Decision letter: Individuals physically interacting in a group rapidly coordinate their movement by estimating the collective goal

Article Figures and data Abstract Introduction Results Discussion Materials and methods Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract How can a human collective coordinate, for example to move a banquet table, when each person is influenced by the inertia of others who may be inferior at the task? We hypothesized that large groups cannot coordinate through touch alone, accruing to a zero-sum scenario where individuals inferior at the task hinder superior ones. We tested this hypothesis by examining how dyads, triads and tetrads, whose right hands were physically coupled together, followed a common moving target. Surprisingly, superior individuals followed the target accurately even when coupled to an inferior group, and the interaction benefits increased with the group size. A computational model shows that these benefits arose as each individual uses their respective interaction force to infer the collective’s target and enhance their movement planning, which permitted coordination in seconds independent of the collective’s size. By estimating the collective’s movement goal, its individuals make physical interaction beneficial, swift and scalable. https://doi.org/10.7554/eLife.41328.001 Introduction A recent social experiment involving the widely acclaimed Pokemon video game ignited enormous public interest, where tens of thousands of players simultaneously controlled the protagonist of the game together and successfully finished the game (Zhang and Liu, 2015). Such collective behavior in humans has been researched when a collective makes a decision verbally (Webb, 1991; Hastie and Kameda, 2005; Bahrami et al., 2010). However, the key to many great human accomplishments, such as carrying stone blocks to construct the Great Pyramids, was enabled by many individuals who needed to coordinate the forces they applied on a stone in order to guide it on top of wooden rollers and move it. Such physical coordination has been investigated in pairs or dyads in the past decade (Basdogan et al., 2000; Sebanz et al., 2006; Reed and Peshkin, 2008; van der Wel et al., 2011; Malysz and Sirouspour, 2013). Previous studies that investigated dyads found evidence of improved task performance (Basdogan et al., 2000; Reed and Peshkin, 2008; Malysz and Sirouspour, 2013), but the underlying mechanism of physical coordination was unknown. In a recent study, we tested dyads interacting in a continuous tracking task, and found that the tracking performance of both partners improved, even when the partner was worse at the task (Ganesh et al., 2014). This mutual improvement during continuous interaction is explained by a mechanism where individuals estimate the partner’s target from the interaction force to improve their prediction of the target’s motion (Takagi et al., 2017). In a second study, we showed that a stronger connection yields a better estimate of the partner’s target, enabling partners to improve more from the interaction (Takagi et al., 2018). We speak of the partner’s target for a tracking task, but this can be generalized to estimating a partner’s movement goal, which we define as the partner’s desired state, for example a position and velocity in time. Although the mechanism of estimating the partner’s movement goal explains coordination in dyads, it is not known whether this interaction mechanism holds for an interactive tracking task with more than one partner. The connection dynamics to multiple partners may help inferior partners in a group but will likely hinder superior partners’ task performance. The dynamics may interfere with the coordination mechanism, which in dyads enabled even the superior partner to improve during the interactive tracking task (Ganesh et al., 2014). It is therefore unclear whether the interaction remains mutually beneficial for large groups. To elucidate this question and investigate how collectives negotiate common actions, we examined a task inspired by dancing in which two, three and four partners have to control their motion while feeling forces from the soft interaction with others. We hypothesized that the stochastic summation of every partner’s actions, yielding the interaction force, would produce a noisier and poorer haptic estimate of the target as the group size increases. We also expected the connection dynamics and the collective’s inertia to have a detrimental effect on the superior partners’ performance. In such a scenario, the dynamics of being physically connected to a collective of partners may characterize the interaction behavior, similar to what was observed in joint reaching movements (Takagi et al., 2016). Could the coordination mechanism proposed in earlier studies (Takagi et al., 2017; Takagi et al., 2018) fully explain the tracking performance observed in collective interaction, or would the dynamics of the collective’s inertia outweigh the benefits of the coordination mechanism in larger groups? Results We tested interaction in dyads, triads and tetrads who tracked a common target together using their right hands, which were all joined together with virtual elastic bands with a stiffness of 100 N/m (Figure 1A and B). 