Effect of Dyadic Haptic Collaboration on Ankle Motor Learning and Task Performance

Optimizing skill acquisition during novel motor tasks and regaining lost motor functions have been the interest of many researchers over the past few decades. One approach shown to accelerate motor learning involves haptically coupling two individuals through robotic interfaces. Studies have shown that an individual’s solo performance during upper-limb tracking tasks may improve after haptically-coupled training with a partner. In this study, our goal was to investigate whether these findings can be translated to lower-limb motor tasks, more specifically, during an ankle position tracking task. Using one-degree-of-freedom ankle movements, pairs of participants (i.e., dyads) tracked target trajectories independently. Participants alternated between tracking trials with and without haptic coupling, achieved by rendering a virtual spring between two ankle rehabilitation robots. In our analysis, we compared changes in task performance across trials while training with and without haptic coupling. The tracking performance of both individuals (i.e., dyadic task performance) improved during haptic coupling, which was likely due to averaging of random errors of the dyadic pair during tracking. However, we found that dyadic haptic coupling did not lead to faster individual learning for the tracking task. These results suggest that haptic coupling between unimpaired individuals may not be an effective method of training ankle movements during a simple, one-degree-of-freedom task.


I. INTRODUCTION
I N EVERYDAY life, humans interact with each other to accomplish difficult tasks (e.g., moving furniture) or to assist one another while (re)learning motor tasks (e.g., physical therapy). An important aspect of human-human interaction (HHI) is physical interaction, allowing individuals to effectively exchange information through forces or tactile cues. With recent advancements in the field of human-robot interfaces, various aspects of complex dyadic behaviors have been explored using upper-limb robotic devices to render virtual physical environments (e.g., spring-damper) between two or more humans [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. These studies have investigated the effect of physical interaction on two main factors: (1) task performance: the individual's ability to accomplish a motor task during interaction (dyadic) or without interaction (solo), (2) individual motor learning: changes in solo task performance before and after a training period [11].
The type of physical interaction most often studied with human-robot interfaces is haptic collaboration, where individuals have a common goal and can exchange forces through a virtual environment [12]. Ganesh et al. [1] reported that when dyads collaborate to track moving targets under visuo-motor rotation with separate manipulators that are virtually connected, the interaction is mutually beneficial as both individuals obtain better dyadic task performance compared to their solo performance. Similar results have also been obtained for a tracking task under a force field [7]. These task performance improvements can be tuned by the stiffness of the virtual connection [3] and are suggested to occur due to estimation of a partner's goals that can be used to improve one's own estimation of a target position [6]. In addition, Takagi et al. [13] showed that when more than two individuals (e.g., triad, tetrad) are virtually connected during a planar tracking task, each individual's performance improves with the size of the group due This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ to estimation of an averaged, collective goal. These findings demonstrated that haptic interactions between individuals have the potential to be scalable and beneficial to both dyads and larger groups in terms of improved task performance.
While results related to the effects of haptic collaboration on task performance during coupling are mostly consistent across studies, results on individual motor learning are limited and contradictory [11]. Takagi et al. [6] reported better individual motor learning following dyadic training for a planar, upperlimb tracking task without disturbances. Ganesh et al. [1] reported better individual motor learning with dyadic training than with solo training for a planar tracking task under visuomotor rotation. On the other hand, Beckers et al. [2] replicated the experimental design of Ganesh et al. [1] and found no difference in motor learning between dyadic training and solo training. Beckers et al. [7] also reported that dyadic training does not result in better motor learning than solo training for a tracking task under a velocity-dependent force field.
