The preparatory state of ground reaction forces in defending against a dribbler in a basketball 1-on-1 dribble subphase

Decentralized policy learning with partial observation and mechanical constraints for multiperson modeling

Extracting the rules of real-world multi-agent behaviors is a current challenge in various scientific and engineering fields. Biological agents independently have limited observation and mechanical constraints; however, most of the conventional data-driven models ignore such assumptions, resulting in lack of biological plausibility and model interpretability for behavioral analyses. Here we propose sequential generative models with partial observation and mechanical constraints in a decentralized manner, which can model agents' cognition and body dynamics, and predict biologically plausible behaviors. We formulate this as a decentralized multi-agent imitation-learning problem, leveraging binary partial observation and decentralized policy models based on hierarchical variational recurrent neural networks with physical and biomechanical penalties. Using real-world basketball and soccer datasets, we show the effectiveness of our method in terms of the constraint violations, long-term trajectory prediction, and partial observation. Our approach can be used as a multi-agent simulator to generate realistic trajectories using real-world data.

Analyses of actions which cause anterior cruciate ligament injuries in the national basketball association players: YouTube-based video analyses

BACKGROUND

Anterior cruciate ligament (ACL) injuries are among the most common injuries in the National Basketball Association (NBA), and it is important to investigate the actual nature of the injury because it can impair a player's performance after returning to the game. Although the moment of injury has been investigated, the details of the movements and circumstances leading to injury in basketball games are unknown. This study aimed to clarify the actions leading to ACL injuries and to investigate their characteristics, based on YouTube video analyses of the NBA players.

METHODS

Players with ACL injuries in the NBA were identified through web-based research over 10 seasons (2011/2012-2021/2022, through October 2021), with 29 recorded videos of ACL injuries in the NBA. Actions were categorized based on basketball-specific gestures, and determined whether the player was in contact with an opponent or not and, if so, the location of the contact was analyzed focusing on two time points: at the injury frame (IF) and one step before the injury frame (IF-1). The "injury leg" timing was counted for each of the first and second steps after ball possession.

RESULTS

The majority (68.2%) of ACL injury occurred during the 2 steps phase (only two steps can proceed after ball retention in basketball, so we defined them as two steps) in the offense action, and most notably during the first step (80.0%). 73.3% of players who were injured during the 2 steps phase got contact to an area other than the knee (Indirect contact) at the IF-1, with 81.8% of contact being located in the upper body contralateral to the respective knee injury. The probability of players with ACL injuries during the 2 steps at the IF-1 who got Indirect contact was statistically significantly greater than those who got no contact with other players (p = 0.042).

CONCLUSIONS

We argue that including pre-injury play and contact falls into the novelty category. Through YouTube-based video analyses, this study revealed that ACL injuries tend to be characterized by specific types of actions, the timing of contact, and the location of contact in NBA players.

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.

Data-Driven Analysis for Understanding Team Sports Behaviors

Understanding the principles of real-world biological multi-agent behaviors is a current challenge in various scientific and engineering fields. The rules regarding the real-world biological multi-agent behaviors such as those in team sports are often largely unknown due to their inherently higher-order interactions, cognition, and body dynamics. Estimation of the rules from data, i.e., via data-driven approaches such as machine learning, provides an effective way to analyze such behaviors. Although most data-driven models have non-linear structures and high predictive performances, it is sometimes hard to interpret them. This survey focuses on data-driven analysis for quantitative understanding of behaviors in invasion team sports such as basketball and football, and introduces two main approaches for understanding such multi-agent behaviors: (1) extracting easily interpretable features or rules from data and (2) generating and controlling behaviors in visually-understandable ways. The first approach involves the visualization of learned representations and the extraction of mathematical structures behind the behaviors. The second approach can be used to test hypotheses by simulating and controlling future and counterfactual behaviors. Lastly, the potential practical applications of extracted rules, features, and generated behaviors are discussed. These approaches can contribute to a better understanding of multi-agent behaviors in the real world.

Preparatory Knee Flexion-Extension Movements Enhance Rapid Sidestepping Performance in Collegiate Basketball Players

Lower-limb weight-bearing load distribution in stationary standing influences the timing of rapid first step initiation of importance for functional movement activities and agility performance in sports. This study investigated the effect of pre-step lower-limb loading and unloading with preparatory knee flexion-extension movements on sidestepping performance in fifteen male collegiate basketball players. Participants performed two-choice (step limb) reaction time sidestepping under two conditions: without preparatory movements before the go cue (no-prep-NP) and with continuous alternating knee extension and flexion movements (prep-P). The reaction signal was provided at the beginning of knee extension and flexion and during these movements which corresponded with the largest and smallest loading instants and the transition states between those instants. Sidestepping performance was assessed with three-dimensional kinematic data and ground reaction forces. Step initiation onset time was significantly faster by 13-15% than the NP condition when initiated in the knee flexion phase (p ≤ 0.028, r ≥ 0.70), whereas step-limb unloading interval from step initiation to step lift-off was significantly faster by 12-15% in the knee extension phase (p ≤ 0.01, r ≥ 0.74). The preparatory movements significantly shortened step lift-off by 10-12% (p ≤ 0.013, r ≥ 0.73) and step duration by 17-21% (p < 0.001, r ≥ 0.85) with 19-22% faster step velocity (p < 0.001, r ≥ 0.84), which resulted in 14-15% shorter overall time to step landing (p < 0.001, r ≥ 0.84), irrespective of the loading phases. These results indicated that lower-limb loading with pre-step knee flexion facilitated faster step initiation, while lower-limb unloading with knee extension facilitated faster step-limb unloading, both resulting in faster step lift-off. Bilateral knee flexion-extension movements as a preparatory action could be utilized by invasion sports players to facilitate reactive stepping performance for more effective movement initiation.

