Human social motor solutions for human-machine interaction in dynamical task contexts

Human-inspired strategies for controlling swarm systems

The control of swarms has emerged as a paradigmatic example of human-autonomy teaming. This review focuses on understanding human coordination behaviours, while controlling evasive autonomous agents, to inform the design of human-compatible teammates. We summarize the solutions employed by human dyads, as well as the verbal communication and division of labour strategies observed in four-person teams using virtual simulations. Additionally, we provide an overview of the design of artificial agents that replicate human-like dynamics using task-dynamical models, and which can be integrated into human-autonomy teams. Finally, we conclude with open questions regarding the preservation of situation awareness and trust within human-autonomous swarming teams.This article is part of the theme issue 'The road forward with swarm systems'.

Modelling human navigation and decision dynamics in a first-person herding task

This study investigated whether dynamical perceptual-motor primitives (DPMPs) could also be used to capture human navigation in a first-person herding task. To achieve this aim, human participants played a first-person herding game, in which they were required to corral virtual cows, called targets, into a specified containment zone. In addition to recording and modelling participants' movement trajectories during gameplay, participants' target-selection decisions (i.e. the order in which participants corralled targets) were recorded and modelled. The results revealed that a simple DPMP navigation model could effectively reproduce the movement trajectories of participants and that almost 80% of the participants' target-selection decisions could be captured by a simple heuristic policy. Importantly, when this policy was coupled to the DPMP navigation model, the resulting system could successfully simulate and predict the behavioural dynamics (movement trajectories and target-selection decisions) of participants in novel multi-target contexts. Implications of the findings for understanding complex human perceptual-motor behaviour and the development of artificial agents for robust human-machine interaction are discussed.

Interpersonal strategy for controlling unpredictable opponents in soft tennis

Competition in sports, unlike cooperation in everyday life, does not involve a single solution because individuals aim to behave unpredictably, thereby preventing others from predicting their actions. This study determined how individuals in court-based sports attempted to control others' unpredictable behaviors, addressing the gap in previous studies regarding the lack of clarity around strategies employed by individuals in competitive situations. We achieved this by applying a switching hybrid dynamics model, considering external inputs to analyze individual behaviors. Consequently, the study indicates that skilled individuals, in contrast to intermediate players, exhibit greater consistency in their behaviors. These skilled individuals lead others to anticipate their consistency and subsequently employ strategies to disrupt these expectations. This strategy exploits the principles of active human inference, implying that competition involves cooperation. This was revealed by an analysis of both human decision-making and behavior in actual matches as discrete and continuous dynamical systems. This interpersonal strategy could assist policymakers in the field of everyday life to enhance competitiveness. This strategy enables policymakers to adopt new policies that promote cooperation with competitors, ultimately increasing competitiveness in various aspects of our daily lives.

Prospects for Augmenting Team Interactions with Real-Time Coordination-Based Measures in Human-Autonomy Teams

Complex work in teams requires coordination across team members and their technology as well as the ability to change and adapt over time to achieve effective performance. To support such complex interactions, recent efforts have worked toward the design of adaptive human-autonomy teaming systems that can provide feedback in or near real time to achieve the desired individual or team results. However, while significant advancements have been made to better model and understand the dynamics of team interaction and its relationship with task performance, appropriate measures of team coordination and computational methods to detect changes in coordination have not yet been widely investigated. Having the capacity to measure coordination in real time is quite promising as it provides the opportunity to provide adaptive feedback that may influence and regulate teams' coordination patterns and, ultimately, drive effective team performance. A critical requirement to reach this potential is having the theoretical and empirical foundation from which to do so. Therefore, the first goal of the paper is to review approaches to coordination dynamics, identify current research gaps, and draw insights from other areas, such as social interaction, relationship science, and psychotherapy. The second goal is to collate extant work on feedback and advance ideas for adaptive feedback systems that have potential to influence coordination in a way that can enhance the effectiveness of team interactions. In addressing these two goals, this work lays the foundation as well as plans for the future of human-autonomy teams that augment team interactions using coordination-based measures.

