The experimental protocol and procedure were approved and in accordance with relevant guidelines and regulations of the Emory University Institutional Review Board. The participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.

Participants

Data collection was completed with ten young adult novices (7 female and 3 male, ages 20 ± 2.3 years, height 1.7 ± 0.12 m, mass 67 ± 14 kg) with no previous partner dancing experience and no diagnosed sensory or motor impairments. The expert paired with each of the ten novices was female, age 46 years, height 1.7 m, mass 67 kg, and had > 20 years of professional teaching experience in partner dancing.

Experiment setup

We collected full-body motion capture data (n = 10) for both the novice and expert and hand interaction forces (n = 8) between the pair. Each partner was instrumented with a full-body Plug-in Gait marker set (Vicon, Centennial, CO). Kinematic data were recorded at 100 Hz by a ten-camera motion capture system (Vicon Nexus) and force data were recorded at 1 kHz. During partnered walking conditions, each partner held opposite ends of a custom handle device with a force-torque sensor (ATI Nano25) in the center that measured hand interaction forces between the partners (Fig. 8a,b).

Experiment procedures

Human dyads consisting of the same expert partner dancer paired with different novices participated in a backleading paradigm, where the expert tried to influence novices to alter their own step frequency through hand interactions. We used a within-subjects experiment design to examine changes in the novice’s step frequency across backleading conditions. To test whether the novice changes gait intuitively and if partners use low interaction forces, we did not give instructions on how to walk or interact at the hands.

## Procedures common to all conditions

To isolate the effects of hand interactions on gait, we masked audiovisual cues of walking. The novice wore a blindfold over both eyes and listened to white noise played through headphones during all walking (Fig. 8a). The expert listened to audio instructions and cues through headphones that blocked ambient sounds. The expert was not blindfolded to ensure safety during walking over several steps.

Throughout the experiment, the novice held a custom force handle (Fig. 8b) in each hand and was instructed to maintain a fixed arm posture with elbows flexed at 90 degrees (Fig. 8a). Maintaining a consistent arm posture has been shown to be important for communicating information through hand interactions during partnered stepping9.

For each trial, the novice was instructed to walk forward 8 steps and collect the feet at the 9th step, starting with the right foot and ending with both feet side-by-side. To demonstrate that hand interactions intuitively influence walking, novices did not receive explicit instructions or training on how to walk and were given only one or two practice trials walking solo and with a partner.

### Solo walking condition

The first condition required the novice to walk forward alone to provide data on their solo preferred gait parameters. Four trials were performed in one block.

## Partnered backleading conditions

Next, the expert influenced changes to the novice’s step frequency in three partnered backleading conditions – Decrease, Maintain, or Increase step frequency relative to the novice’s Solo preferred step frequency. The Maintain condition was designed to result in similar gait kinematics as the Solo condition while allowing measurement of hand interaction forces. The expert held the opposite ends of the custom force handles and walked backwards while the novice walked forwards (Fig. 8a).

All backleading conditions occurred in one block. At the beginning of the block, the novice was instructed that “Your partner may nonverbally suggest that you walk in a different way; try to cooperate with your partner.” 8 trials were performed for each backleading condition, with trial order randomized. 5-minute seated rest breaks were enforced after every 10 trials.

At the beginning of each trial, the expert received audio instructions on how to influence the novice’s step frequency (Decrease, Maintain, or Increase). The novice was then given an audio cue through the headphones to start walking, and the expert started walking in response to the novice’s gait initiation. After the start cue to the novice, the expert listened to metronome beats occurring at 75, 100, or 125% of the novice’s Solo preferred step frequency, depending on the condition (Decrease, Maintain, or Increase step frequency, respectively).

Data preprocessing

All motion capture data were labeled and gapfilled in Vicon Nexus and exported to Matlab to be low-pass filtered at 10hz with a 4th order Butterworth filter. Velocity data were obtained from the time derivative of marker position data.

Force data were also low-pass filtered at 10hz with a 4th order Butterworth filter and then downsampled to match the sampling rate of motion capture data. To account for sensor drift, we subtracted zero-force voltage bias from force data for each partnership. We calculated zero-force voltage bias during the first solo walking trial after the block of partnered backleading conditions, except for one participant who was missing data from this trial, for whom we used the last solo walking trial before the partnered conditions. We analyzed hand interaction forces in the anterior-posterior direction only from the sensor held by the novice’s right hand (and the expert’s left hand) as data appeared similar between both force sensors.

