arm using a joystick, but other control interfaces have been tried for individuals with complex physical impairments, including those with stroke and cerebral palsy [21], [22]. Since the symptoms associated with these disorders can vary widely, appropriate interventions must focus on the specific disorders and conditions of each individual [23]. This is particularly relevant for robots used in rehabilitation where quantitative assessment of spasticity is important for evaluating potential effects of treatment [24], guiding the design of a robotic system that complies with the individual’s needs and motion tolerances [25], and ensuring individual’s safety and comfort during robotic intervention [26]. In particular, it is crucial that the robot be adaptable to the human limb segment lengths, range of motion, forces, and velocity. Furthermore, This paper appears in IEEE Transactions on Medical Robotics and Bionics, 2021. DOI: 10.1109/TMRB.2021.3050512