Dyadic body competence predicts movement synchrony during the mirror game

The process of synchronizing our body movements with others is known to enhance rapport, affect, and prosociality. Furthermore, emerging evidence suggests that synchronizing activities may enhance cognitive performance. Unknown, by contrast, is the extent to which people's individual traits and experiences influence their ability to achieve and maintain movement synchrony with another person, which is key for unlocking the social and affective benefits of movement synchrony. Here, we take a dyad-centered approach to gain a deeper understanding of the role of embodiment in achieving and maintaining movement synchrony. Using existing data, we explored the relationship between body competence and body perception scores at the level of the dyad, and the dyad's movement synchrony and complexity while playing a 2.5-min movement mirroring game. The data revealed that dyadic body competence scores positively correlate with movement synchrony, but not complexity, and that dyadic body perception scores are not associated with movement synchrony or complexity. Movement synchrony was greater when the more experienced member of the dyad was responsible for copying movements. Finally, movement synchrony and complexity were stable across the duration of the mirror game. These findings show that movement synchrony is sensitive to the composition of the dyad involved, specifically the dyad's embodiment, illuminating the value of dyadic approaches to understanding body movements in social contexts.

Autistic young people adaptively use gaze to facilitate joint attention during multi-gestural dyadic interactions

LAY ABSTRACT

Autistic people have been said to have 'problems' with joint attention, that is, looking where someone else is looking. Past studies of joint attention have used tasks that require autistic people to continuously look at and respond to eye-gaze cues. But joint attention can also be done using other social cues, like pointing. This study looked at whether autistic and non-autistic young people use another person's eye gaze during joint attention in a task that did not require them to look at their partner's face. In the task, each participant worked together with their partner to find a computer-generated object in virtual reality. Sometimes the participant had to help guide their partner to the object, and other times, they followed their partner's lead. Participants were told to point to guide one another but were not told to use eye gaze. Both autistic and non-autistic participants often looked at their partner's face during joint attention interactions and were faster to respond to their partner's hand-pointing when the partner also looked at the object before pointing. This shows that autistic people can and do use information from another person's eyes, even when they don't have to. It is possible that, by not forcing autistic young people to look at their partner's face and eyes, they were better able to gather information from their partner's face when needed, without being overwhelmed. This shows how important it is to design tasks that provide autistic people with opportunities to show what they can do.

A Typology for the Application of Team Coordination Dynamics Across Increasing Levels of Dynamic Complexity

OBJECTIVE

This review and synthesis examines approaches for measuring and assessing team coordination dynamics (TCD). The authors advance a system typology for classifying TCD approaches and their applications for increasing levels of dynamic complexity.

BACKGROUND

There is an increasing focus on how teams adapt their coordination in response to changing and uncertain operational conditions. Understanding coordination is significant because poor coordination is associated with maladaptive responses, whereas adaptive coordination is associated with effective responses. This issue has been met with TCD approaches that handle increasing complexity in the types of TCD teams exhibit.

METHOD

A three-level system typology of TCD approaches for increasing dynamic complexity is provided, with examples of research at each level. For System I TCD, team states converge toward a stable, fixed-point attractor. For System II TCD, team states are periodic, which can appear complex, yet are regular and relatively stable. In System III TCD, teams can exhibit periodic patterns, but those patterns change continuously to maintain effectiveness.

RESULTS

System I and System II are applicable to TCD with known or discoverable behavioral attractors that are stationary across mid-to long-range timescales. System III TCD is the most generalizable to dynamic environments with high requirements for adaptive coordination across a range of timescales.

CONCLUSION

We outline current challenges for TCD and next steps in this burgeoning field of research.

APPLICATION

System III approaches are becoming widespread, as they are generalizable to time- and/or scale-varying TCD and multimodal analyses. Recommendations for deploying TCD in team settings are provided.

Social and nonlinear dynamics unite: musical group synchrony

Synchronization, the human tendency to align behaviors in time with others, is necessary for many survival skills. The ability to synchronize actions with rhythmic (predictable) sound patterns is especially well developed in music making. Recent models of synchrony in musical ensembles rely on pairwise comparisons between group members. This pairwise approach to synchrony has hampered theory development, given current findings from social dynamics indicating shifts in members' influence within larger groups. We draw on social theory and nonlinear dynamics to argue that emergent properties and novel roles arise in musical group synchrony that differ from individual or pairwise behaviors. This transformational shift in defining synchrony sheds light on successful outcomes as well as on disruptions that cause negative behavioral outcomes.

