Reliability in Robotics and Intelligent Systems: Mathematical Modeling and Algorithmic Innovations
Issametova M. Martyushev N.V. Malozyomov B.V. Demin A.Y. Pogrebnoy A.V. Kuleshova E.E. Valuev D.V.
February 2026Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2026#14Issue 3
The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the probability of the end-effector falling into a given area of permissible poses. The proposed framework integrates a deterministic kinematic model, a stochastic representation of Denavit–Hartenberg parameters and control variables, analytical methods for estimating probabilities, and numerical modeling using the Monte Carlo method. The methodology has been tested on the widely used industrial robot FANUC LR Mate 200iD/7L. The results demonstrate a significant dependence of geometric reliability on the kinematic configuration of the manipulator, with maximum reliability in compact poses and a significant reduction in elongated configurations near singularities. Comprehensive validation was carried out, including numerical experiments on a planar prototype, high-precision physical measurements on a real robot and analysis of operational data, which confirmed the adequacy of the proposed model. The developed approach provides a powerful tool for designing, optimizing and predicting the reliability of robotic cells in high-precision automation environments.
Denavit–Hartenberg parameters , FANUC , geometric reliability , industrial robotics , Monte Carlo method , positioning accuracy , probabilistic modeling , robot kinematics
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Department of Mechanical Engineering, Institute of Energy and Mechanical Engineering, Satbayev University, Almaty, KZ-050000, Kazakhstan
Department of Information Technology, Tomsk Polytechnic University, Tomsk, 634050, Russian Federation
Department of Electrotechnical Complexes, Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation
Yurga Technological Institute (Branch), Tomsk Polytechnic University, Yurga, 652055, Russian Federation
Department of Mechanical Engineering
Department of Information Technology
Department of Electrotechnical Complexes
Yurga Technological Institute (Branch)
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026