Difference Between Intentional and Reactive Movement in Side-Steps: Patterns of Temporal Structure and Force Exertion

Intentional and reactive movements are dissimilar in terms of execution time. Previous studies reported that reactive movements are faster than intentional movements (“Bohr’s law” or “Gunslinger effect”), however, these studies focused only on hand-reaching tasks, such as pressing buttons. No studies assessed whole-body movements involving movement of the center of mass (CoM). This movement is characterized by many degrees of freedom because it involves many joints and requires more force than the hand-reaching movement. In this study, we determined the differences in the patterns of temporal structure and force exertion to elucidate the mechanism of “Bohr’s law” in whole-body movement involving movement of the CoM. Ten participants performed a sidestepping task, which requires at least two steps: (1) an intentional movement, in which the movement started with the participants’ own timing; and (2) a reactive movement, in which the movement started the moment a light-emitting diode bulb in front of the participants lit up. We collected data on the ground reaction forces and coordinates of 20 body points. The time of movement onset was calculated and defined based on the ground reaction force, which has the earliest onset compared with velocity and position. The execution time was significantly shorter in the reactive movement condition than in the intentional movement condition (772 vs. 715 ms, p = 2.9 × 10^–4). We confirmed that Bohr’s law was applicable not only in hand-reaching tasks but also in whole-body movement. Moreover, we identified three phases, including the velocity reversal phenomenon associated with the produced mechanism of Bohr’s law, and provided the temporal structure. The difference in the pattern of force exertion accompanying the two styles of motor planning with different accuracies was strongly associated with this motor characteristic. These findings may serve as important basic data to scientifically clarify the mechanism of complex physical tactics implemented in one-on-one dueling in various sports.

Physically-interpretable classification of biological network dynamics for complex collective motions

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of principles of biological complex network dynamics from the perspective of nonlinear dynamical systems.

Spatiotemporal characteristics of an attacker's strategy to pass a defender effectively in a computer-based one-on-one task

For modern humans, chase-and-escape behaviors are fundamental skills in many sports. A critical factor related to the success or failure of chase-and-escape is the visuomotor delay. Recent studies on sensorimotor decision making have shown that humans can incorporate their own visuomotor delay into their decisions. However, the relationship between the decision of an attacker and the visuomotor delay of a defender is still unknown. Here, we conducted a one-on-one chase-and-escape task for humans and investigated the characteristics of the direction changes of the attacker and the responses of the defender. Our results showed that the direction change of the attacker has two characteristics: uniformity of spatial distribution and bimodality of temporal distribution. In addition, we showed that the response of the defender did not depend on the position but it was delayed to the direction change of the attacker with a short interval. These results suggest that the characteristics of direction change of an attacker increased unpredictability, and it could be useful for preventing the predictive response of the defender and to receive the benefit of an extra response delay of tens of milliseconds, respectively.

Data-driven spectral analysis for coordinative structures in periodic human locomotion

Living organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not reflect dynamical properties in principle. Here we regard coordinative structures in biological periodic systems with unknown and redundant dynamics as a nonlinear limit-cycle oscillation, and apply a data-driven operator-theoretic spectral analysis, which obtains dynamical properties of coordinative structures such as frequency and phase from the estimated eigenvalues and eigenfunctions of a composition operator. Using segmental angle series during human walking as an example, we first extracted the coordinative structures based on dynamics; e.g. the speed-independent coordinative structures in the harmonics of gait frequency. Second, we discovered the speed-dependent time-evolving behaviours of the phase by estimating the eigenfunctions via our approach on the conventional low-dimensional structures. We also verified our approach using the double pendulum and walking model simulation data. Our results of locomotion analysis suggest that our approach can be useful to analyse biological periodic phenomena from the perspective of nonlinear dynamical systems.

Underlying structure in the dynamics of chase and escape interactions

Chase and escape behaviors are important skills in many sports. Previous studies have described the behaviors of the attacker (escaper) and defender (chaser) by focusing on their positional relationship and have presented several key parameters that affect the outcome (successful attack or defense). However, it remains unclear how each individual agent moves, and how the outcome is determined in this type of interaction. To address these questions, we constructed a chase and escape task in a virtual space that allowed us to manipulate agents' kinematic parameters. We identified the basic strategies of each agent and their robustness to changes in their parameters. Moreover, we identified the determinants of the outcome and a geometrical explanation of their importance. Our results revealed the underlying structure of a simplified human chase and escape interaction and provided the insight that, although each agent apparently moves freely, their strategies in two-agent interactions are in fact rather constrained.