12 fours carried out the experiment in 12 triads and 12 tetrads, and 12 dyads were tested separately (see Figure 1D and the Materials and methods for details on the protocol). Individuals in the collective had to control a robotic handle using their right hand, which moved a cursor on their own respective monitor, to track a moving target (Figure 1A). The same target was used for all individuals of the collective. Each individual saw, on their own monitor, the positions of the target and their hand, but not the partners’ cursor positions. Individual performance at the task was calculated for each 15 s trial by measuring the average distance between their cursor and the target, defined as the tracking error. Two types of trials were tested: in solo trials, each individual tracked the target alone; in connected trials, the individuals’ right hands were coupled together by elastic bands. Figure 1 with 2 supplements see all Download asset Open asset Dyads, triads and tetrads, whose right hands were connected, tracked a common target together to investigate collective physical interaction. (A) Subjects were recruited in twos or fours (schematic shows a tetrad). Each participant held onto a robotic handle with their dominant right hand to control a cursor on a monitor and track the same randomly moving target. Only one’s own cursor and the target were displayed on the monitor. (B) Physical coordination for dyads, triads and tetrads was enabled by forces exerted through the robotic handle that elastically connected all individuals’ right hands together. The interaction was removed in some trials to measure each individual’s solo tracking error as a function of the deviation in the target spots’ velocities. (C) The target was composed of five spots were spread thinly or widely to control each individual’s tracking performance. The deviation in the spots’ velocities, which was fixed during a trial, was randomized at every trial so participants could not know their skill relative to their partners beforehand. (D) Experimental protocol for twos and fours, where each circle represents an individual denoted by color. A dash indicates the individual was connected to partners. Both twos and fours experienced 10 solo training trials to become acquainted to the task. Twos then experienced 30 pairs of trials with and without the elastic connection, that is connected-solo-connected-solo etc. for 30 repetitions, and then 10 connected trials. For fours, three individuals of a tetrad were selected, forming all four different combinations of triads, and interacted in triads for one block per combination. In the first and last of these triad blocks, triads experienced 10 pairs of connected-solo trials, while the second and third triad blocks was composed of 10 connected trials. This was done to intersperse the solo trials to have a robust measure of the relationship between visual noise level and tracking error. In the final block, all individuals interacted as a tetrad for 30 trials. https://doi.org/10.7554/eLife.41328.002 To test how interaction with inferior or superior partners influenced tracking performance, we manipulated the tracking ability of subjects by applying visual noise to the target (Körding and Wolpert, 2004) as described in the Materials and methods (see Figure 1C and Video 1 and 2 for visual noise during tracking task). The tracking error of subjects was linearly and tightly related to the standard deviation of this visual noise, such that greater visual noise resulted in larger tracking errors (see Figure 2B for sample subjects). A different amount of visual noise, which was randomly selected but fixed during each connected trial, was applied to each member of a collective for every trial. This enabled us to test the influence of interaction with participants of different selected tracking ability. As the visual noise was linearly related to the tracking error, we could calculate the change in each subject’s tracking error during the interaction relative to the visual noise that we applied. We dispersed the solo trials throughout the entire experiment to verify that the relationship between visual noise level and tracking error did not drift with time, for example due to fatigue, which is the rationale for having a complicated protocol for twos and fours (see Figure 1D). Figure 2 Download asset Open asset Sample trajectories from a single trial, and how the tracking error is tightly related with the visual noise imposed by the experimenter on each individual’s target. (A) Raw data showing the trajectories in the x-axis from a sample tetrad, where the black trace is the target and each dashed colored trace (red, green, blue and magenta) is one subject. The top panel shows the x-axis position of all subjects in a tetrad in a solo trial (all disconnected), whereas the bottom two panels are the x-axis position and force from a sample connected trial where all four subjects were coupled to each other via elastic bands. Subjects’ positions in both the sample solo and connected trials were all delayed with respect to the target due to visual feedback delays in anticipating the target’s motion. The force felt by each partner is approximately zero mean, and depended on each individual’s relative position to their partners in the group. (B) Linear fit of the standard deviation of spots’ velocities versus the tracking error from a sample tetrad. Each level of noise was tested for three trials without the elastic band to assess individual tracking error. This data was linearly regressed to estimate the expected tracking error of each individual as a function of the visual noise on the target imposed by the experimenter. This enabled us to test collectives composed of individuals with different tracking skill. https://doi.org/10.7554/eLife.41328.005 Figure 2A shows raw data of the x-axis positions and forces experienced by a sample tetrad in solo and connected trials. The positions of the subjects lagged the target’s motion due to visual feedback delays