The core problem the team set out to solve is a familiar one in sports robotics. Exoskeleton robots, the most common type of wearable training aid, attach rigid links and motors directly to the athlete’s joints. That adds substantial inertia to the limbs, which is precisely what a speed skater does not need. A bulky frame strapped to the hips and legs can constrain the very fluid, high-speed movements the athlete is trying to refine. Cable-driven robots offer an elegant alternative: the motors sit on a stationary chassis, and lightweight, high-strength cables transmit forces to the athlete’s waist, legs, and ankles. The cables decouple the heavy drive hardware from the human body, and their inherent compliance softens the risk of rigid collisions. The trade-off is that controlling eight cables to move a platform in six degrees of freedom is a genuinely hard control problem, and existing control schemes were not precise enough for competitive skating.

The robot itself is built around a gantry of vertical columns and crossbeams, with pulleys guiding the cables along smooth force-transmission paths. Eight functional modules make up the machine: the load-bearing columns, the crossbeams that stabilize the gantry, the pulleys, ergonomically curved handrails that give the skater balance support, servo drivers housed in the chassis with high-precision encoders providing millisecond-level feedback, lightweight composite cover plates for protection and quick maintenance, a chassis integrating counterweights and shock absorption, and a polished mirror surface whose friction coefficient is tuned to resemble real ice. Cables connect to key points on the athlete’s waist, legs, and ankles, forming a closed-loop force control network. The design accommodates athletes from 1.65 to 1.98 meters tall, with a drive unit capable of 380 newtons of pulling force and a suspension rated for 500 kilograms, margins engineered to withstand the explosive peak loads of a skater’s push-off.

The drive unit combines an S7-1200 programmable logic controller, a 400-watt permanent magnet synchronous motor rated at 3000 revolutions per minute, and a type 1204 ball screw. When the motor spins, it turns the screw, which drives a slider that reels a cable in or out, adjusting both its length and tension in real time. This hybrid scheme lets the robot provide upward lifting assistance during the take-off phase and apply controllable damping at the moment of ice landing, cushioning joint impact. Because the motors live on the chassis rather than on the athlete, the components attached to the body stay light, preserving the flexibility that rigid exoskeletons sacrifice.

To make the machine useful, the researchers first had to solve its kinematics: the mathematical mapping between the pose of the moving platform, which carries the skater’s leg brace, and the lengths of the eight cables. They established a fixed coordinate system at the geometric center of the robot’s base frame and a moving coordinate system fixed to the platform at the center of the athlete’s thigh. Assuming the cables remain fully tensioned and can be treated as ideal massless straight segments, they derived the inverse kinematics, which computes cable lengths from a desired pose, using a closed vector quadrilateral approach combined with a rotation matrix built from roll, pitch, and yaw angles. Forward kinematics, the harder reverse problem of recovering the platform’s position and orientation from known cable lengths, was solved with the Newton-Raphson iterative method, chosen over analytical approaches for its rapid convergence and precision.

The Newton-Raphson method converges quadratically near the true root, but it is sensitive to the initial guess. The team exploited a practical trick: because the servo control system samples at millisecond intervals, the platform barely moves between consecutive control cycles, so the pose from the previous cycle serves as an excellent starting point for the next iteration. This guarantees robust, real-time convergence. To validate the model, the researchers ran simulations in MATLAB using five sets of pose points within the robot’s workspace, feeding them through inverse kinematics to get cable lengths and then through forward kinematics to recover the poses. The maximum deviation between the original and recovered poses was 0.95 percent, below the 1 percent threshold the team set as evidence that the kinematic model is sound.

With the mechanics settled, the heart of the paper is its control strategy. Conventional proportional-integral-derivative controllers, while simple and robust, struggle with the nonlinear coupling and sudden disturbances that characterize skating, such as abrupt changes in ice friction or the athlete’s own movements. Active disturbance rejection control offers a way forward: an extended state observer continuously estimates the combined internal and external disturbances acting on the system and compensates for them in real time. But traditional ADRC architectures include a tracking differentiator, a component that shapes the response to step inputs to avoid overshoot by ramping the control output up gradually. That conservatism introduces delays and sluggish response, a poor fit for the high-frequency movements of skating, like rapid ice pushes and sudden stops.

The researchers’ solution is a fractional-order active disturbance rejection controller, or FOADRC, with two key innovations. First, they removed the tracking differentiator entirely, allowing the large initial error to drive the system promptly and sharpen the dynamic response. Second, they replaced the conventional state feedback error law with a fractional-order PD control law and upgraded the observer to a fractional-order extended state observer. Fractional-order calculus, which uses non-integer differentiation and integration operators, gives the controller adjustable amplitude-frequency slopes and better high-frequency noise suppression than integer-order designs, along with superior robustness to complex disturbances. The fractional-order observer was tuned using a bandwidth parameterization borrowed from integer-order observer theory, so that only a single parameter needs adjustment, dramatically simplifying calibration. The fractional-order operators themselves were approximated in a practical frequency band using the Oustaloup method, a standard rational-fitting technique accurate enough at fifth order.

