Background: Manual treadmill training is used for rehabilitating locomotor impairments but can be physically demanding for trainers. This has been addressed by enlisting robots, but in doing so, the ability of trainers to use their experience and judgment to modulate locomotor assistance on the fly has been lost. This paper explores the feasibility of a telerobotics approach that allows patients to receive physical assistance from robotically augmented trainers.Methods: In the approach, a trainer holds onto a small robotic manipulandum that shadows the motion of a large robotic arm, which is magnetically attached to the leg of a locomoting patient. When the trainer deflects the manipulandum, the robotic arm applies a proportional force to the patient. After an initial evaluation of the telerobotic system’s ability to follow the leg during unassisted locomotion with unimpaired participants, a small feasibility study was performed with six patients with prior strokes. Over six days, the patients interacted with two robotically augmented trainers (separately), who assisted in altering a targeted gait feature: an increase in the affected leg’s swing length. Results: During unassisted walking, unwanted robot interaction forces averaged 3−4 N (swing−stance) for unimpaired individuals and 2−3 N for the patients who survived strokes. Transients averaging about 10 N were sometimes present at heel-strike/toe-off. For five of six patients, these forces increased with treadmill speed during stance (R2 = .99; p < .001) and increased with patient height (R2 = .71; p = .073) during swing. During assisted walking, the trainers applied 3.0 ± 2.8 N (mean ± standard deviation across patients) and 14.1 ± 3.4 N of force anteriorly and upwards, respectively. The patients exhibited a 20 ± 21% increase in unassisted swing length between Days 1−6 (p = .058). Conclusions: The results support the feasibility of locomotor assistance with a telerobotics approach. Simultaneous measurement of trainer manipulative actions, patient motor responses, and the forces associated with these interactions may prove useful for testing sensorimotor rehabilitation hypotheses. Further research with clinicians as operators and randomized controlled trials with more comprehensive outcome measures are needed before conclusions regarding efficacy can be reached.

A methodology to compute and design the delay margin (DM) of large-scale linear time-invariant systems is presented. Different from existing work, this methodology is scalable; does not impose restrictions on the system to be able to invoke simultaneous triangularization or simultaneous diagonalization; and sheds light on how the finite number of delay-free system eigenvalues can be effectively utilized to compute or design the DM. KEYWORDSdelay margin, delay margin design, time-delay systems INTRODUCTIONThe presence of time delays in feedback control systems has attracted tremendous interest in engineering, mathematics, and physics communities for over six decades. [1][2][3][4][5][6] The main reason for this is that delays can dramatically affect the dynamics of control systems. Notably, they can cause poor performance and even instability; and this must be properly dealt with either through controller design or through system design. Virtually, in all control applications, delays exist because it takes time to transmit information, sense information, formulate a proper decision, and execute such decisions. Widely studied problems include machine tool chatter, 7,8 teleoperation, 9,10 human reaction times in driving 11,12 and when operating an aircraft, 13,14 power networks, 15,16 population dynamics, 17,18 supply chain networks, 19,20 and gene regulatory networks. 21,22 In the pursuit of addressing the fundamental stability analysis and control design needs, one faces numerous challenges and opportunities. For example, the presence of delays makes the system infinite dimensional. In linear time-invariant (LTI) systems, this means that one has to deal with infinitely many poles, and thus, standard tools available for finite-dimensional problems are immediately ruled out as prospects to analyze stability and/or design controllers. Moreover, the presence of delay is not necessarily detrimental to the dynamics. An appropriate amount of delay can render improved disturbance rejection capabilities, 23 can increase stability margins, 24 can be deliberately introduced as part of a controller to enhance the performance of a closed-loop system, 25-28 or can provide stability. 29,30 One of the widely studied problems in the context of time-delay systems is the problem of computing the delay margin * (DM) of a system. An LTI system is stable for all delays from zero up to the DM ∈ [0, * ), which implies that when the delay value is equal to the DM = * , the system has at least one pole on the imaginary axis of the complex plane. 1 Many techniques have been developed to calculate the DM of LTI systems. Efforts in this direction possibly go back to 31 where the authors developed an approach to create "stability maps" of LTI systems with delay. These maps represent, on the plane of the delay and a parameter of interest, the boundaries along which the system can have imaginary poles ∓ j and which side of the boundaries indeed correspond to the stable operation of the system. Approaches to obtain similar maps have also been deve...

Background Manual treadmill training is used for rehabilitating locomotor impairments but can be physically demanding for trainers. This has been addressed by enlisting robots, but in doing so, the ability of trainers to use their experience and judgment to modulate locomotor assistance on the fly has been lost. This paper explores the feasibility of a telerobotics approach for locomotor training that allows patients to receive remote physical assistance from trainers. Methods In the approach, a trainer holds a small robotic manipulandum that shadows the motion of a large robotic arm magnetically attached to a locomoting patient's leg. When the trainer deflects the manipulandum, the robotic arm applies a proportional force to the patient. An initial evaluation of the telerobotic system’s transparency (ability to follow the leg during unassisted locomotion) was performed with two unimpaired participants. Transparency was quantified by the magnitude of unwanted robot interaction forces. In a small six-session feasibility study, six individuals who had prior strokes telerobotically interacted with two trainers (separately), who assisted in altering a targeted gait feature: an increase in the affected leg’s swing length. Results During unassisted walking, unwanted robot interaction forces averaged 3−4 N (swing–stance) for unimpaired individuals and 2−3 N for the patients who survived strokes. Transients averaging about 10 N were sometimes present at heel-strike/toe-off. For five of six patients, these forces increased with treadmill speed during stance (R2 = .99; p < 0.001) and increased with patient height during swing (R2 = .71; p = 0.073). During assisted walking, the trainers applied 3.0 ± 2.8 N (mean ± standard deviation across patients) and 14.1 ± 3.4 N of force anteriorly and upwards, respectively. The patients exhibited a 20 ± 21% increase in unassisted swing length between Days 1−6 (p = 0.058). Conclusions The results support the feasibility of locomotor assistance with a telerobotics approach. Simultaneous measurement of trainer manipulative actions, patient motor responses, and the forces associated with these interactions may prove useful for testing sensorimotor rehabilitation hypotheses. Further research with clinicians as operators and randomized controlled trials are needed before conclusions regarding efficacy can be made.

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