Explainable Machine Learning Model Predicts Robotic Joint Torque at Sub-Millisecond Speeds

Robotics researchers have introduced an explainable machine learning framework capable of predicting joint torque in industrial manipulators with sub-millisecond computational latency. Developed as an alternative to physical torque sensors and opaque deep neural networks, the approach couples tree-based ensemble learning with explainability tools to deliver high-speed, continuous kinetic regression for robotic joints. The system is designed to meet the rigorous temporal demands of high-bandwidth control loops while maintaining analytical consistency with established rigid body dynamics.

Accurate torque estimation across robotic joints serves as a critical prerequisite for compliant control, rapid collision detection, and safe physical human-robot interaction. While dedicated physical torque sensors deliver direct kinetic measurements, their integration introduces mechanical compliance, elevates joint mass, raises hardware costs, and leaves mechanisms vulnerable to mechanical shock loads. Virtual torque sensing has emerged as a data-driven substitute, but conventional deep neural network baselines regularly encounter computational latency bottlenecks spanning 1.5 to 2.5 milliseconds, which prevents deterministic execution within 500-hertz control loops.

To overcome both the latency bottlenecks of deep neural networks and the diagnostic limitations of earlier robotics explainability tools, the researchers formulated an architecture based on dedicated single-joint estimators. By deploying isolated XGBoost models for each joint, the system directly captures actuator-specific electromechanical dynamics without resorting to unphysical cross-joint data pooling. Interpretability is embedded directly into the regression pipeline through Shapley Additive Explanations and Partial Dependence Plots, allowing the model’s inner decision logic to be inspected and compared against classical mechanics.

The experimental evaluation was conducted using 7.2 million multi-joint telemetry points recorded from an industrial Universal Robots UR5 six-degree-of-freedom manipulator. The empirical dataset spanned an extensive library of movement trajectories and variable operational payloads ranging from 0 to 5 kilograms. Model assessments focused on the manipulator’s primary load-bearing shoulder joint, designated as Joint 2, while tracking fidelity metrics across all six articulations of the robotic arm.

On the primary load-bearing shoulder joint, the optimized gradient-boosted decision tree architecture attained a coefficient of determination of R² = 0.988, a mean absolute error of 0.108 newton-meters, and a root mean square error of 0.142 newton-meters. This represents an error reduction ranging between 55 percent and 78 percent when benchmarked against recent deep learning baselines. Across all six joints of the manipulator, the dedicated estimation models demonstrated consistent predictive accuracy, maintaining an R² value greater than or equal to 0.976.

In terms of computational performance, the regression framework achieved an inference latency of 0.124 milliseconds per sample. This duration consumes 6.2 percent of a standard 2.0-millisecond control cycle, verifying the model’s operational capability for high-bandwidth robotic control loops operating at frequencies up to 500 hertz. The complete sensing and collision mitigation architecture was experimentally validated at 100 hertz using the manipulator’s integrated real-time data exchange interface.

Unlike conventional black-box regressors or purely qualitative monitoring tools, the continuous Shapley attributions and partial dependence profiles were mapped directly onto the analytical terms of classical rigid body dynamics. This structural alignment provides empirical confirmation of physical consistency and plausibility within the learned decision boundaries. In dynamic physical testing comprising 60 collaborative collision trials across variable impact velocities and payloads, the pipeline achieved an average detection latency of 12.1 ± 1.4 milliseconds.

During these collaborative impact trials, the pipeline constrained peak impact forces to 14.5 ± 1.8 newtons without requiring dynamic parameter re-identification. The experimental results demonstrated an 87 percent performance improvement over classical momentum observers while recording zero false alarms during operation.

The research addresses fundamental limitations in earlier explainability tools applied to robotic systems. Prior applications of explainable artificial intelligence in the field were almost entirely confined to maintenance alarms and discrete diagnostic classification tasks. By expanding these interpretive mechanisms into continuous kinetic regression, the authors bridged an established operational gap between black-box statistical learning and mechanical engineering principles.

Rather than treating decision boundaries as arbitrary statistical artifacts, the framework specifically connects continuous Shapley values and partial dependence behaviors to the analytical terms that govern traditional rigid body dynamics. This validation confirms that the learned relationships reflect actual physical plausibility rather than ungrounded numerical correlations. Furthermore, because each joint relies on dedicated models rather than pooled datasets, the architecture captures electromechanical dynamics unique to individual actuators without introducing unphysical cross-joint dependencies. By maintaining reliable sub-millisecond execution, the approach establishes viable virtual sensing for high-speed industrial manipulation.

Subject of Research: Explainable machine learning for sub-millisecond virtual torque sensing in robotic joints

Article Title: Intelligent torque prediction in robotic joints using explainable machine learning

Article References: Washimkar, D., Mahadik, S., Agrawal, D., & Bhosle, S. (2026). Intelligent torque prediction in robotic joints using explainable machine learning. International Journal of Intelligent Robotics and Applications. https://doi.org/10.1007/s41315-026-00612-0

Image Credits: AI Generated

DOI: 10.1007/s41315-026-00612-0

Keywords: robotics, joint torque estimation, explainable artificial intelligence, XGBoost, Shapley Additive Explanations, partial dependence plots, Universal Robots UR5, collision detection, physical human-robot interaction, virtual torque sensing, rigid body dynamics, actuator dynamics, computational latency, real-time data exchange, robotic manipulators, torque prediction