in anticipating the target’s movement. For each subject, we assessed the performance improvement 1-ec/e, where ec was an individual’s tracking error in a connected trial and e was the same subject’s solo error, which was estimated from the visual noise applied during the connected trial. This ratio quantifies an individual’s tracking ability during the interaction relative to tracking alone. We analyzed this performance improvement as a function of the partners’ relative error, 1-ep/e, where ep was the mean of the partners’ solo errors, which was also estimated from the visual noise applied to the partners in the connected trial. This ratio is a measure of how the partners’ average tracking ability compared with the individual’s. This enabled us to study how each individual’s tracking ability changed when they interacted with ‘superior’ or ‘inferior’ partners. The results of the collective physical interaction are plotted in Figure 3 (the data in Figure 3—source data 1 was used for all subsequent analysis). First, we assessed how the collective as a whole improved from the physical interaction, which is shown in Figure 3A, by taking the mean performance improvement from all individuals in the collective from every connected trial, and averaging over all trials for each collective. Two-sample t-tests revealed that the collective’s mean improvement increased with its size (between dyads and triads: t(22)=2.53, p<0.02; between dyads and tetrads: t(22)=6.07, p<10−5), revealing the benefits of interacting in larger collectives. To observe how each individual’s improvement changed as a function of the partners’ performance, we plotted each individual’s performance improvement as a function of the partners’ mean relative error for dyads (red trace), triads (green) and tetrads (blue) in Figure 3B. The data was fit using a linear mixed-effects model, where each recruited group of twos and fours were treated as a random factor to control for individual differences in their inherent ability to improve from the interaction (see Equation 2 in the Materials and methods for details). A mixed-effects analysis showed that the collective’s size modulated the individual’s performance improvement (χ2(2)=412, p<10−15, see Materials and methods for details). Figure 3 Download asset Open asset Collective physical interaction was surprisingly beneficial with coordination emerging rapidly in seconds, with the benefit in performance increasing with the number of partners. (A) The collective improvement for dyads, triads and tetrads increased with the collective’s size, reflecting the advantage of larger collectives. (B) Performance improvement as a function of the partners’ relative error for dyads (red trace), triads (in green) and tetrads (in blue). The solid traces come from a linear mixed-effects fit of the raw data (points come from all connected trials from all groups). Interacting with a superior group was found to improve one’s performance, which was graded by the collective’s size such that a larger collective resulted in more improvement. We expected a similar effect when interacting with an inferior collective, but interacting with more inferior partners did not degrade a superior member’s performance. (C) The performance improvement of a sample tetrad is plot in increments of 0.5 s from the start to the end of the trial as a function of the partners’ relative error. The improvement rapidly converged to the improvement curve observed in Figure 3B. (D) The deviation of the improvement curve in Figure 3B from the final improvement curve is plotted as a function of the trial time for dyads, triads and tetrads. The solid line is the mean of all groups, and the area represents one standard error. The rate at which they deviated from the collective mean was independent of group size. https://doi.org/10.7554/eLife.41328.006 Figure 3—source data 1 Data of the partners’ mean relative error, improvement, group label and the group size used in the linear mixed-effects analysis. This data was also used in Figure 4 and 5. https://doi.org/10.7554/eLife.41328.007 Download elife-41328-fig3-data1-v2.txt We split the data into the superior (1−ep/e<0) and inferior (1−ep/e>0) individuals of the collective for dyads, triads and tetrads to examine how they were affected by physically interacting with superior or inferior partners. One-sample t-tests were carried out on the inferior and superior individuals’ improvements using a Bonferroni correction of significance 0.05/6. Inferior individuals improved when coupled to a superior collective, regardless of its size (dyads: t(11)=10.8, p<10−6; triads: t(11)=24.0, p<10−10, t(11)=23.0; tetrads: p<10−9). Surprisingly, superior individuals in dyads, triads and tetrads maintained their performance with respect to their solo error (dyads: t(11)=-2.22, p>0.05; triads: t(11)=-1.53, p>0.15; tetrads: t(11)=3.01, p>0.012). A superior individual could sustain their tracking performance even if they were physically coupled to an inferior collective regardless of how many inferior individuals were part of the collective. An individual’s improvement was dependent on the performance of the others in the collective, but did the performance improvement change within the 15 s trial? We examined the improvement plot of Figure 3B for each collective as a function of time by calculating the improvement from the start of the trial to a specific trial time in increments of 0.5 s. Figure 3C shows the evolution of the improvement of a sample tetrad, where each trace is a second-order polynomial fitted to the data. The improvement was observed to significantly change over time. To