Given the discrepancies in the literature on shared motor tasks, it is unclear whether or not haptic collaboration between individuals can actually benefit individual motor learning. While some studies suggest that haptic interaction provides supplemental information that can be integrated into one's own strategy [1], [6], others suggest that the reduction of errors during dyadic training prevents enhanced learning of the task [2], [14]. Moreover, to the best of our knowledge, there is no study that investigates the effects of physical interaction between multiple people during lower-limb tasks. Therefore, there is no evidence on whether potential benefits of haptic interaction observed in some upper-limb studies would translate to the lower-limb. Elucidating the learning effects of dyadic interaction in the lower-limb has the potential to improve existing control strategies of robotic devices that have been developed for individuals with sensorimotor impairments (e.g., stroke, spinal cord injury) [15]. For instance, developing robotic training paradigms for more accurate position and force control of the ankle joint can lead to more effective rehabilitation interventions, given the impact of impaired ankle motor control on walking speed and gait symmetry in individuals post-stroke [16], [17].
The goal of our study was to investigate the effects of haptic collaboration on task performance and individual motor learning during an ankle tracking task. Participants were asked to move their ankle in a one-degree-of-freedom (1-DOF) tracking task (dorsal and plantar flexion) so that a continuous, visual trajectory representing their ankle angle followed a desired trajectory. Each participant's ankle was attached to a 1-DOF ankle robot, and haptic collaboration between dyads was achieved by a virtual spring that acts to reduce the error between the two ankle angles. We first introduce the experimental setup, which has been previously reported [18]. We then introduce the experimental protocol designed to see how haptic collaboration affects task performance and individual motor learning. Finally, we present our results to determine if haptic collaboration affects the rate of individual motor learning as well as task performance during haptic coupling.

A. Description of the Infrastructure for Haptic Collaboration
Two commercially-available ankle rehabilitation robots (M1 AnkleMotus, Fourier Intelligence, China) were used in this study. The M1 robots were designed to 1) measure ankle joint angle, angular velocity and interaction torque between the user and the robot, and 2) provide assistive/resistive torque during ankle dorsal and plantar flexion. A custom interaction torque controller was used to provide transparent ankle movements for each M1 robot and to render virtual haptic environments between two M1 robots [18]. The controller was implemented using the CANOpen Robot Controller (CORC) software stack [19] and consists of 1) an inner layer with a feedforward component to compensate for gravity and friction in the system and 2) an outer layer to render haptic torque between the two M1 robots using a feedback component to apply the desired interaction torque between the user's foot and the robot. We have showed in our previous study that the controller is sufficiently transparent so as to not alter muscle activation compared to barefoot movements [18]. The virtual connection for haptic collaboration was implemented as a rotational spring with a positive stiffness and zero neutral length. The desired interaction torque between user A and user B was calculated using Eq.1: where λ int is the interaction torque applied between the two users, K virt is the virtual stiffness that is applied between the ankle angular positions of the two users, and θ is the ankle angular position measured from each M1 robot.

B. Experimental Setup for Dyadic Ankle Motor Tasks
The experimental setup used in this study is shown in Fig. 1. Each participant donned the M1 robot using foot and shank braces as shown in Fig. 1B. The participant's foot location was adjusted so that the heel was in contact with the back heel support, and the knee angle was adjusted by changing the height of the calf support and distance between the chair and the device to align the ankle with the M1 robot. Participants were seated side by side, and a physical divider was placed between the two participants to prevent any verbal or visual communication. Each participant was given a monitor that displayed the target trajectory and his/her own actual ankle trajectory. The target trajectory was represented by a red solid line and the user's actual trajectory was represented with a blue solid line. The thickness of the actual trajectory was greater than the thickness of the target trajectory to prevent occlusion. Both trajectories were updated in real-time using a forward-scrolling design (i.e., vertical axis represented target and actual angles in radians, horizontal axis represented time in seconds). In addition to the current position of each trajectory, participants received past history (last 5 seconds) of the target and actual trajectories (see user view in Fig. 1A). Two audio speakers were installed on each side of the physical divider to provide audio cues when the tracking task begins.