(Mis)align: a simple dynamic framework for modeling interpersonal coordination

As people coordinate in daily interactions, they engage in different patterns of behavior to achieve successful outcomes. This includes both synchrony-the temporal coordination of the same behaviors at the same time-and complementarity-the coordination of the same or different behaviors that may occur at different relative times. Using computational methods, we develop a simple framework to describe the interpersonal dynamics of behavioral synchrony and complementarity over time, and explore their task-dependence. A key feature of this framework is the inclusion of a task context that mediates interactions, and consists of active, inactive, and inhibitory constraints on communication. Initial simulation results show that these task constraints can be a robust predictor of simulated agents' behaviors over time. We also show that the framework can reproduce some general patterns observed in human interaction data. We describe preliminary theoretical implications from these results, and relate them to broader proposals of synergistic self-organization in communication.

Abduction and Deduction in Dynamical Cognitive Science

This paper reviews the recent history of a subset of research in dynamical cognitive science, in particular that subset that allies itself with the sciences of complexity and casts cognitive systems as interaction dominant, noncomputational, and nonmodular. I look at this history in the light of C.S. Peirce's understanding of scientific reasoning as progressing from abduction to deduction to induction. In particular, I examine the development of a controversy concerning the use of the interaction dominance of human cognitive systems as an explanation of the ubiquitous 1/f noise, multifractality, and complexity matching in human behavior.

Predicting and understanding human action decisions during skillful joint-action using supervised machine learning and explainable-AI

This study investigated the utility of supervised machine learning (SML) and explainable artificial intelligence (AI) techniques for modeling and understanding human decision-making during multiagent task performance. Long short-term memory (LSTM) networks were trained to predict the target selection decisions of expert and novice players completing a multiagent herding task. The results revealed that the trained LSTM models could not only accurately predict the target selection decisions of expert and novice players but that these predictions could be made at timescales that preceded a player's conscious intent. Importantly, the models were also expertise specific, in that models trained to predict the target selection decisions of experts could not accurately predict the target selection decisions of novices (and vice versa). To understand what differentiated expert and novice target selection decisions, we employed the explainable-AI technique, SHapley Additive explanation (SHAP), to identify what informational features (variables) most influenced modelpredictions. The SHAP analysis revealed that experts were more reliant on information about target direction of heading and the location of coherders (i.e., other players) compared to novices. The implications and assumptions underlying the use of SML and explainable-AI techniques for investigating and understanding human decision-making are discussed.

Conversation dynamics in a multiplayer video game with knowledge asymmetry

Despite the challenges associated with virtually mediated communication, remote collaboration is a defining characteristic of online multiplayer gaming communities. Inspired by the teamwork exhibited by players in first-person shooter games, this study investigated the verbal and behavioral coordination of four-player teams playing a cooperative online video game. The game, Desert Herding, involved teams consisting of three ground players and one drone operator tasked to locate, corral, and contain evasive robot agents scattered across a large desert environment. Ground players could move throughout the environment, while the drone operator's role was akin to that of a "spectator" with a bird's-eye view, with access to veridical information of the locations of teammates and the to-be-corralled agents. Categorical recurrence quantification analysis (catRQA) was used to measure the communication dynamics of teams as they completed the task. Demands on coordination were manipulated by varying the ground players' ability to observe the environment with the use of game "fog." Results show that catRQA was sensitive to changes to task visibility, with reductions in task visibility reorganizing how participants conversed during the game to maintain team situation awareness. The results are discussed in the context of future work that can address how team coordination can be augmented with the inclusion of artificial agents, as synthetic teammates.

