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Modeling of Industrial Robot Kinematics using a Hybrid Analytical and Statistical Approach



Vinh Nguyen, Jeremy Marvel


Industrial robots are highly desirable in applications including manufacturing and surgery. However, errors in the modelling of the kinematics of robotic arms limit their positional accuracy in industrial applications. Specifically, analytical kinematic models of the robot arm suffer from errors in coefficient calibrations and the inability to account for effects including gear backlash. However, statistical modelling methods require an extensive amount of points for calibration, which is infeasible in practical industrial environments. Hence, this paper describes, develops, and experimentally validates a hybrid modelling methodology combining both analytical and statistical methods to describe the robot kinematics in an intuitive manner that is easily adaptable for small scale industries. By formulating an explicitly described analytical kinematic model as a prior mean distribution of a Gaussian Process, the prior distribution can be updated with experimental data using statistical Bayesian Inference, thus enabling more accurate description of the robot kinematics with fewer data points. The hybrid model is demonstrated to outperform both an analytical model and a Gaussian Process Regression model with no prior in predicting both the forward and inverse kinematics of a UR5 and UR10. Also, the error propagation of the inverse kinematic solutions is studied. In addition, the testing framework used in this work can be used as a standardized benchmark to evaluate alternative kinematic models.
Journal of Mechanisms and Robotics


Nguyen, V. and Marvel, J. (2022), Modeling of Industrial Robot Kinematics using a Hybrid Analytical and Statistical Approach, Journal of Mechanisms and Robotics, [online],, (Accessed May 19, 2024)


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Created February 21, 2022, Updated November 29, 2022