C. Experimental Protocol
A total of 24 unimpaired participants (age 27.5 ± 8.7, 14 males and 10 females) participated in this study. For each participant, their right leg was their dominant leg (i.e., primary leg used to kick a ball). Within the previous six months, no participant had history of lower leg injury that could prevent their full participation during the experiment. Participants were paired through age-matching (i.e., less than a 5-year difference) and gender-matching to minimize ageor gender-related discrepancies. Participants gave informed consent for their participation in the experimental protocol that was conducted in accordance with the Declaration of Helsinki and approved by the institutional review board (IRB) of Northwestern University (STU00212684). The study protocol was registered on clinicaltrials.gov (trial number NCT04578665).
The concept of visuo-motor tracking was explained to the participants before the experiment. Participants were told that the aim of the experiment was to investigate motor learning at the ankle level. To prevent any social interaction, the two participants were told that they were working individually but might experience some disturbances from the M1 robots. After we explained the experiment, each dyad familiarized themselves with the M1 robots while the robots operated in transparent mode (λ int = 0) with no haptic connection rendered. Participants were asked to perform an ankle tracking task where they had to follow a sine waveform for 10 cycles in which the amplitude and frequency were varied every cycle. The amplitude and frequency were selected based on a uniform random number generator with ranges of [0.3, 1.2] rad for the amplitude and [0.15, 0.45] Hz for the frequency. After tracking 10 cycles of this waveform, participants were provided a 20-seconds rest. This process, tracking and resting, was repeated for 11 trials. Identical sine waveforms were used for both participants across the 11 trials. After familiarization, participants were provided with 300 seconds of rest. Then they performed the main tracking experiment where they tracked an identical multi-sine function as defined by Eq.2: where φ 1 , φ 2 , φ 3 are random phase shifts chosen for each block. The amplitude (0.33 radians) and frequencies (0.16, 0.33, 0.5 Hz) of the three components of the multi-sine waveform were selected to emulate ankle trajectories during different gait patterns [20]. The main tracking experiment included three solo training blocks and three dyad training blocks. The training sequence between solo (S) and dyad (D) blocks was randomized. For the randomization process, constraints were given to avoid three consecutive blocks with identical training types. For example, one dyad could experience a SDDSSD sequence while another dyad could experience a DSDSDS sequence. In each block, participants performed 11 tracking trials; the solo blocks consisted of 11 solo trials and the dyad blocks alternated between solo and dyad trials (6 solo trials, 5 dyad trials) (Fig. 2).
In the solo trials, participants tracked the target trajectory while the M1 robots operated in transparent mode (λ int = 0) and no haptic connection was rendered. In the dyad trials, participants tracked the target trajectory while a virtual spring was rendered between the two M1 robots. The stiffness of the virtual spring (K virt ) was set to 20 Nm/rad, which was selected based on a pilot study to allow a compliant connection between participants; this stiffness allowed participants to exchange forces and track their targets independently, preventing any possible slacking (i.e., in which one participant does most of the work) that could occur with a rigid connection.
In each trial, participants tracked the target trajectory for 26 seconds, then rested for 20 seconds. Random phase shifts (φ 1 , φ 2 , φ 3 ) were added, thus, the tracking trajectory was different in each block. A random time shift (t r ) was added to change the starting point of the cyclic trajectory from trial to trial. This helped prevent fast learning (i.e., memorization) of the target trajectory [1]. In summary, a total of 66 trials were performed so that all participants experienced three blocks of solo training and three blocks of dyad training. Based on pilot testing, the trial/rest time and total number of trials were selected to maintain the participants' concentration levels throughout the experiment.