study the evolution of the interaction’s beneficial effect on performance, we analyzed the improvement curve’s deviation from the final improvement, defined as the improvement at the end of the 15 s trial, that is the improvement during the entire trial, for dyads, triads and tetrads. Figure 3D shows the Euclidean distance between the second-order polynomial fits on the data at different times and the final improvement as a function of time for dyads, triads and tetrads. The improvement increased rapidly during the 15 trials for all collectives. To compare the rate of convergence between dyads, triads and tetrads, we fitted an exponential function to each collective of the form a1+a2exp(-λt), where a1,a2>0 are parameters, λ>0 is the decay constant and t>0 is the trial time. Mann-Whitney U-tests revealed that the decay constant was similar between dyads and triads (U=122, n1=12, n2=12, p>0.11 two tailed), and between dyads and tetrads (U=136, n1=12, n2=12, p>0.44 two tailed). Thus, the time constant for the collective’s improvement did not depend on its size. Remarkably, it took only 7.4±0.9 s (mean ± standard error) for the collective to reach 90% of the final improvement. The empirical data shows that the collective physical interaction was beneficial for most individuals in the collective. How could individuals cause the performance improvement during collective interaction? To determine the behavioral strategy that individuals employed during collective interaction, we compared the empirical data from collective interaction with a simulation of it using the control models represented in Figure 4A and C to predict the outcome of the collective interaction experiment. In the simulation, we assumed that each individual sent motor commands to their arm to minimize the distance between their hand and the moving target. Simulated individuals relied on proprioception and vision for feedback of their hand and target positions, respectively. The simulated individuals had two free parameters that controlled the jerkiness of their movement and the strength of the controller, that is the control gain to bring the hand to the target. We carried out a sensitivity analysis to find values for these parameters that explained the empirical data best for each interaction model proposed in this study (see Supplementary material for details). Two, three and four such individuals were simulated in parallel with and without the elastic coupling to measure their performance at the tracking task during interaction and solo practice. Figure 4 with 2 supplements see all Download asset Open asset Simulations of the two proposed models of collective interaction and their predictions. (A) The no exchange model was simulated by assuming that individuals cannot interpret the interaction forces and track the target as if they were alone under the influence of the mechanics of the elastic band. (B) This model predicted a larger inferior collective to be a greater hindrance to a superior individual of the collective, unlike the data where superior individuals maintained their performance. (C) In the neuromechanical goal sharing model, each individual built a representation of the partners’ average behavior to estimate the collective target. (D) The predictions from this model best explained the improvement of both inferior and superior individuals in the collective, and its modulation with the collective’s size. https://doi.org/10.7554/eLife.41328.008 We first tested whether the performance improvements observed in groups larger than dyads can be explained by a model where the physical connection to a superior or inferior collective with greater inertia dominates the interaction outcome. This model also tests whether the averaging of multiple partners’ trajectories during the tracking task helped to reduce tracking errors due to a cancellation of tracking errors. In this no exchange model (Figure 4A), individuals track a target estimated from vision whilst under the influence of the forces from the elastic bands. This model predicted an improvement that was linearly dependent on the partners’ relative error, which was different from the data (Figure 4B). Importantly, the model predicted that a superior individual in the collective was hindered by inferior partners, and the hindrance was greater with more inferior individuals in contrast to the data (Figure 3B). The mismatch between the experimental data and the no exchange model’s prediction for triads and tetrads suggests that individuals interacting in large groups use the interaction force to exchange information that is relevant to the task, as was found in dyads in our previous study (Takagi et al., 2017). What kind of information did the individuals in triads and tetrads estimate from the interaction with their partners during the tracking task? In earlier studies (Takagi et al., 2017; Takagi et al., 2018), we showed that partners in dyads estimated each other’s target through the interaction force to improve their prediction of the target’s motion. Individuals in triads and tetrads may also extract useful information from haptics to improve tracking performance. We hypothesized that individuals interpret the summed interaction force as originating from one entity that tracks a collective target. According to this hypothesis, the individuals’ central nervous system (CNS) recognizes some correlation between the interaction force and the target motion (Parise and Ernst, 2016), then builds a representation of the entity that tracks the target. We assume that every individual’s CNS in the group estimates one collective target from the summed interaction