Human arm weight compensation in robotic rehabilitation
In the acute phase post-stroke, approximately 66%−80% of patients experience reduced arm function due to paresis and subsequent arm weakness [1, 2]. In chronic stroke patients abnormal synergies restrict the patient’s movement  and workspace  as a loss of independent joint control. In both acute and chronic patients, arm weight compensation can extend the patient’s workspace and, therefore, allow training of tasks that have higher relevance for activities of daily living [4–6]. The training of these tasks is according to the known “use it and improve it, or lose it” principle of neurorehabilitation, which is considered a key factor for successful rehabilitation . Therefore, many rehabilitation robots with arm weight compensation functions have been developed. The common robot types that provide system-dependent arm weight compensation can be divided in gantry-based robots [8–10], passive exoskeletons [11, 12], actuated exoskeletons [4, 11, 13, 14], and actuated end-effector robots [5, 6, 15–18].
For actuated rehabilitation robots, assist-as-needed control strategies are also commonly used. These strategies not only support the patients along the movement direction, but also against the gravity in an indirect way [19, 20]. However, in this paper, we focus only on the arm weight compensation as an independent assistance dimension, since the support along movement direction may not always be desirable. Furthermore, there are adaptive control strategies that readjust assistance over time . However, since arm weight is constant over time, we aim to estimate the arm weight parameters once in the beginning of the therapy session and not to adapt them during the therapy. From a literature review [8, 22] and our own experience, the following four requirements of ideal, generalizable weight compensation for robot-assisted training of activities of daily living were deduced: Freedom of movement, no additional disturbances, scalability, and applicability to other systems .
Freedom of movement
The degrees of freedom of the human arm joints should not be restricted by the robot. From the shoulder to the wrist joint, the human arm can be approximated by five degrees of freedom (shoulder horizontal abduction/adduction, shoulder elevation, shoulder internal/external rotation, elbow flexion/extension, forearm pronation/supination). Arm weight compensation should be provided in any pose without restricting or hindering any possible degree of freedom. However, most end-effector robots can restrict the user’s freedom of movement while providing arm weight compensation due to mechanical limitations and missing human joint angle information, e.g., [5, 6, 15–18].
No additional disturbances
With the exception of arm weight compensation, each robot should behave mechanically transparent during physical human-robot interactions . Ideally, weight is a static force, and thus, the robot torques providing arm weight compensation should only depend on pose, arm weight, and arm length. Generally, end-effector robots support arm weight only at the end-effector without knowledge of the user’s arm joint angles, which can lead to over- or under-compensation of arm weight. In particular, systematic disturbances due to spring properties are present in passive exoskeletons , and unwanted horizontal forces due to the vertical sling attachments are present in gantry-based robots .
A progressive reduction in arm weight compensation during rehabilitation therapy can lead to an increased active range of motion . Furthermore, scalability of arm weight compensation can be used for assessment of arm weight-induced impairments . Independent upper and lower arm weight scalability could allow more individualized assessments and therefore, tailored rehabilitation therapies for arm weight-induced impairments.
Applicability to other systems
The applicability of arm weight compensation methods to other systems is robot type-dependent. Exemplarily, a passive exoskeleton can entail mechanical spring-based arm weight compensation , which needs to be mechanically adapted for applications in different types of robots. Ideally, the method should be a software solution, that can be easily applied to a variety of rehabilitation robots with actuation.
Evaluation of arm weight compensation efficacy
The highest arm weight compensation efficacy is reached through correctly compensating for gravity contributing to arm weight in every possible arm pose, i.e., overcompensation or undercompensation of arm weight leads to a lower arm weight compensation efficacy. Arm weight compensation has been proven to be an important factor for enabling patients to train for tasks that require longer reaching distances  and an increased workspace [6, 24–27]. Furthermore, improvements in arm weight compensation efficacy are expected to lead to an even greater increase in workspace for stroke patients . However, most studies of arm weight compensation by rehabilitation robots have focused on the gains that stroke patients achieve in clinical scores rather than the provided arm weight compensation . While gains in clinical scores are good indicators of performance development in general, it is difficult to assess the contribution of the provided weight compensation to these gains. Namely, the efficacy of weight compensation per se was not evaluated in parallel, i.e., how much unloading is effectively applied for a certain unloading condition and arm pose. Therefore, the results of clinical studies that evaluate weight compensation for one particular rehabilitation device are difficult to generalize to other devices, as the weight compensation performance might differ among devices. In summary, the efficacy of arm weight compensation in rehabilitation robotics has been rarely investigated . However, several papers have investigated the efficacy of arm weight compensation through additional electromyography (EMG) measurements of relevant muscles [29–33]. For example, arm weight compensation decreased EMG activity during static holding  and reaching tasks [29–31], and the transfer of this effect to stroke patients was also shown . However, static holding was performed in only one pose , not over the whole workspace to analyze pose-dependent effects of arm weight compensation. Furthermore, previous EMG signal analyses have mainly focused on individual muscle evaluations [29–31] instead of a combined evaluation of all relevant muscles with respect to their passive reference measurements as a score. Additional active EMG reference measurements to adapt to a subject’s specific behavior and physiology have not been a main focus . Finally, the arm weight relief efficacies of different arm weight compensation methods have never been compared, even for use of the same device.
In this paper, we present three different arm weight compensation methods Average, Full, and Equilibrium. These arm weight compensation methods are based on arm models that are developed to address the presented four critical requirements. Each method has advantages and disadvantages regarding the technology used, hardware costs, and calibration effort/time. All three compensation methods are consecutively implemented and compared using the rehabilitation robot ARMin. This paper sequentially presents the following studies: First, the estimation results of the arm weight compensation methods are analyzed for spatial and temporal sensitivity. The efficacies of all three methods are subsequently tested with EMG measurements in healthy subjects. Finally, the most successful method is tested in stroke patients. During the assessment with stroke patients, the horizontal workspace is assessed at three different height levels to determine if there is a height-dependence of arm weight compensation over the workspace.[…]