Hiroki Murakami

Human motor control has long been described within traditionally deterministic frameworks that emphasize consistency and error minimization. However, accumulating evidence across motor learning, coordination dynamics, and information theory suggests that variability and uncertainty are not merely sources of noise but fundamental resources for adaptive behavior. This review synthesizes theoretical, empirical, and methodological advances to propose an integrative probabilistic framework for motor control. Drawing on complex-systems theory, entropy-based analyses, and hierarchical coordination models, motor behavior is conceptualized as a self-organizing process that continuously balances stability and flexibility under uncertainty. Variability is reinterpreted as functionally regulated, supporting exploration, reorganization, and context-sensitive adaptation rather than reflecting control failure. To formalize this perspective, a Probabilistic Landscape Model is introduced, in which motor behaviors are represented as trajectories within a dynamic landscape of multiple attractors. Within this framework, entropy captures the structured organization of uncertainty, metastability enables rapid transitions between coordination states, and probabilistic stability characterizes the system’s capacity to maintain effective performance across changing constraints. Beyond synthesizing existing research, this review introduces the Probabilistic Landscape Model (PLM), a conceptual framework that integrates nonlinear coordination dynamics, entropy-based variability analysis, and probabilistic interpretations of motor behavior. By integrating insights from motor learning, sports performance, rehabilitation, and predictive processing, this review provides a unified account of adaptive motor control as an inherently probabilistic and self-organizing system. The proposed framework offers conceptual and practical implications for training design, rehabilitation strategies, and human–machine interaction in uncertain environments.

The speed-accuracy trade-off, described by Fitts’ law, has been well studied in fine motor tasks but remains insufficiently explored in whole-body movements, such as jumping. This gap limits our ability to identify universal motor control principles applicable to fine and gross motor tasks. To address this, we investigated the influence of landing accuracy constraints on vertical jump performance. Twelve participants performed jumps under four conditions: no accuracy constraints and progressively smaller target areas (100%, 65%, and 36% of the force-plate surface). Stricter accuracy demands a reduced jump height and systematic adjustments in the magnitude and direction of the take-off velocity. Notably, these trade-offs occurred despite the participants’ inability to continuously monitor the target during the jump, relying instead on the initial recognition of accuracy constraints. Entropy analysis revealed decreased variability in landing positions, reflecting precise motor adaptations to meet the task requirements. These findings suggest that principles similar to Fitts’ law govern speed-accuracy trade-offs in whole-body movements. This study provides valuable insights for sports, rehabilitation, and robotics applications by illustrating how accuracy constraints shape dynamic full-body movements.

The mirror-drawing task has been widely used in motor learning research to investigate procedural memory and movement control. However, studies have primarily focused on global performance measures such as movement time and the number of errors and lack insight into localized learning patterns. This case study aimed to analyze motor learning characteristics by combining traditional measures with entropy analysis, a method for capturing movement stability and complexity. Using a star-shaped figure divided into 12 segments, a single participant performed 100 trials of the mirror-drawing task. The movement coordinates were recorded at 60 Hz using a stylus on a mirrored tablet screen. The results showed that movement time decreased over the trials and entropy values showed an initial increase, followed by a decrease, suggesting exploratory behavior and subsequent stabilization. In particular, the interference side segments requiring complex visual–motor transformations showed prolonged instability and delayed control stabilization compared with the noninterference side segments. The integration of entropy analysis allowed a clearer visualization of the trial-and-error phases and movement instability, providing novel insights into the motor learning process. These findings, though limited to a single case, contribute to the understanding of adaptive movement control strategies and suggest that local learning properties should be considered in skill acquisition research.

Human movements are governed by a tradeoff between speed and accuracy. Previous studies that have investigated the tradeoff relationship in sports movements involving whole-body movements have been limited to examining the relationship from the perspective of competition-specific movements, and the findings on whether the relationship is valid have not been unified. Therefore, this study incorporated a vertical jump task with the introduction of a condition in which landing position control was added to evaluate the essence of a sports movement that requires both speed and accuracy. Accuracy was examined using a method that quantifies the coordinates of the landing and takeoff positions using entropy. The mechanism of that tradeoff was then examined by confirming the phenomenon and analyzing the 3D vector trajectories. An increase in accuracy and a decrease in speed were observed when the landing position was the control target, even in the vertical jumping task normally performed at maximum effort, and the 3D velocity vector was characterized by the following: a reduced scalar and a more vertical direction. While the entropy from the takeoff to the landing position seemed to decrease when the accuracy of the landing position improved, the following noteworthy results were obtained given the characteristics of the vertical jump. Unlike traditional feedback control in the entropy reduction in hand movements, the trajectory is predetermined in a feedforward-like manner by controlling the initial velocity vector at takeoff, which allows the landing point to be adjusted.

Fitts’ approach, which examines the information processing of the human motor system, has the problem that the movement speed is controlled by the difficulty index of the task, which the participant uniquely sets, but it is an arbitrary speed. This study rigorously aims to examine the relationship between movement speed and information processing using Woodworth’s method to control movement speed. Furthermore, we examined movement information processing using an approach that calculates probability-based information entropy and mutual information quantity between points from trajectory analysis. Overall, 17 experimental conditions were applied, 16 being externally controlled and one being self-paced with maximum speed. Considering that information processing occurs when irregularities decrease, the point at which information processing occurs switches at a movement frequency of approximately 3.0–3.25 Hz. Previous findings have suggested that motor control switches with increasing movement speed; thus, our approach helps explore human information processing in detail. Note that the characteristics of information processing in movement speed changes that were identified in this study were derived from one participant, but they are important characteristics of human motor control.

Fitts studied the problem of information capacity and transfer in the speed–accuracy motor paradigm using a theoretical approach developed from Shannon and Weaver’s information theory. The information processing (bit/s) estimated in Fitts’ study is calculated from the movement time required to achieve the required task index of difficulty but is essentially different from Shannon’s information entropy. Thus, we estimated the information entropy of multiple human movement trajectories and the mutual information among trajectories for the continuous aiming task in Fitts’ paradigm. Further, we estimated the information processing moment by moment. Two methods were considered: (1) encoded values encompassing the coordinates of the three dimensions and (2) coordinate values associated with each direction in the three dimensions. Information entropy indicates the magnitude of variation at each time point, and the structure of this variation varies with the index of difficulty. The ratio of entropy to mutual information was examined, and it was found that information was processed from the first half of the trajectory in difficult tasks. In addition, since these values calculated from the encoded method were higher than those from the conventional method, this method may be able to estimate these values successfully.

Interpersonal synchronization in competitions has been proposed according to the result of an analysis of a race in which a 100-meter sprint world record was set; however, the phenomenon has not been experimentally verified. In this study, we investigated this phenomenon using a simple reciprocating movement of the body in a laboratory setting. Synchronization was examined from the relative phase values obtained from the normalized time-series coordinate data of the two participants who engaged in periodic movement of the arms (participating in competition with one another). The results showed that, in trials where in-phase or anti-phase synchronization occurred, three patterns emerged: the movement time (MT) of both subjects decreased, the MT of both subjects increased, and the MT of one subject decreased and the MT of the other subject increased. The relationship between synchronization and MT in competition, as shown by the results, is not uniform and has not yet been clarified; however, it shows that synchronization occurs between two subjects in competition, despite being thought to move independently.