D. Data Analysis 1) Task Performance: Task performance, measured by the tracking error of each trial, was the primary outcome measure Fig. 2. Example of the study protocol. During a "Dyad trial" of a "Dyad block", both participants were connected with a virtual spring while performing the tracking task. During a "Solo trial" of a "Dyad block", there was no connection between participants. For the "Solo block", all trials were "Solo trials". used in our statistical analysis. The tracking error (E) was quantified by the root-mean-square error (RMSE) of the difference between the target trajectory and actual ankle trajectory using Eq.3: where θ des is the target trajectory, θ is the actual angle trajectory, and N is the total number of samples (time points). For our analysis, the first 2 seconds and last 2 seconds of the 26-second tracking trajectory were removed to minimize the inter-participant delay in initiating the tracking task after the audio cues were provided. Within each dyad block, relative partner performances ( E P S ) were computed by taking the difference between each participant's solo trial tracking error (E S ) and their partner's solo tracking error (E P S ), normalized by the participant's solo tracking error (E S ) In Eq.4, positive values of E P S indicate trials where a participant's partner was a better performer while negative values indicate trials where the partner was a worse performer. Dyadic improvements were computed by taking the difference between each participant's solo trial tracking error (E S ) and their tracking error in the previous dyad trial (E D ), normalized by the participant's solo tracking error (E S ) In Eq.5, positive values of E D indicate better task performance as a result of the haptic coupling (compared to subsequent solo performance) while negative values indicate a degradation in performance due to the haptic coupling. E D was computed relative to the previous dyad trial to exclude the learning effect across trials, providing a conservative estimate of the improvements due to coupling [1]. Because there were 11 trials per dyad block, and only 5 pairs of dyad trials followed by solo trials, we calculated 5 values of E D and E P S per participant within each block (15 values total per participant across all dyad blocks).
2) Statistical Analysis: The goal of this study was to assess whether dyadic haptic coupling improves individual motor learning and task performance for an ankle tracking task. Specifically, we assessed two hypotheses: 1) participants will demonstrate better individual motor learning of the task as a result of the haptic coupling, and 2) participants will track the target more accurately when haptically coupled and these improvements will be linearly related to the skill level of one's partner (i.e., improvements will increase when coupled with a better partner). To test our hypotheses related to motor learning and differences between solo and dyad block performance, we generated a linear mixed-effects model with tracking error (i.e., RMSE) as a dependent variable, trial number as a continuous variable, block type and trial type as fixed factors, and participant as a random factor. To determine the relationship between the relative performance and dyadic improvements, we used another linear mixed-effects model with the tracking improvement in the dyad trials as a dependent variable, difference in partner performances as a continuous variable, and participant as a random factor. The linear mixed-effects models were fit using restricted error maximum likelihood, and the degrees-of-freedom were estimated using a Satterthwaite approximation [21]. Significance was set to 0.05 for all hypotheses.
In our analysis, motor learning was quantified by the learning rate (i.e., the slope of the tracking error relative to the trial number from the fitted model). Task performance was quantified by the baseline tracking error (i.e., the intercept of the tracking errors from the fitted model). We tested our first hypothesis, whether participants would demonstrate better individual motor learning as a result of the haptic coupling, by determining if there was a difference in the learning rate between the solo block and dyad block. We also determined the difference in baseline tracking error between the solo trials of the solo block and solo trials of the dyad block to assess changes in individual performance immediately following haptic coupling. We tested our second hypothesis by determining the difference in the baseline tracking error between solo trials and dyad trials. In addition, we analyzed the relationship between relative partner performances and improvements in task performance during dyad trials according to previous studies [2], [3], [6].

III. RESULTS
For all participants, the tracking error between the target trajectory and the actual trajectory decreased with trial number. As shown by a representative participant in Fig. 3, despite the considerable amount of trial-to-trial variability, there was a decrease in tracking error across trials, which was modeled  with a linear fit. This was seen across all participants as our linear mixed-effects model had an R 2 of 0.54. There was a small but significant decrease in tracking error across all trial types (Fig. 4). On average, tracking error decreased by 3.9 ± 0.7 x 10 −4 rad/trial (t 130 = −5.8, p < 0.0001). This amounted to a drop in tracking error of 25% from trial 1 to trial 66.