Outcome metrics

## Time periods of analysis

As we were interested in steady-state behavior, not gait initiation or termination, we determined the novice’s steady-state walking period for each trial. Heelstrike events were identified from local minima of vertical position of heel markers, except for one participant with poor marker fill, for whom we used local minimal of anterior-posterior velocity of ankle markers. Heelstrike events were inspected manually and corrected when necessary. To analyze the same number of steps for each trial, we selected the middle 4 steps starting with the second right heelstrike and ending with the 4th right heelstrike (Fig. 8c, top). To check that the novice maintained constant gait velocity, we tested for a significant linear trend in torso velocity during this period (Fig. 8c, bottom). Outcome metrics were calculated for the trial if either a) there was no significant trend (p > 0.05) or b) there was a significant trend (p < 0.05) and the coefficient corresponding to acceleration was below a threshold of 0.001 m/s2.

To remove variability due to the partners resetting their starting positions in the room before each trial, several steady-state metrics were normalized by subtracting the mean from a baseline “pre-move” period when both partners were standing still. The “pre-move” period for each trial was selected as the 0.49s before the earliest movement onset of either partner, which was determined by when the novice or expert’s torso velocities crossed above a threshold of 0.1 m/s.

## Novice gait parameters

We calculated several gait parameters during the steady-state period to examine both the intended changes to step frequency and any additional changes potentially due to gait coupling. Step frequency was calculated as the inverse of the elapsed time between successive heelstrike events (Fig. 8c, top). The mean across the middle 4 steps was calculated for each trial. Step length was calculated as the anterior-posterior distance between foot markers at heelstrike events (Fig. 8c, top), and the mean was calculated per trial. Gait speed was calculated as the anterior-posterior displacement of the torso marker divided by time elapsed during the steady-state period. Step frequency, step length, and gait velocity were all normalized to each participant’s means during the Solo walking condition.

Young persons without walking or balance impairments have been shown to maintain a constant “walk ratio” between step length and step frequency across gait speeds during preferred solo walking25–27. Thus, we calculated the walk ratio as a metric of gait coupling, using the normalization procedure established in previous literature25.

## Force and power metrics

We analyzed both the signs and magnitudes of force and power to examine whether this data contained information on desired walking behavior and/or mechanically constrained human movement. The mean signed and absolute value of force and power were calculated during the steady-state period for each trial (Fig. 2a,c). To obtain the full range of forces and power used, we calculated histograms including every time sample (after downsampling) of every trial and participant for each backleading condition, using Sturges’ rule52 to choose the number of bins.

We calculated mechanical power at both the interaction point between partners and at the novice’s torso to check for any differences between these locations. Mechanical power was calculated as anterior-posterior force multiplied by anterior-posterior velocity of a) the interaction point marker – chosen as either the marker located slightly proximal of the novice’s right metacarpophalangeal joint (n = 4) or the marker on the novice’s right radial styloid process (n = 6) and b) the novice’s torso marker. All power metrics were normalized by each participant’s body mass. Power calculations for the two locations resulted in nearly identical values (compare middle and bottom rows in Supplementary Figure S1 online), so we examined only power at the interaction point for further analyses.

To examine whether hand interactions relied on mechanical effects to alter the novice’s gait, we compared the magnitudes of interaction point power measured during backleading to estimated power from the lower limbs for propelling solo walking. Whereas interaction forces and power transfer between wearable robotic devices and the human body are difficult to measure29,30 and seldom reported31, the mechanical power for propelling locomotion can be estimated as the power exerted by human lower limbs on the center-of-mass to maintain constant-speed walking without external aid28. The estimated power was calculated using an equation describing power for performing step-to-step transitions as a function of step length during constant-speed solo walking in unimpaired adults28. We calculated power for step-to-step transitions for each backleading condition using mean step lengths measured for each novice as inputs to the equation. To examine changes in power magnitudes between conditions (i.e., Maintain – Decrease and Increase – Maintain), we also calculated the change in measured interaction point power and change in estimated step-to-step transition power for changes in measured step lengths.

## Spatiotemporal metrics characterizing control strategies

We examined several spatiotemporal metrics to characterize how the partnership coordinated gross body movement with each other and how each partner contributed to inter-partner coordination.

