Ophrie’s mechatronics system.

The interactive arm is a 2D closed-loop five-link mechanism formed by two equal-sized distal links (0.175 m), two equal-sized proximal links (0.110 m), and a ground link (0.040 m). This direct drive 2D mechanism is driven by two servo motors (AKM32E-ANCNAA00: Kollmorgen Corp., VA, USA) placed on either side of the ground link. Each servo motor requires a servo drive (AKD-P00606-NBEC-0000: Kollmorgen Corp., VA, USA) for power supply, encoder feedback, and control. These servo drives are controlled through a central real-time controller (cRIO 9045: NI, TX, USA). A force/torque sensor (mini45: ATI Industrial Automation, NC, USA) is lodged on top of the joint of two distal links at the end of the robotic manipulator. A custom-made interaction handle is placed on top of the sensor as shown in Fig 1. The servo drives and force/torque controller are AC powered, whereas cRIO uses a 24V DC power supply through AC to DC converter. Two additional 24V power supply modules (PS-16: NI, TX, USA) are required to provide the logic power to the servo drives. All these mechatronics units are placed on the robot’s body and are powered by an external AC source via wire.

The mobile base is a four-wheel differential drive robot (IG52-DB4 Heavy duty chain and sprocket kit: SuperDroidRobots, NC, USA). A 12V DC supply powers it through two rechargeable lithium-ion batteries seated on top of its frame. It is controlled using a micro-controller (RoboClaw 2x30A: Basicmicro Motion Control, CA, USA) which ultimately receives the command from the central controller.

The central controller is a central processing unit. It communicates with servo drives through a master-slave EtherCAT protocol and the base micro-controller through RS-232 serial communication protocol. It also accepts analog voltage data from the force sensor via force/torque controller (ATI Industrial Automation, NC, USA); a C-series module (9252 voltage input module: NI, TX, USA) is required to input voltage data to the controller. For monitoring the health of the force/torque controller, a separate digital input-output module (9401 module: NI, TX, USA) is required. Fig 2 shows the flowchart for Ophrie’s mechatronic system.

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Fig 2. The flowchart for Ophrie’s mechatronics system.

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LabVIEW programming language (LabVIEW 2018 with SoftMotion and Real-Time module: NI, TX, USA) is used to deploy the commands to the central controller from the remote computer. The designated computer and the real-time controller (on the robot) are connected through Ethernet maintaining the same subnet mask.

Data acquisition.

To study the interaction dynamics during a pHRI experiment, it is essential to measure and record the interaction forces at the end effector as well as the subject’s hand location kinematics. The forces at the end effector can be measured with respect to the force sensor axis and can later be transformed into the robot axis using an appropriate rotation matrix. The motor position can be recorded using a single-turn absolute Biss sine encoder (2048 LPR) embedded in the servo motors. The point of interaction, which is the end of the manipulator or the hand position, can be calculated from the motor positions by using the forward kinematics of the robotic arm. The data are recorded with a sampling rate of 1kHz.

When necessary, the arm length—as presented in section ‘Observations from Ophrie-human interaction’—can be obtained from the Vicon motion capture system (Vicon Motion Systems Ltd., Oxford, UK). For this purpose, reflective markers can be placed in the hand and the shoulder. This data is then be processed afterward using Vicon Nexus and Vicon PorCalc Software. The sampling rate of the Vicon system is 200 Hz.

If the Vicon data were used for the analysis, the data from the robot was decimated to 200Hz before combining the two data. Then, the angular position provided by the motor encoders was compared with the respective position obtained from the Vicon system, which is estimated with the help of 6 reflective markers attached to the robot arm (see Fig 1).

Robot control.

The robot arm can be programmed to provide force or position modulation with PID control with 1 kHz. The robot can also provide force perturbations (<10 N) when needed. The position modulation can be used to provide a spring-like background force field towards the center of the workspace such that the handle position (and thus the human hand position) is kept away from the edges of the workspace. This background stiffness can be low (e.g., 50∼100 N/m) to allow smooth interaction with the user. Having this background stiffness is particularly important for an overground robot because, unlike in most seated pHRI tasks, it is very easy for the human user to move the handle outside the robot arm’s workspace. Sufficient yet gentle background stiffness is thus crucial to help the endpoint of the robot arm to remain within the workspace during overground pHRI tasks.

The robot base is independently controlled and takes an input command of linear and angular velocity. The quadrature encoder reading from the motors of the robot’s rear wheels is used for determining the instantaneous position, which later can be used for velocity control of the robot. The iteration rate for base control was 40 Hz.

Subjects.

A total of 5 healthy young adults (3 male and 2 female, 27.4±1.817 years) without any self-reported neurological disorder took part in the study. Subjects signed a written consent form before participating in the experiment. The research protocol was approved by the Institutional Review Board of the University of Missouri System.

Experiment procedure.

