Toward Personalized Darts Training: A Data-Driven Framework Based on Skeleton-Based Biomechanical Analysis and Motion Modeling

Abstract

As sports training becomes more data-driven, traditional dart coaching based mainly on experience and visual observation is increasingly inadequate for high-precision, goal-oriented movements. Although prior studies have highlighted the importance of release parameters, joint motion, and coordination in dart throwing, most quantitative methods still focus on local variables, single-release metrics, or static template matching. These approaches offer limited support for personalized training and often overlook useful movement variability. This paper presents a data-driven dart training assistance system. The system creates a closed-loop framework spanning motion capture, feature modeling, and personalized feedback. Dart-throwing data were collected in markerless conditions using a Kinect 2.0 depth sensor and an optical camera. Eighteen kinematic features were extracted from four biomechanical dimensions: three-link coordination, release velocity, multi-joint angular configuration, and postural stability. Two modules were developed: a personalized optimal throwing trajectory model that combines historical high-quality samples with the minimum jerk criterion, and a motion deviation diagnosis and recommendation model based on z-scores and hierarchical logic. A total of 2,396 throwing samples from professional and non-professional athletes were collected. Results show that the system generates smooth personalized reference trajectories consistent with natural human movement. Case studies indicate that it can detect poor trunk stability, abnormal elbow displacement, and imbalanced velocity control, then provide targeted recommendations. The framework shifts dart evaluation from deviation from a uniform standard to deviation from an individual's optimal control range, improving personalization and interpretability for darts training and other high-precision target sports.

Figures (6)

• Figure 1: Four Factors Affecting Darts Throwing (A) Postural Stability: Demonstrates the supporting role of global postural control. By establishing a stable foundation and minimizing the sway of the body's center of mass and trunk, it effectively suppresses the error amplification effect transmitted from lower-body disturbances to the upper-body kinetic chain. (B) Joint Angles: This section explains the spatial characteristics of the shoulder joint's pitch angle, elbow joint's extension angle, and wrist joint's flexion angle at the moment of release. The angular configuration of these key joints directly determines the direction of the dart's initial velocity vector; even the slightest angular disturbance can cause significant deviations in the flight trajectory. (C) Three-Link Motion Model: This model abstracts the throwing arm as a mechanical system composed of the upper arm (Link 1), forearm (Link 2), and hand (Link 3). It intuitively illustrates the physical framework and spatial coordination of the multi-link mechanisms—including the shoulder, elbow, and wrist—throughout the complete throwing cycle. (D) Release Velocity: This reveals the progressive energy transfer pattern based on the kinetic chain. Momentum strictly follows a "proximal-to-distal sequence," starting from the shoulder, transmitting through the elbow joint to the wrist joint, thereby achieving the most efficient power output at the moment of release at the distal end.
• Figure 2: Data preprocessing and dart-to-bullseye distance measurement pipeline. Figure (a) displays the raw captured image exhibiting significant perspective distortion and tilt. Figure (b) shows the geometrically restored image following an inverse perspective projection using chessboard calibration parameters. Figure (c) illustrates the bullseye localization process, isolating the red outer ring via HSV color space conversion. Figure (d) presents the isolated dart tip mask generated through frame differencing and morphological operations. Finally, Figure (e) demonstrates the completed recognition result, accurately pinpointing both the bullseye center and the dart tip to compute the exact Euclidean landing distance.
• Figure 3: Flow chart of optimal trajectory fitting. This figure illustrates the data-driven pipeline for generating a personalized optimal dart-throwing trajectory. The process initiates by aggregating the athlete's most recent 200 throwing actions from historical data. Subsequently, a high-quality subset of 30 representative actions is extracted using a rigorous weighting scheme that evaluates both dart-to-bullseye accuracy and kinematic smoothness (jerk rating). Finally, these superior actions are synthesized via hyperparameter optimization and refined using a minimum-jerk kinematic model. This automated filtering and fitting mechanism ultimately yields a smooth, physiologically natural reference trajectory tailored to the individual athlete.
• Figure 4: Visualization of the optimal trajectories for seven dart players. The figures in this experiment visualize the fitting results. The top four images show the fitting results for professional athletes, while the bottom three show those for non-professional athletes. You can observe each athlete's throwing process and hand movements. The green segments represent the motion from the wrist to the fingertips, orange segments represent the motion from the elbow to the wrist, and blue segments represent the motion from the shoulder to the elbow. These visualizations of the optimal fitting trajectories effectively illustrate the athletes' throwing processes, providing valuable references for darts training.
• Figure 5: Fitted optimal throwing trajectory for athlete S3. This figure shows the time series of the personalized optimal throwing trajectory generated using the minimum jitter fitting method (from frame 15 to frame 120). The red curve depicts a smooth and continuous spatial path of the hand in the XY plane, indicating no excessive trembling or unnecessary fluctuations. Consistent with the principles of the three-link kinematic model, the athlete's shoulder remains highly stable throughout the entire movement. During the initial backward swing phase (frames 15 to 45), the elbow joint remains in a relatively fixed position to ensure mechanical stability. Subsequently, during the forward acceleration and release phases (frames 60 to 105), the elbow naturally rises to extend the acceleration path, ensuring efficient energy transfer.