To generate realistic control targets, the team captured real skating motion using a NOKOV infrared motion capture system with eight cameras sampling at 100 hertz and a spatial positioning error under 0.1 millimeters. A 25-year-old male speed skater, 178 centimeters tall and weighing 70 kilograms, performed standard straight-line skating cycles while retroreflective markers on his hip, thigh, lower leg, and ankle tracked the movement. The researchers focused on the hip joint, the hub connecting trunk and legs that carries body weight and fine-tunes the center of gravity during skating. Raw marker data were smoothed with a fourth-order zero-phase Butterworth low-pass filter at a 6 hertz cutoff and gaps from marker occlusion were filled with cubic spline interpolation. The resulting hip joint angle time series, covering sagittal-plane flexion-extension and coronal-plane abduction-adduction, was fitted with an eighth-order Fourier series to produce a smooth, reproducible reference trajectory, and measured cable tensions grounded the simulation in realistic loads.

The payoff came in comparative simulations against a traditional PID controller, evaluated by motor angle tracking error on the drive units for the first two cables. The FOADRC strategy narrowed the error range substantially and improved motion control precision, and, crucially, the tracking error profiles of the two motors were highly consistent despite following different trajectories and load variations. That uniformity matters enormously in multi-cable systems, where all drives must stay synchronized to avoid unbalanced internal tensions or uncoordinated movements. The authors are candid about the study’s limits: everything so far rests on simulation and data from a single subject. The next step is building a physical prototype and running multi-subject trials in real training environments. If those succeed, the combination of flexible cable actuation and fractional-order disturbance rejection could become a template not just for skating, but for a broader generation of intelligent training equipment across competitive sports.

Subject of Research: Cable-driven skating training robot kinematics and fractional-order active disturbance rejection control

Article Title: Research on kinematics and fractional order active disturbance rejection control of skating training robot

Article References: Wang, B., Zhao, X., Gong, Y., Sun, L., & Yang, Z. (2026). Research on kinematics and fractional order active disturbance rejection control of skating training robot. Mechanical Sciences, 17(2), 731-746. https://doi.org/10.5194/ms-17-731-2026

Image Credits: AI Generated

DOI: 10.5194/ms-17-731-2026

Keywords: speed skating, cable-driven robot, fractional-order control, active disturbance rejection, kinematics, Newton-Raphson method, permanent magnet synchronous motor, motion capture, sports robotics, trajectory tracking, training technology, Mechanical Sciences

The research team, led by Zhanpeng Liu and Wensheng Xiao, combined failure mode and effects analysis, Bayesian networks, risk matrices, and fuzzy comprehensive evaluation into one integrated method. Each technique has well-known strengths and blind spots. FMEA can systematically identify potential failure modes but is highly subjective. Bayesian networks excel at quantitative forward and backward inference yet cannot judge how severe a failure’s consequences would be. Risk matrices offer a visual representation of occurrence and severity but cannot assess the risk level of the system as a whole. Fuzzy comprehensive evaluation handles vague, uncertain information but again depends on subjective judgment. By weaving these approaches together, the researchers aimed to let each method compensate for the weaknesses of the others, producing a single assessment that yields both the system failure probability and the risk level of every individual failure mode.

The workflow begins with a fault tree analysis of the motor, in which twenty bottom-event failure modes across six components, the rotor, bearings, windings, permanent magnets, controller, and mechanical seal, are mapped into a Bayesian network. Prior probabilities are derived from historical failure rates in the OREDA offshore reliability database, adjusted upward by expert judgment to reflect the brutal conditions of underground drilling. Bayesian forward inference then computes the overall system failure probability, while backward diagnostic inference produces posterior probabilities revealing which failure modes are most likely responsible when the system fails. In the baseline assessment, the system failure probability came out at 0.428, a strikingly high figure that underscores how punishing the drilling environment is for these machines.

Next comes importance analysis, a mathematical step that quantifies how much each failure mode contributes to system failure. The team calculated three indices: probabilistic importance, which measures the impact of a component’s failure probability on system failure; structural importance, which reflects a component’s position in the system architecture; and critical importance, which combines both failure probability and sensitivity. Because all twenty failure modes feed the system through identical OR-gate logic, their structural importance is equal, but their probabilistic and critical importance diverge dramatically. Rotor breakage, for instance, posted a probabilistic importance of 1.3782, far above its peers, while bearing wear registered a posterior probability of 0.612, the highest of any mode, simply because bearings grind against each other every moment the motor spins.

These quantitative outputs then feed the qualitative side of the framework. The posterior probability of each failure mode determines its occurrence rating on a five-level scale, from improbable to frequent, while the critical importance determines its severity rating, from negligible to catastrophic. The two ratings fuse into a composite risk index called ROS, weighted 0.4 toward occurrence and 0.6 toward severity, a deliberate choice reflecting the safety-critical nature of drilling, where even rare events with devastating consequences demand priority attention. The resulting ROS values map onto a fuzzy evaluation matrix through a parabolic membership function, and the weights of that matrix come directly from the importance analysis rather than from pure expert opinion, reducing the subjectivity that plagues conventional assessments.