Assessing Team Effectiveness by How Players Structure Their Search in a First-Person Multiplayer Video Game

People working as a team can achieve more than when working alone due to a team's ability to parallelize the completion of tasks. In collaborative search tasks, this necessitates the formation of effective division of labor strategies to minimize redundancies in search. For such strategies to be developed, team members need to perceive the task's relevant components and how they evolve over time, as well as an understanding of what others will do so that they can structure their own behavior to contribute to the team's goal. This study explored whether the capacity for team members to coordinate effectively can be related to how participants structure their search behaviors in an online multiplayer collaborative search task. Our results demonstrated that the structure of search behavior, quantified using detrended fluctuation analysis, was sensitive to contextual factors that limit a participant's ability to gather information. Further, increases in the persistence of movement fluctuations during search behavior were found as teams developed more effective coordinative strategies and were associated with better task performance.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Synchrony in triadic jumping performance under the constraints of virtual reality

The use of an immersive virtual reality system as a work space for sports and physical education can help maintain physical communication from separate places. In this study, we verified the possibility of constructing a movement synchrony system by reproducing the mathematical ordered pattern of “triadic jumping” in a virtual space. Three jumpers were asked to move together in a space that was cramped and insufficient for them to pass each other. Within this restricted space, the ordered pattern of the jumpers’ synchrony systematically transited to another state depending on the geometrical configuration of the work space. Although the temporal rigidity of the synchrony was partially lost, the ordered pattern of the “triadic jumping” synchrony that emerged in the virtual space was qualitatively equivalent to that emerging in real space. We believe the idea of expanding the work space for physical education to a virtual one could turn into reality if the sensory feedback of the collision successfully improves the spatial-temporal rigidity of the joint action ordered pattern.

Assessing attentive monitoring levels in dynamic environments through visual neuro-assisted approach

Objective

This work aims to establish a framework in measuring the various attentional levels of the human operator in a real-time animated environment through a visual neuro-assisted approach.

Background

With the increasing trend of automation and remote operations, understanding human-machine interaction in dynamic environments can greatly aid to improve performance, promote operational efficiency and safety.

Method

Two independent 1-hour experiments were conducted on twenty participants where eye-tracking metrics and neuro activities from electroencephalogram (EEG) were recorded. The experiments required participants to exhibit attentive behaviour in one set and inattentive in the other. Two segments ("increasing flight numbers" and "relatively constant flight numbers") were also extracted to study the participants' visual behavioral differences in relation to aircraft numbers.

Results

For the two experimental studies, those in the attentive behavioral study show incidences of higher fixation count, fixation duration, number of aircraft spotted, and landing fixations whereas those in inattentive behavior study reveal higher zero-fixation frame count. In experiments involving 'increasing flight numbers', a higher percentage of aircraft were spotted as compared to those with 'constant flight numbers' in both the groups. Three parameters (number of aircraft spotted, and landing fixations and zero-fixation frame count) are newly established. As radar monitoring is a brain engagement activity, positive EEG data were registered in all the participants. A newly Task Engagement Index (TEI) was also formulated to predict different attentional levels.

Conclusion

Results provide a refined quantifiable tool to differentiate between attentive and inattentive monitoring behavior in a real-time dynamic environment, which can be applied across various sectors.

Recommendation

With the quantitative TEI established, this paves the way for future studies into attentional levels by regions, time based, as well as eye signature studies in relation to visual task engagement and management and determining expertise levels to be explored. Factors relating to fatigue could also be investigated using the TEI approach proposed.

Herding stochastic autonomous agents via local control rules and online target selection strategies

We propose a simple yet effective set of local control rules to make a small group of “herder agents” collect and contain in a desired region a large ensemble of non-cooperative, non-flocking stochastic “target agents” in the plane. We investigate the robustness of the proposed strategies to variations of the number of target agents and the strength of the repulsive force they feel when in proximity of the herders. The effectiveness of the proposed approach is confirmed in both simulations in ROS and experiments on real robots.