A. Haptic Coupling Did Not Lead to Faster Individual Learning Rate or Better Individual Performance
In the previous section, we reported learning rate throughout the experiment across all trial types. Here, we compare measures between trial types, presenting the results of our linear mixed-effects model from 1 to 11 trials to minimize the uncertainty due to extrapolating to a larger number of trials. There was no significant difference in the individual learning rate as a result of the haptic coupling (Fig. 5). The rate of decrease in tracking error in the dyad block was similar to that in the solo block ( = 1.4 ± 1.2 × 10 −4 rad/trial, t 135 =1.2, p = 0.23). Additionally, we compared the tracking error of the solo trials from the solo block to that of the solo trials from the dyad block to assess whether the dyadic coupling helped performance in future solo trials. We found no difference between the tracking error in the solo trials of the dyad block and that in the solo trials of the solo block, once we accounted for the overall learning rate ( = 6.3 ± 8.2 x 10 −4 rad, t 52 = 0.8, p = 0.45).

B. Task Performance Improved During Haptic Coupling
Depending on the Performance of One's Partner Participants decreased their tracking error when haptically coupled with another participant in a dyad (Fig. 6). The baseline tracking error, the error extrapolated back to trial 0, was 8.0 ± 1.4 x 10 −3 rad (t 31 = −5.5, p < 0.0001) lower in the dyad trials compared to the solo trials in the solo block, which corresponds to a decrease in error of 7.6%. In addition, we compared the relative performances within each dyad ( E P S ) to the degree of improvements while haptically coupled ( E D ) (Fig. 7). We found that dyadic improvements in task performance linearly increased with relative partner performance (t 197 = 11.8, p < 0.0001).   6. Task performance improved in the dyad trials while partners were haptically coupled. A) Predicted tracking error as function of trial number for the solo trials from the solo block and the dyad trials from the dyad block, as predicted by the linear mixed-effects model. The dyad trials showed a consistent decrease in tracking error compared to solo trials, but no difference in the learning rate (i.e., slope of the tracking error relative to the trial number). B) Swarmplot showing the difference in baseline tracking error between these two trial types for each participant.
This means that interacting with a partner who was better at the tracking task resulted in greater improvements while haptically coupled. Haptic coupling also improved task performance while tracking with a worse partner, to a certain extent (i.e., −25% < E P S < 0%). However, beyond this threshold, the interaction negatively affected task performance (i.e., E P S < −25%).

C. Improved Task Performance During Dyad Trials Was Likely Due to the Averaging of Errors Within Each Dyad
The likely mechanism explaining the improved performance in the dyad trials was the averaging of random errors between partners due to the haptic coupling. We explored whether this mechanism explained the improvements in task performance by comparing changes in the tracking errors during dyad trials to the tracking errors during simulated dyad trials. Previous work has shown that human joints, including the ankle, can be modeled as a spring or set of springs with active and passive stiffness components [22]. Therefore, simulated trials were computed by modeling the dyadic interaction as a system of three springs in series, where each participant's simulated position was determined by the stiffness of their own ankle, the stiffness of the virtual spring and the stiffness of their partner's ankle. This simulation was analogous to taking the weighted average of two participant's trajectories, suggesting that improvements in task performance during the dyad trials were due to the mechanics of the coupling rather than the mutual estimation of partner goals [6]. We used experimental data from the solo trials of the solo block (i.e., no haptic coupling) as an input to the three spring model to generate these simulated trajectories. Balancing forces across each spring yields the following equation: where θ sim is the simulated ankle position of each participant at a given time point, K is the physiological ankle stiffness of each participant, K virt is the virtual spring stiffness, and θ is the ankle position measured from each M1 robot during the solo trials of the solo blocks. Simulated trajectories were calculated by solving for θ sim in the following equation: Because we did not measure instantaneous ankle stiffness during our experiment, we assumed a constant stiffness for all participants in this analysis (K i = K j ). We also assumed that the ankle stiffnesses of our cohort could be approximated by the passive stiffness of the joint, as the interaction torques observed during the dyad trials were relatively small in magnitude (mean range: −1.9 to 1.5 Nm). Based on a study from Roy et al. quantifying the passive stiffness of the ankle in dorsal and plantar flexion with a ramp-and-hold displacement profile [23], we obtained a range of stiffness values (18 to 30 Nm/rad) from their young, healthy cohort and selected K = 24 Nm/rad for Eq.7. Tracking errors for the simulated dyad trials were calculated by taking the RMSE between the desired and simulated trajectories (Eq.3). Note that a rigid connection (i.e., K virt K ) could be represented by an unweighted average, where both participant's simulated trajectories are identical.