force regardless of the number of partners in the group. In this extended neuromechanical goal sharing model, we propose that individuals track the optimally weighted average of the collective target and one’s own target from vision (see Figure 4C for schematic of the model). As an example, for tetrads, we simulated four connected individuals who each estimated a collective target from the three other partners, and who then integrated this haptic estimate of the target with their own visual estimate of the target’s position (see Equation 9 in the Materials and methods). The weights between vision and haptics were assumed to be known by every partner as we were interested in comparing the steady-state predictions of the model with the data. we for the haptic noise that due to the of the In our earlier study (Takagi et al., 2018), we found that a the haptic noise when estimating the partner’s target. us that an individual in a triad who is connected to two partners by a of two each of stiffness 100 an force to being connected to the average of the two partners’ positions by a of stiffness N/m (see Equation in Materials and et al., 2013). In other individuals in larger groups they are connected to the average position by a stronger The error due to a specific connection was for in the as noise (see Materials and methods for details on the haptic tracking experiment to measure this error due to the in the in dyads, triads and tetrads, and Figure 1 for the results of the haptic tracking The simulation of the neuromechanical goal sharing model predicted a performance improvement that the of the improvement as a function of the partners’ relative error with deviation from the data when tested in a sensitivity analysis (Figure and Figure The performance improvement increased for inferior and superior individuals their performance even when coupled to an inferior collective. the improvement was modulated by the collective’s size, such that tetrads improved the followed by triads, and then results that individuals in collectives of different use the same coordination strategy of a haptic estimate of the collective target position from the interaction Discussion This study tested physically interacting dyads, triads and tetrads in a tracking task to assess the effect of the size and its skill on the individuals’ tracking performance. We found that the performance increased with the group size, where inferior individuals in the group improved more in larger groups, and superior individuals were of their superior tracking performance even when connected to a group of individuals with inferior performance. to the results of our previous study (Ganesh et al., the superior individuals of the dyads in the study did not This in the results is likely due to the amount of visual noise to the target in order to each individual’s tracking performance. In our the performance improvements observed in dyads, triads and tetrads did not but during the trial such that 90% of the final performance improvement over the entire was s. As Figure 3C the partners’ movements depend only on the dynamics with Figure 4A and and a model of the interaction dynamics enabling to benefit from this interaction. The in the between dyads, triads and tetrads in reaching their performance improvement at the end of the trial may that the same coordination mechanism may be regardless of the size of the interacting group. The in these for physical interaction in contrast with or where significantly time is needed with more This the advantage of the of haptic relative to the in and In order to the coordination mechanism that explained the improvements from collective physical interaction, we used a computational model to test the of interaction, to predict their effect on the performance improvement, and compare the predictions with the empirical data. The neuromechanical goal sharing model, which the improvements from the empirical suggests a mechanism individuals extract task relevant information from and it with their own visual information of the target’s motion to improve tracking performance during interaction. In this model, we assumed that each individual a haptic estimate of the target from the interaction As this haptic estimate of the target is optimally with the individual’s visual target, this their tracking performance even when connected to partners having a inferior performance. The haptic estimate of the target from the summed interaction force, which is composed of the elastic to multiple partners, that is to one elastic coupling to the average partner (see Equation in the Materials and methods). the haptic estimate of the target is from summed interaction force, which is a function of the average partner’s then the performance improvement from this haptic depend only on the average partner’s tracking error, and not on the number of partners in the collective. did the simulation in Figure of the neuromechanical goal sharing model predict improvements that were dependent on both the average partner’s error and the size of the may be two for the graded performance improvement with group size. First, the connection dynamics alone could have graded the improvement, the no exchange model (in Figure 4A and also predicted improvements that were graded by group size. the effect of the noise in the haptic estimate of the target due to the of the elastic coupling may explain the graded improvement (see Equation in Materials and methods). To assess the of these two on the predicted performance improvement, we simulated the neuromechanical goal sharing model

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