Human unintentional and intentional interpersonal coordination in interaction with a humanoid robot

In order to establish natural social synchrony between two humans, two requirements need to be fulfilled. First, the coupling must be bi-directional. The two humans react to each other's actions. Second, natural social bodily synchronization has to be intentional or unintentional. Assuming that these essential aspects of human-human interactions are present, the present paper investigates whether similar bodily synchrony emerges between an interacting human and an artificial agent such as a robot. More precisely, we investigate whether the same human unintentional rhythmic entrainment and synchronization is present in Human Robot Interaction (HRI). We also evaluate which model (e.g., an adaptive vs non adaptive robot) better reproduces such unintentional entrainment. And finally, we compare interagent coordination stability of the HRI under 1) unidirectional (robot with fixed frequency) versus bidirectional (robot with adaptive frequency) rhythmic entrainment and 2) human intentional versus unintentional coupling. Fifteen young adults made vertical arm movements in front of the NAO robot under five different conditions of intentional/unintentional and unidirectional/bidirectional interactions. Consistent with prior research investigating human-human interpersonal coordination, when humans interact with our robot, (i) unintentional entrainment was present, (ii) bi-directional coupling produced more stable in-phase un-intentional and intentional coordination, (iii) and intentional coordination was more stable than unintentional coordination. To conclude, this study provides a foundation for modeling future social robots involving unintentional and bidirectional synchronization-aspects which seem to enhance humans' willingness to interact with robots.

Human-machine-human interaction in motor control and rehabilitation: a review

BACKGROUND

Human-human (HH) interaction mediated by machines (e.g., robots or passive sensorized devices), which we call human-machine-human (HMH) interaction, has been studied with increasing interest in the last decade. The use of machines allows the implementation of different forms of audiovisual and/or physical interaction in dyadic tasks. HMH interaction between two partners can improve the dyad's ability to accomplish a joint motor task (task performance) beyond either partner's ability to perform the task solo. It can also be used to more efficiently train an individual to improve their solo task performance (individual motor learning). We review recent research on the impact of HMH interaction on task performance and individual motor learning in the context of motor control and rehabilitation, and we propose future research directions in this area.

METHODS

A systematic search was performed on the Scopus, IEEE Xplore, and PubMed databases. The search query was designed to find studies that involve HMH interaction in motor control and rehabilitation settings. Studies that do not investigate the effect of changing the interaction conditions were filtered out. Thirty-one studies met our inclusion criteria and were used in the qualitative synthesis.

RESULTS

Studies are analyzed based on their results related to the effects of interaction type (e.g., audiovisual communication and/or physical interaction), interaction mode (collaborative, cooperative, co-active, and competitive), and partner characteristics. Visuo-physical interaction generally results in better dyadic task performance than visual interaction alone. In cases where the physical interaction between humans is described by a spring, there are conflicting results as to the effect of the stiffness of the spring. In terms of partner characteristics, having a more skilled partner improves dyadic task performance more than having a less skilled partner. However, conflicting results were observed in terms of individual motor learning.

CONCLUSIONS

Although it is difficult to draw clear conclusions as to which interaction type, mode, or partner characteristic may lead to optimal task performance or individual motor learning, these results show the possibility for improved outcomes through HMH interaction. Future work that focuses on selecting the optimal personalized interaction conditions and exploring their impact on rehabilitation settings may facilitate the transition of HMH training protocols to clinical implementations.

Task dynamics define the contextual emergence of human corralling behaviors

Social animals have the remarkable ability to organize into collectives to achieve goals unobtainable to individual members. Equally striking is the observation that despite differences in perceptual-motor capabilities, different animals often exhibit qualitatively similar collective states of organization and coordination. Such qualitative similarities can be seen in corralling behaviors involving the encirclement of prey that are observed, for example, during collaborative hunting amongst several apex predator species living in disparate environments. Similar encirclement behaviors are also displayed by human participants in a collaborative problem-solving task involving the herding and containment of evasive artificial agents. Inspired by the functional similarities in this behavior across humans and non-human systems, this paper investigated whether the containment strategies displayed by humans emerge as a function of the task's underlying dynamics, which shape patterns of goal-directed corralling more generally. This hypothesis was tested by comparing the strategies naïve human dyads adopt during the containment of a set of evasive artificial agents across two disparate task contexts. Despite the different movement types (manual manipulation or locomotion) required in the different task contexts, the behaviors that humans display can be predicted as emergent properties of the same underlying task-dynamic model.