To compare the improvements in task performance between experimental and simulated dyad trials, we performed an analysis similar to what was described in the previous section (Fig. 7C). In this analysis, we compared relative partner performances ( E P S ) to the degree of improvements observed as a result of simulating the haptic coupling within each dyad ( E A ). We observed similarities when comparing relative partner performances to experimental dyadic improvements and simulated dyadic improvements (Fig. 7F) as both were sufficiently described by linear fits with E P S as the predictor (R 2 = 0.36). Compared to experimental dyadic improvements, the rate of increase in the simulated improvements with respect to relative partner performances was not significantly different ( = 0.05 ± 0.03 %, t 641 = 1.7, p = 0.09). In instances of equal partner performances ( E P S = 0%), there was no significant difference between the simulated and experimental dyadic improvements ( = −1.1 ± 0.8%, t 63 = −1.4, p = 0.16).

IV. DISCUSSION
In this study, we evaluated how haptic coupling between individuals translates to an ankle tracking task when visual feedback is provided, which is in line with the results shown in [2] and [7]. We found that for the 1-DOF continuous tracking task, in which participants were required to follow a target trajectory with their ankles, dyadic haptic coupling did not lead to faster individual motor learning. Dyadic task performance improved during haptic coupling depending on the individual performance of one's partner. Such improvements were likely due to averaging of errors of the dyadic pair during tracking.

A. Individual Motor Learning Was Not Affected by Haptic Collaboration
For the proposed study on ankle motor learning, haptic coupling did not lead to better short-term individual motor learning compared to performing the task alone. Our results are in line with findings from the study of Beckers et al. [2], [7], but do not indicate an individual learning benefit of haptic coupling reported in the studies of Ganesh et al. [1] and Takagi et al. [6]. Comparing our study to these previous haptic collaboration studies, our experimental design most closely resembles that of Takagi et al., which used a 2-DOF tracking task without visual or haptic disturbances. However, it is important to note that motor learning is complex and can be affected by many factors. One possible reason we had contradicting results with the aforementioned study [6] is the discrepancies between the experimental designs. Most previous studies investigating haptic collaboration and motor learning used a between-subjects design, namely, having two separate groups perform either solo training or training with alternating solo and dyad trials [1], [2], [6], [7]. However, Ganesh et al. [1] and Takagi et al. [6] used randomly alternating solo and dyad trials for the dyad training group, while Beckers et al. [2], [7] alternated every other trial for the dyad group. In this study, we used a crossover design to take advantage of within-subjects comparisons and to have higher power with the number of participants recruited. Our experimental design may have led to less apparent learning effects and therefore difficulty in distinguishing between training conditions. Also, it has been reported in several studies, which investigated the effects of haptic modalities (i.e., performanceenhancing and performance-degrading haptic methods) on motor learning, that the experimental design and task difficulty play an important role on the advantages brought by additional haptic feedback [24]. Several studies have compared training with visual feedback and training with a combination of visual and assistive haptic feedback, finding no significant differences in learning the spatial aspects of simple continuous tracking tasks and discrete reaching tasks [25], [26], [27]. Therefore, the 1-DOF design in this study may have been simple enough to achieve full motor learning capabilities through visual processing of errors, making the haptic forces exchanged between the dyads redundant. In addition, studies have suggested that haptic training modalities are less effective in learning the spatial aspects of tasks that incorporate velocity constraints [28], [29], [30]. It is possible that the forward-scrolling design of our tracking task may have limited each participant's ability to fully perceive and respond to haptic feedback from their partner.