The experiment was designed to have twelve different cases defined by the various combinations of the following three variables: (a) visual condition (eyes open or eyes closed), (b) the background stiffness level of the robotic arm (50 N/m, 75 N/m, or 100 N/m), and (c) the level of force perturbation (3 N or 5 N). Trials were performed in four blocks, each randomly arranging the twelve cases mentioned above. The total number of trials per subject was 48. In this study, Ophrie acted as a leader, considering the complexities that have to be dealt with when the robot acts as a follower (see the section ‘Observations from Ophrie-human interaction’).

After necessary preparation for motion capture, subjects were detailed about what was expected from them during the experiment. The robot’s height was then adjusted to align the interaction handle to the subject’s elbow level. Subjects were informed that the robot would stop if the interaction handle goes out of the workspace—a 0.15x0.15m² region inside which the subjects were asked to keep the hand while interacting with the robotic arm. The presence of the background stiffness helped with this. The level of background stiffness differed for different trials based on experiment design. At the beginning of each trial, the subjects were asked to stand upright next to Ophrie by holding the interaction handle (see Fig 3). Subjects were informed whether they had to keep their eyes closed or open for the upcoming trial and then were asked to shake the handle three times in the y-axis (see Fig 3) for data synchronization purposes. The process was followed by activating the background stiffness controller; it positioned the robotic arm to the center of the workspace. Subjects were asked to relax the arm and let Ophrie position its interaction handle to the center of the workspace during this process. Lastly, they were asked to start walking alongside Ophrie, as shown in Fig 3. The robot was programmed to maintain a constant linear velocity of 0.5 m/s throughout the 5.7 m straight-line trajectories. At the midway of the trajectory, the robot applied a force perturbation (rectangular pulse with 1 second duration) in the axis perpendicular to the robot’s movement direction and towards the interacting subject (- y in Fig 3). The stiffness control loop was disabled and replaced by the force controller during the perturbation. For each trial, the amount of force perturbation was different. The magnitude was determined by adding (i) the interaction forces due to the background stiffness control at the instant when the perturbation was to be applied and (ii) the level of perturbation commanded (i.e., 3 N or 5 N). Subjects were asked to follow the robot with a relaxed arm throughout the entire trial except during the perturbation period in which they were asked to keep their hand within the workspace of the robot arm. Each trial took approximately 20 seconds.

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Fig 3. Schematic of the overground pHRI experiment.

https://doi.org/10.1371/journal.pone.0276980.g003

For each trial, the manipulator’s endpoint position (which is identical to the human hand position), the manipulator’s endpoint velocity (which is identical to the human hand velocity), and the interaction forces between the robot and the human hand were obtained. The endpoint position and forces were measured directly from the motor encoders and the force sensor, respectively. The position data was filtered with a zero-phase digital filter in both forward and reverse directions with a low-pass cutoff frequency of 40 Hz using Matlab (The MathWorks Inc., MA, USA) to reject high frequency electrical noise and to keep low frequency human movement data. The velocity was obtained from the position data using numerical differentiation.

Estimation of the arm stiffness.

From the obtained forces and kinematics, the interaction dynamics can be estimated. For initial validations, this work used one of the simplest and widely used models, which involves passive, linear, and time-invariant second-order dynamics, such that: (1) where f is the interaction force measured after the perturbation onset and x, , and are the position, velocity and acceleration of the interaction point after the perturbation, respectively. m, b, and k are the endpoint impedance parameters namely inertia, damping and stiffness, respectively [33–35]. Here, m incorporates the inertia of both the human arm and the interaction handle, whose mass is (∼0.05 kg). x₀, , and are the mean hand position, velocity, and acceleration of the interaction point just before the perturbation, respectively. Since the length of the data for analysis is short (on average, 335.636 ms—see Results), the effect of the musculoskeletal system as well as the effect of short-term neuromechanical response are captured as the lumped impedance parameters in this linear model [19]. The data of 0.1 second window before the perturbation onset was used for averaging and are used as the operating point from which all deviations are measured. For simplicity, only the kinematics in the direction of the force perturbation are considered, such that the parameters m, b, and k as well as the kinematics x, , , x₀, , and are scalars.

The measured kinematics and forces were fitted on the Eq 1 using Matlab fitlm function to estimate m, b, and k. The intercept was constrained to zero to match the linear model in fitlm with Eq 1. Otherwise, default settings were used such that modelspec was set to linear and the observation weights were set to one. The stiffness value (k) was the main outcome of interest, while the inertia (m) and damping (b) values were used to verify that the regression result was acceptable (e.g., both m and b are positive and realistic). This regression method is similar to the ARX model regression used in [35]. Further details and justifications can be found in the discussion section ‘Assumptions and challenges’, and in the supplementary material. Lastly, the equilibrium point for each trial was obtained by applying the estimated m, b, and k values into Eq 2, which represent the interaction dynamics just before the perturbation: (2) where x_eq is the position of the equilibrium point of the hand.

Statistical analysis.