Gaze facilitates responsivity during hand coordinated joint attention

The coordination of attention between individuals is a fundamental part of everyday human social interaction. Previous work has focused on the role of gaze information for guiding responses during joint attention episodes. However, in many contexts, hand gestures such as pointing provide another valuable source of information about the locus of attention. The current study developed a novel virtual reality paradigm to investigate the extent to which initiator gaze information is used by responders to guide joint attention responses in the presence of more visually salient and spatially precise pointing gestures. Dyads were instructed to use pointing gestures to complete a cooperative joint attention task in a virtual environment. Eye and hand tracking enabled real-time interaction and provided objective measures of gaze and pointing behaviours. Initiators displayed gaze behaviours that were spatially congruent with the subsequent pointing gestures. Responders overtly attended to the initiator’s gaze during the joint attention episode. However, both these initiator and responder behaviours were highly variable across individuals. Critically, when responders did overtly attend to their partner’s face, their saccadic reaction times were faster when the initiator’s gaze was also congruent with the pointing gesture, and thus predictive of the joint attention location. These results indicate that humans attend to and process gaze information to facilitate joint attention responsivity, even in contexts where gaze information is implicit to the task and joint attention is explicitly cued by more spatially precise and visually salient pointing gestures.

Navigational Behavior of Humans and Deep Reinforcement Learning Agents

Rapid advances in the field of Deep Reinforcement Learning (DRL) over the past several years have led to artificial agents (AAs) capable of producing behavior that meets or exceeds human-level performance in a wide variety of tasks. However, research on DRL frequently lacks adequate discussion of the low-level dynamics of the behavior itself and instead focuses on meta-level or global-level performance metrics. In doing so, the current literature lacks perspective on the qualitative nature of AA behavior, leaving questions regarding the spatiotemporal patterning of their behavior largely unanswered. The current study explored the degree to which the navigation and route selection trajectories of DRL agents (i.e., AAs trained using DRL) through simple obstacle ridden virtual environments were equivalent (and/or different) from those produced by human agents. The second and related aim was to determine whether a task-dynamical model of human route navigation could not only be used to capture both human and DRL navigational behavior, but also to help identify whether any observed differences in the navigational trajectories of humans and DRL agents were a function of differences in the dynamical environmental couplings.

Unifying Large- and Small-Scale Theories of Coordination

Coordination is a ubiquitous feature of all living things. It occurs by virtue of informational coupling among component parts and processes and can be quite specific (as when cells in the brain resonate to signals in the environment) or nonspecific (as when simple diffusion creates a source–sink dynamic for gene networks). Existing theoretical models of coordination—from bacteria to brains to social groups—typically focus on systems with very large numbers of elements (N→∞) or systems with only a few elements coupled together (typically N = 2). Though sharing a common inspiration in Nature’s propensity to generate dynamic patterns, both approaches have proceeded largely independent of each other. Ideally, one would like a theory that applies to phenomena observed on all scales. Recent experimental research by Mengsen Zhang and colleagues on intermediate-sized ensembles (in between the few and the many) proves to be the key to uniting large- and small-scale theories of coordination. Disorder–order transitions, multistability, order–order phase transitions, and especially metastability are shown to figure prominently on multiple levels of description, suggestive of a basic Coordination Dynamics that operates on all scales. This unified coordination dynamics turns out to be a marriage of two well-known models of large- and small-scale coordination: the former based on statistical mechanics (Kuramoto) and the latter based on the concepts of Synergetics and nonlinear dynamics (extended Haken–Kelso–Bunz or HKB). We show that models of the many and the few, previously quite unconnected, are thereby unified in a single formulation. The research has led to novel topological methods to handle the higher-dimensional dynamics of coordination in complex systems and has implications not only for understanding coordination but also for the design of (biorhythm inspired) computers.