Automatically recognizing strategic cooperative behaviors in various situations of a team sport

Understanding multi-agent cooperative behavior is challenging in various scientific and engineering domains. In some cases, such as team sports, many cooperative behaviors can be visually categorized and labeled manually by experts. However, these actions which are manually categorized with the same label based on its function have low spatiotemporal similarity. In other words, it is difficult to find similar and different structures of the motions with the same and different labels, respectively. Here, we propose an automatic recognition system for strategic cooperative plays, which are the minimal, basic, and diverse plays in a ball game. Using player’s moving distance, geometric information, and distances among players, the proposed method accurately discriminated not only the cooperative plays in a primary area, i.e., near the ball, but also those distant from a primary area. We also propose a method to classify more detailed types of cooperative plays in various situations. The proposed framework, which sheds light on inconspicuous players to play important roles, could have a potential to detect well-defined and labeled cooperative behaviors.

Switching Adaptability in Human-Inspired Sidesteps: A Minimal Model

Humans can adapt to abruptly changing situations by coordinating redundant components, even in bipedality. Conventional adaptability has been reproduced by various computational approaches, such as optimal control, neural oscillator, and reinforcement learning; however, the adaptability in bipedal locomotion necessary for biological and social activities, such as unpredicted direction change in chase-and-escape, is unknown due to the dynamically unstable multi-link closed-loop system. Here we propose a switching adaptation model for performing bipedal locomotion by improving autonomous distributed control, where autonomous actuators interact without central control and switch the roles for propulsion, balancing, and leg swing. Our switching mobility model achieved direction change at any time using only three actuators, although it showed higher motor costs than comparable models without direction change. Our method of evaluating such adaptation at any time should be utilized as a prerequisite for understanding universal motor control. The proposed algorithm may simply explain and predict the adaptation mechanism in human bipedality to coordinate the actuator functions within and between limbs.

Mutual and asynchronous anticipation and action in sports as globally competitive and locally coordinative dynamics

Humans interact by changing their actions, perceiving other’s actions and executing solutions in conflicting situations. Using oscillator models, nonlinear dynamics have been considered for describing these complex human movements as an emergence of self-organisation. However, these frameworks cannot explain the hierarchical structures of complex behaviours between conflicting inter-agent and adapting intra-agent systems, especially in sport competitions wherein mutually quick decision making and execution are required. Here we adopt a hybrid multiscale approach to model an attack-and-defend game during which both players predict the opponent’s movement and move with a delay. From both simulated and measured data, one synchronous outcome between two-agent (i.e. successful defence) can be described as one attractor. In contrast, the other coordination-breaking outcome (i.e. successful attack) cannot be explained using gradient dynamics because the asymmetric interaction cannot always assume a conserved physical quantity. Instead, we provide the asymmetric and asynchronous hierarchical dynamical models to discuss two-agent competition. Our framework suggests that possessing information about an opponent and oneself in local-coordinative and global-competitive scale enables us to gain a deeper understanding of sports competitions. We anticipate developments in the scientific fields of complex movement adapting to such uncontrolled environments.

Preparatory Body State before Reacting to an Opponent: Short-Term Joint Torque Fluctuation in Real-Time Competitive Sports

In a competitive sport, the outcome of a game is determined by an athlete’s relationship with an unpredictable and uncontrolled opponent. We have previously analyzed the preparatory state of ground reaction forces (GRFs) dividing non-weighted and weighted states (i.e., vertical GRFs below and above 120% of body weight, respectively) in a competitive ballgame task and demonstrated that the non-weighted state prevented delay of the defensive step and promoted successful guarding. However, the associated kinetics of lower extremity joints during a competitive sports task remains unknown. The present study aims to investigate the kinetic characteristics of a real-time competitive sport before movement initiation. As a first kinetic study on a competitive sport, we initially compared the successful defensive kinetics with a relatively stable preparatory state and the choice-reaction sidestep as a control movement. Then, we investigated the kinetic cause of the outcome in a 1-on-1 dribble in terms of the preparatory states according to our previous study. The results demonstrated that in successful defensive motions in the non-weighted state guarding trial, the times required for the generation of hip abduction and three extension torques for the hip, knee, and ankle joints were significantly shortened compared with the choice-reaction sidestep, and hip abduction and hip extension torques were produced almost simultaneously. The sport-specific movement kinetics emerges only in a more-realistic interactive experimental setting. A comparison of the outcomes in the 1-on-1 dribble and preparatory GRF states showed that, in the non-weighted state, the defenders guarded successfully in 68.0% of the trials, and the defender’s initiation time was earlier than that in the weighted state (39.1%). In terms of kinetics, the root mean squares of the derivative of hip abduction and three extension torques in the non-weighted state were smaller than those in the weighted state, irrespective of the outcome. These results indicate that the preparatory body state as explained by short-term joint torque fluctuations before the defensive step would help explain the performance in competitive sports, and will give insights into understanding human adaptive behavior in unpredicted and uncontrolled environments.