Another possible reason for contradictory results may be due to the difference between the lower-and upper-limb physiology. All previous studies showing improved motor learning with haptic collaboration were conducted on 2-DOF endpoint upper-limb reaching tasks, whereas, to the best of our knowledge, our study is the first to apply haptic collaboration on the lower-limb in a dyadic setup. In the cerebral cortex, the motor area of the upper-limb is significantly larger [31] than that of the lower-limb, allowing for more precise control of the arms and hands. Additionally, it has been shown that the central pattern generators and muscle synergies, which generate rhythmic patterns for more efficient movements, may play a key role in spinal control of human locomotion rather than direct, high-resolution corticospinal projections [32]. Therefore, it is possible that lower-resolution control and proprioceptive feedback at the ankle joint could result in increased reliance on visual systems and limit the extent of learning compared to upper-limb tasks.

B. Task Performance Improves During Haptic Coupling
In our study, haptic coupling resulted in improved task performance for the proposed paradigm, which coincides with the studies on 1-and 2-DOF upper-limb tracking tasks [1], [2], [3], [6]. Haptic coupling resulted in an average decrease in RMSE of 7.6% when compared to performing the task alone. Exploring the mechanism of these changes in task performance, we found that the improvements during haptic coupling were similar to the improvements obtained through averaging solo trials of the dyadic pair. These findings are consistent with a model proposed by Takagi et al., where dyadic improvements are linearly dependent on relative partner performances during trajectory tracking tasks [6], [13]. This model, termed no exchange or no computation, suggests that participants track targets independently while haptically coupled; any improvements in dyadic performance are due to the cancellation of tracking errors as a result of an elastic connection. However, Takagi et al. reported that averaging the noise from multiple participants is different than dyadic collaboration based on comparisons between experimental data and predictive models [6], [13]. They found that their observed improvements were better described by a model that incorporates continuous exchange of haptic information between partners in order to enhance target estimation.
Another study from Takagi et al. suggested that decreasing the stiffness of the virtual connection between participants limits the exchange of haptic information during a 1-DOF tracking task using wrist flexion-extension, and that dyadic improvements in the presence of softer connections (i.e., small spring constants relative to the stiffness of the joint) are linearly related to relative partner performances [3]. This linear relationship is consistent with the "no exchange" model and experimental data from our study. Takagi et al. used a cursor to represent the user's actual position and a cloud of points with visual noise for the target position as opposed to the continuous visual traces of the actual and desired trajectories used in our design. As previously mentioned, these design considerations can have an effect on the difficulty of the task, changing the magnitude and type of errors between users which are proportional to the forces experienced during dyadic interactions. In addition, the three levels of stiffness defined by Takagi et al. are as follows: soft (i.e., 0.3 Nm/rad), medium (i.e., 1.7 Nm/rad) and hard (i.e., 17.2 Nm/rad). Based on this characterization, and considering the passive stiffness quantified in flexion-extension for the human wrist [33] and ankle [23] joints, the relative strength of the virtual stiffness used in our design (K virt = 20 Nm/rad) could be described as soft to medium. Therefore, it is likely that the phenomenon of averaged errors during dyadic ankle tracking is due to a combination of the virtual stiffness and the relatively small magnitude of errors observed in our tracking task. Further work is needed to determine the mechanisms of haptic interaction at the ankle joint during tasks with higher difficulty (e.g., visual noise) as a function of the virtual spring stiffness, both in terms of dyadic task improvements and individual motor learning. Takagi et al. [3] did not assess differences in individual learning as a result of haptic collaboration at lower stiffness values; however, our results would suggest that reducing errors through error averaging is not an effective strategy for enhancing motor learning in the context of haptic physical interaction between healthy individuals. In the context of robot-mediated training, this is in agreement with previous findings suggesting that haptic guidance strategies which reduce tracking errors are generally ineffective compared to training without haptic assistance [34], [35], [36].