The experiment was conducted in four blocks with a randomized complete block (RCB) design. Each trial from the experiment produced one scalar stiffness value along the axis of the perturbation (y-direction, see Fig 3), which was always perpendicular to the robot movement. Out of 240 trials across all subjects, five trials that resulted in a negative stiffness and one other trial whose data was lost due to exporting error were discarded. From the remaining data, outliers—defined as the values three times the inerquartile range past the 25^th and the 75^th quartiles—were screened out using JMP statistical software (SAS Institute Inc., NC, USA). There were a total of 3 outliers that were excluded from further analysis. The effects of the robot settings (background stiffness level and the magnitude of the perturbation force) and the effect of the experimental condition (eyes open/closed) were tested on the remaining 231 trials using ANOVA (JMP statistical software). The hypothesis was that the robot settings do not affect the overground pHRI dynamics, but the availability of vision affects the human response and alters the overground pHRI dynamics. A significance level of p = 0.05 was used.

Perturbation method.

A perturbation is provided for estimating the dynamics of physical interactions while the response is collected and interpreted. Two types of perturbations exist—force or position perturbations. Position perturbation has widely been used for human arm stiffness estimation since it was first introduced in mid 80’s [16, 17, 20–27, 29, 34]. Position perturbation is useful when the expected movement trajectory of the hand is known, such as when the arm is at rest or when the unperturbed trajectory is provided [21]. However, in overground experiments similar to one presented in this work, predicting the unperturbed trajectory of the human arm/hand is nearly impossible due to the variability of the human movement while walking alongside the robot (as seen in Fig 4). Hence position perturbation may not be applicable.

Given this unique situation in overground pHRI, force perturbation is the only alternative for estimating the interaction dynamics; the recorded resultant displacement and the known applied force can be used for system identification assuming the arm dynamics to be linear second-order model. Force perturbation may be applied in the form of continuous perturbations with rich frequency components. [18, 41] used pseudo-random binary sequence (PRBS) force inputs continuously for the entire period of the trial to estimate the joint mechanical properties in limb motion tasks. These studies used multiple repeated trials to obtain the ensemble mean trajectory from which deviations are calculated for estimating the impedance parameters. Alternatively, time-frequency analysis was performed using force pulse to measure arm stiffness—which eliminated the requirement of multiple trials. For example, [42] used the estimates of body segment parameters that require a rich understanding of the inertial characteristics of the arm. In contrast, another [43] did not require such parameters. It used a parametric and a non-parametric estimator to estimate the continuous-time linear time-varying system of the arm dynamics. These methods require continuous mechanical perturbations in mostly stationary body segments. However, for the proposed pHRI experiment in this work, the arm configuration can neither be consistent within a trial nor between the trials. Hence the continuous force perturbation may not be applicable.

Because of these constraints, this work tested the feasibility of applying a single force perturbation instead of continuous force pulses and then using system identification similar to the methods used in previous studies by [19, 32]. This would not intervene with the continuous overground physical interaction process throughout the entire trial as well as eliminate the need for baseline unperturbed trajectory. To this end, in this work, we propose a method to estimate the stiffness within one trial, as presented in the section ‘Estimation of the arm stiffness’.

Assumptions and challenges.

The biggest challenge of the above method is to ensure that, at the time of the perturbation, the state of the system is similar across trials. For example, if the perturbation was applied at the middle of the trial, the arm configuration better be identical at that instant across all trials. However, it is nearly impossible to achieve this during overground pHRI tasks because the arm cannot be constrained due to the nature of the task. As a result, in this experiment, the perturbation may have been applied to the hand at varying arm configurations. This may have resulted in the stiffness parameter’s relatively large variance along with inter-subject variabilities such as the muscle cross-sectional area and co-contraction. Nonetheless, acknowledging the possible sources of deviations, larger sample sizes (or the number of trials) may help discern subtle changes in the parameters between experimental conditions. Indeed, as shown in Table 1b, statistical significance can be tested and discerned despite the potential variability.

A substantial assumption of the proposed method of estimating the dynamics of overground pHRI is that the dynamics is passive second-order as represented in Eq 1. While simple, this model, which was previously used in [41], served as a starting point in estimating the pHRI dynamics during overground tasks for the first time. Other studies, such as [33–35], have also used a similar mathematical model to represent the human arm dynamics. Consistent with the assumed model, the velocity response showed the characteristics of passive second-order dynamics between 0 ms and 250–400 ms. This allowed the estimation of the inertia, damping, and stiffness parameters of Eq 1. The estimated stiffness values were reasonable, with only five occurrences of below-zero stiffness out of 239 trials. These few aberrant values may have occurred due to the inherent variability of the overground pHRI experiment. The estimated damping and inertia values were also reasonable, although the variability seemed higher than for stiffness (Fig 7). This was somewhat expected since the first- and second-derivatives of the hand position are inevitably noisier than the position data. Hence, in this work, we used these parameters as indicators of the performance of the linear regression and the resulting stiffness estimate. The estimated inertia values were mostly positive and similar to the expected inertia of the lower arm (0.3∼0.5 Kg). Also, the average damping was low and mostly positive, as expected. It was also comparable to the damping reported in [35]. Thus we concluded that the proposed method for estimating the dynamics is informative despite the simplicity.