To characterize spatial synchrony between partners, the Inter-torso Distance (ITD) was calculated as the anterior-posterior distance between partners’ torsos during the steady-state period (Fig. 4a) and is based on the “whole-body synchronization” metric9. Change in ITD was calculated by subtracting the mean ITD during the pre-move period (Fig. 4a) from the mean ITD during steady state for each trial. Change in ITD is negative if partners are closer together and positive if they are further apart during steady-state walking relative to the pre-move period.

To characterize temporal synchrony between partners during steady-state walking, we calculated cross-correlations between anterior-posterior torso velocities (Fig. 4b). Torso velocity during the steady state period was first mean-subtracted, and then cross-correlation was calculated for time delays up to ¼ of the novice’s mean step time – the inverse of mean step frequency – for the trial to avoid ambiguity in the signs of cross-correlation and time delay for cyclical signals. The maximum absolute cross-correlation and its corresponding time delay were obtained as the temporal synchrony metrics for each trial.

To determine individual contributions to inter-partner spatial synchrony, the Effective Arm Length (EAL) for each partner was calculated as the anterior-posterior distance between each partner’s torso marker and the interaction point marker (Fig. 5a). Similar to the Change in ITD, Change in EAL was calculated by subtracting the mean EAL during the pre-move period (Fig. 5a) from the mean EAL during steady state for each trial.

To characterize temporal order of movement for each partner’s torso relative to the interaction point during steady-state walking, we performed cross-correlation analysis between torso and interaction point velocities for each partner (Fig. 5b) using the same procedure as for the cross-correlation between partners’ torso velocities.

## Impedance models of control strategies

We fit mechanical spring-damper models to kinematic and force data to glean principles from pHHI control strategies applicable to pHRI control. The partnership inter-torso and individual arm impedance models were created using the Change in ITD and Change in EAL for displacement (“x” in Fig. 6’s equations), respectively. Displacement was differentiated with respect to time to obtain velocity. The regression algorithm for each trial consisted of 1) regressing to both displacement and velocity terms, 2) discarding any non-significant terms, as defined by regression coefficients with confidence intervals that included zero, and repeating steps 1) and 2) until only significant terms or no terms remained in the final regression model. If the final regression model reached statistical significance (p < 0.05), the coefficients from the trial were included in calculations of the average stiffness and damping values for the partnership. The R2 value of the final model was calculated to assess quality of fit for each trial. A similar method for estimating mechanical impedance through linear regression of time-series data has been validated for spring stiffness53.

## Statistical analysis

First, to validate Maintain as an appropriate baseline/control condition for metrics measured both during Solo and partnered conditions, we verified that the partnered Maintain condition was not statistically different from the Solo walking condition. We compared paired samples using either a parametric or non-parametric test depending on if data were normally distributed, as determined by the Lilliefors test. If both samples were normally distributed, we used the Student’s t test for equal sample sizes or Welch’s t test for unequal sample sizes. If either sample was not normally distributed, we used the Wilcoxon sign-rank test for equal sample sizes or Mann-Whitney U test (a.k.a. the “rank sum test”) for unequal sample sizes. We found no significant difference (p > 0.05) between Maintain and Solo condition means for step frequency, step length, gait velocity, Change in EAL, time delay between torso velocities, maximum absolute cross-correlation between torso velocities, or mean interaction point velocity. Thus, we used the Maintain condition for all further statistical analysis.

We then performed repeated measures ANOVAs to examine the effect of backleading condition (Decrease, Maintain, Increase) on each outcome metric. First, we performed Mauchly’s test of sphericity. We then calculated the F-value, and if sphericity was violated, we used the Greenhouse-Geisser correction for the degrees of freedom and p-value. We followed up significant ANOVAs with Bonferroni-corrected pairwise comparisons between condition means. An alpha-value of 0.05 was used for all tests of significance.

To examine whether impedance matching between partners occurred, we performed linear correlations on novice and expert arm stiffness and damping values obtained from the fitting the spring-damper model. Correlations between paired samples (novice and expert) arm stiffness and damping were tested separately for each backleading condition. We first used the Lilliefors test to determine if each sample was normally distributed and then Pearson’s correlation or Spearman’s rank correlation for data with normal or non-normal distributions, respectively. An alpha-value of 0.05 was used to test for significant correlations.