The baseline results identified winding phase-to-phase short circuit as the single highest-risk failure mode, with a ROS value of 4.2 placing it firmly in the high-risk category. Rotor dynamic eccentricity and permanent magnet partial demagnetization followed at 3.6 each, classed as medium-high risk. Perhaps more revealing were the failure modes with severe consequences but vanishingly low occurrence, including rotor breakage, bearing breakage, and permanent magnet breakage, all rated medium risk despite being improbable. The framework’s dual weighting captured exactly the kind of nuance that pure probability-based methods miss: a rare failure that destroys the motor deserves as much managerial attention as a common one that merely degrades performance. The fuzzy evaluation concluded that the system sat at medium risk with a membership probability of 0.498, but with a worrying 0.351 probability of medium-high risk.

Armed with this diagnosis, the researchers proposed targeted countermeasures for every failure mode, ranging from corona-resistant enameled wire and vacuum pressure impregnation for the windings to hastelloy springs and fluorocarbon or EPDM elastomers for the seals, matched to oil-based and water-based mud chemistries respectively. For winding faults, they applied weak magnetic current injection, multi-phase redundancy, and winding redundancy, allowing the motor to shed faulty phases gracefully while maintaining partial power. After implementing the improvements, the system failure probability dropped from 0.428 to 0.394, the mean time between failures rose from 1,847 to 2,032 hours, and the medium-high risk membership probability fell from 0.351 to 0.245. The highest-risk failure mode, the winding short circuit, saw its ROS value plunge from 4.2 to 3.2, a 23.8 percent risk reduction.

What distinguishes this study from earlier hybrid approaches is its unusually rigorous treatment of uncertainty and validation. The team ran a Monte Carlo simulation with 10,000 samples, assuming failure rates follow log-normal distributions with a 20 percent coefficient of variation, and found that the 95 percent confidence intervals of key outputs remained narrow, less than 15 percent of their mean values. A perturbation analysis of the weighting coefficients showed that risk rankings stay stable, with Spearman rank correlations above 0.88, as long as severity retains reasonable dominance, confirming the wisdom of the 0.4-0.6 split. The importance-based weights were cross-checked against the entropy weight method and the CRITIC method, with Kendall’s coefficient of concordance reaching 0.82, indicating strong agreement between expert judgment and data-driven weighting. A paired bootstrap test and a Wilcoxon signed-rank test both confirmed that the post-improvement risk reduction was statistically significant, with p below 0.001.

The authors also introduced three methodological innovations that broaden the framework’s reach. A risk coupling coefficient quantifies how strongly each failure mode couples with environmental loads such as vibration, high temperature, current fluctuations, and high-pressure drilling fluid, distilled from a multi-factor coupling matrix that identified twenty high-probability coupled failure modes. An adaptive risk transfer function models nonlinear propagation from component-level risk to system-level risk, capturing synergistic effects that simple OR-gate logic overlooks. And a risk entropy metric measures how dispersed or concentrated the system’s risk profile is; it fell from 1.42 before improvement to 1.24 after, signaling reduced uncertainty in the risk landscape.

The framework is not without limitations, which the authors acknowledge candidly. Integrating four methodologies creates a complex model with substantial computational overhead, and exact Bayesian inference scales exponentially with the number of failure modes, though hierarchical decomposition into sub-networks reduces the complexity from an intractable O(2^100) to a manageable O(10 times 2^10) for a hundred-mode system split across ten components. Prior probabilities still lean on the OREDA database and expert experience, which update infrequently, and the static Bayesian network does not yet ingest real-time sensor data. Future work, the team suggests, will move toward dynamic Bayesian networks fed by live monitoring evidence, adaptive neuro-fuzzy membership functions optimized by backpropagation, and hierarchical architectures spanning failure mode, component, subsystem, and system layers. For now, the study offers drilling engineers something genuinely valuable: a single, statistically validated assessment that tells them not just whether their motor is likely to fail, but exactly which of twenty failure modes deserves their attention first, and how much safer each repair will make it.

Subject of Research: Hybrid fuzzy risk assessment of drilling permanent magnet synchronous motors using FMEA and Bayesian networks

Article Title: An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors

Article References: Liu, Z., Xiao, W., Cui, J., Wang, H., & Mei, L. (2026). An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors. Results in Engineering, 32, Article 113047. https://doi.org/10.1016/j.rineng.2026.113047

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113047

Keywords: risk assessment, FMEA, Bayesian network, fuzzy comprehensive evaluation, permanent magnet synchronous motor, drilling motor, reliability engineering, risk matrix, Monte Carlo simulation, importance analysis, oil and gas drilling, failure modes