Coordination Dynamics: A Foundation for Understanding Social Behavior

Humans' interactions with each other or with socially competent machines exhibit lawful coordination patterns at multiple levels of description. According to Coordination Dynamics, such laws specify the flow of coordination states produced by functional synergies of elements (e.g., cells, body parts, brain areas, people…) that are temporarily organized as single, coherent units. These coordinative structures or synergies may be mathematically characterized as informationally coupled self-organizing dynamical systems (Coordination Dynamics). In this paper, we start from a simple foundation, an elemental model system for social interactions, whose behavior has been captured in the Haken-Kelso-Bunz (HKB) model. We follow a tried and tested scientific method that tightly interweaves experimental neurobehavioral studies and mathematical models. We use this method to further develop a body of empirical research that advances the theory toward more generalized forms. In concordance with this interdisciplinary spirit, the present paper is written both as an overview of relevant advances and as an introduction to its mathematical underpinnings. We demonstrate HKB's evolution in the context of social coordination along several directions, with its applicability growing to increasingly complex scenarios. In particular, we show that accommodating for symmetry breaking in intrinsic dynamics and coupling, multiscale generalization and adaptation are principal evolutions. We conclude that a general framework for social coordination dynamics is on the horizon, in which models support experiments with hypothesis generation and mechanistic insights.

Hopf Bifurcations in Complex Multiagent Activity: The Signature of Discrete to Rhythmic Behavioral Transitions

Most human actions are composed of two fundamental movement types, discrete and rhythmic movements. These movement types, or primitives, are analogous to the two elemental behaviors of nonlinear dynamical systems, namely, fixed-point and limit cycle behavior, respectively. Furthermore, there is now a growing body of research demonstrating how various human actions and behaviors can be effectively modeled and understood using a small set of low-dimensional, fixed-point and limit cycle dynamical systems (differential equations). Here, we provide an overview of these dynamical motorprimitives and detail recent research demonstrating how these dynamical primitives can be used to model the task dynamics of complex multiagent behavior. More specifically, we review how a task-dynamic model of multiagent shepherding behavior, composed of rudimentary fixed-point and limit cycle dynamical primitives, can not only effectively model the behavior of cooperating human co-actors, but also reveals how the discovery and intentional use of optimal behavioral coordination during task learning is marked by a spontaneous, self-organized transition between fixed-point and limit cycle dynamics (i.e., via a Hopf bifurcation).

Combat as an Interpersonal Synergy: An Ecological Dynamics Approach to Combat Sports

In combat sports, athletes continuously co-adapt their behavior to that of the opponent. We consider this interactive aspect of combat to be at the heart of skilled performance, yet combat sports research often neglects or limits interaction between combatants. To promote a more interactive approach, the aim of this paper is to understand combat sports from the combined perspective of ecological psychology and dynamic systems. Accordingly, combat athletes are driven by perception of affordances to attack and defend. Two combatants in a fight self-organize into one interpersonal synergy, where the perceptions and actions of both athletes are coupled. To be successful in combat, performers need to manipulate and take advantage of the (in)stability of the system. Skilled performance in combat sports therefore requires brinkmanship: combatants need to be aware of their action boundaries and purposefully act in meta-stable regions on the limits of their capabilities. We review the experimental literature to provide initial support for a synergetic approach to combat sports. Expert combatants seem able to accurately perceive action boundaries for themselves and their opponent. Local-level behavior of individual combatants has been found to lead to spatiotemporal synchronization at the global level of a fight. Yet, a formal understanding of combat as a dynamic system starting with the identification of order and control parameters is still lacking. We conclude that the ecological dynamics perspective offers a promising approach to further our understanding of skilled performance in combat sports, as well as to assist coaches and athletes to promote optimal training and learning.

Neurologically Motivated Coupling Functions in Models of Motor Coordination

We present an analysis of two Haken-Kelso-Bunz (HKB) oscillators coupled by a neurologically motivated function. We study the effect of time delay and weighted self-feedback and mutual feedback on the synchronization behavior of the model. We focus on identifying parameter regimes supporting experimentally observed decrease in oscillation amplitude and loss of anti-phase stability that has inspired the development of the HKB model. We show that a combination of cross-talk and nonlinearity in the coupling, along with physiologically relevant time delay, is able to quantitatively account for both drop in oscillation amplitude and loss of anti-phase stability in a frequency dependent manner. Furthermore, we demonstrate that the transition between discrete and rhythmic movements could be captured by this model. To this end, we carry out theoretical and numerical analysis of the emergence of in-phase and anti-phase oscillations.