While haptic guidance strategies may not be effective for healthy individuals, improvements in shared task performance may lead to improved motor learning for individuals with sensorimotor impairments. Training with haptic guidance (i.e., performance-enhancing feedback) improves learning temporal aspects of motor tasks in patients with chronic stroke, as evidenced by an upper-limb study evaluating robotic training methods [37]. Robot-assisted gait training has been shown to improve clinical measures such as walking speed in patients with chronic stroke through assist-as-needed strategies (e.g., using compliant force field to guide patients towards a reference trajectory) [38], [39]. In the context of dyadic haptic interaction, improved task performance can have similar effects as an assist-as-needed strategy since attractive forces are applied towards the target trajectory for individuals who deviate from the target trajectory. This effect will increase with larger group sizes, as the combined task performance improves with the number of individuals haptically connected [13].

C. Future Directions
Although there was a significant linear decrease in tracking error across trials for all participants, the change was small due to the simplicity of the task (i.e., 1-DOF continuous tracking with visual feedback) and there was a considerable amount of trial-to-trial variability. Also, the total number of trials were limited in order to maintain concentration levels throughout the experiment, which led to shorter time to learn the task and less overall motor learning. In future studies, it would be interesting to investigate tasks that lead to larger drops in tracking error (i.e., greater changes in task performance relative to the number of trials), to maximize the potential effect size of the experimental condition relative to noise in the data. We believe one way to accomplish this is by choosing tasks that do not primarily rely on visual feedback. This may also be more relevant to ankle functions in real-life scenarios (i.e., gait and balancing) that rely less on visual feedback and require sensorimotor integration of proprioceptive and vestibular inputs in order to successfully execute movements [40]. Generally, vision is useful for initial path planning through identification of obstacles or changes in an environment [41] while proprioception is used for adaptions during early execution of a movement [42]. Therefore, in the context of gait rehabilitation, it may be relevant to design an ankle training paradigm where proprioception is targeted through a task with limited visual feedback. As in a previous study, terminal visual feedback can provide individuals with a cue for planning a movement [43] while haptic feedback can be implemented in real-time to guide or resist the user along a given trajectory. With this approach, the dyadic coupling described in this study could accelerate the learning of a non-visual task with a greater potential to translate to walking, given the similarities in involved sensory systems. Another approach is to focus on a task that involves adaptation to higher impedance virtual environments. This can be achieved by adding a haptic force field to the tracking task, as demonstrated in previous dyadic haptic collaboration studies [7], or with an inverted pendulum balancing task [44]. Complex virtual environments can also be designed to leverage the intrinsic stiffness of the ankle, as a previous study has shown that task performance is strongly coupled to the impedance of the ankle during sinusoidal force tracking [45]. Tasks incorporating higher, more complex impedance environments would likely require more training to master due to higher difficulty compared to position tracking without disturbances. In addition, there is greater potential for learning to transfer to functional improvements, especially for patients with lower-limb motor impairments, as walking and balancing involve contact between the foot and high impedance surfaces.

V. CONCLUSION
We observed individual motor learning of the tracking task as participants were able to reduce their tracking error throughout the session. Consistent with results from Beckers et al. [7], we found no difference in individual motor learning as a result of training with haptic collaboration compared to training alone. In addition, we found that participants improve tracking accuracy during haptic coupling, depending on the relative ability of their partner. These findings were consistent with models proposed by Takagi et al., suggesting that tracking with a soft spring stiffness has the effect of noise cancellation in dyads [3], [6]. Though the task implemented here is much simpler than the task in previous experimental setups [1], [7] (i.e., 1-DOF, no visuo-motor rotation), the results lay the groundwork for studies exploring the effects of haptic interactions between individuals during lower-limb tasks. Future work should involve evaluation of various connection types between users (e.g., soft versus hard spring) as well as tasks that do not primarily rely on visual feedback or tracking in the presence of haptic or visual disturbances.