Estimation of External Force-Torque Vector Based on Double Encoders of Industrial Robots Using a Hybrid Gaussian Process Regression and Joint Stiffness Model
More details
Hide details
Machine Tool Technology, Institute for Machine Tools and Factory Management, Germany
Institute for Production Systems and Design Technology IPK, Fraunhofer Society, Germany
Julian Blumberg   

Machine Tool Technology, Institute for Machine Tools and Factory Management, Pascalstr., 10587, Berlin, Germany
Submission date: 2023-05-10
Final revision date: 2023-05-30
Acceptance date: 2023-06-01
Online publication date: 2023-06-05
Industrial robots are increasingly used in industry for contact-based manufacturing processes such as milling and forming. In order to meet part tolerances, it is mandatory to compensate tool deflections caused by the external force-torque vector. However, using a third-party measuring device for sensing the external force-torque vector lowers the cost efficiency. Novel industrial robots are increasingly equipped with double encoders, in order to compensate deviations caused by the gearboxes. This paper proposes a method for the usage of such double encoders to estimate the external force-torque vector acting at the tool centre point of an industrial robot. Therefore, the joint elasticities of a six revolute joint industrial robot are identified in terms of piecewise linear functions based on the angular deviations at the double encoders when an external force-torque vector is applied. Further, initial deviations between the encoder values caused by gravitational forces and friction are modelled with a Gaussian process regression. Combining both methods to a hybrid model enables the estimation of external force-torque vectors solely based on measurements of the joint angles of secondary encoders. Based on the proposed method, additional measurement equipment can be saved, which reduces investment costs and improves robot dynamics.
UHLMANN E., HEITMÜLLER F., MATHEI M., REINKOBER S., 2013, Applicability of Industrial Robots for Machining and Repair Processes, Procedia CIRP 11, 234–238.
VERL A., VALENTE A., MELKOTE S., BRECHER C., OZTURK E., TUNC L.T., 2019, Robots in Machining, CIRP Annals – Manufacturing Technology, 68, 799–822.
CAO M.Y., LAWS S., RODRIGUEZ Y., BAENA F., 2021, Six-Axis Force/Torque Sensors for Robotics Applications: A Review, IEEE Sensors Journal, 21/24, 27238–27251.
PHONG L.D., CHOI J., KANG S., 2013, External Force Estimation Using Joint Torque Sensors and its Application to Impedance Control of a Robot Manipulator, 13th International Conference on Control, Automation and Systems, 1794–1798.
MURAKAMI T., NAKAMURA R., YU F., OHNISHI K., 1993, Force sensorless impedance control by Disturbance Observer, Conference Record of the Power Conversion Conference, 352–357.
QIN J., LEONARD F., ABBA G., 2013, Experimental External Force Estimation Using a Non-Linear Observer for 6 axes Flexible-Joint Industrial Manipulators, 9th Asian Control Conference, 1–6.
SIMPSON J.W.L., COOK C.D., LI Z., 2002, Sensorless Force Estimation for Robots with Friction, Proceedings of Australasian Conference on Robotics and Automation, 94–99.
CALOME A., PARDO D., ALENYA G., TORRAS C., 2013, External Force Estimation During Compliant Robot Manipulation, IEEE International Conference on Robotics and Automation, 3535–3540.
VIJAYAKUMAR S., SCHAAL S., 2000, Locally Weighted Projection Regression: An O(n) Algorithm for Incremental Real Time Learning in High Dimensional Space, 17th International Conference on Machine Learning, 1079–1086.
SMITH A.C., HASHTRUDI-ZAAD K., 2005, Application of Neural Networks in Inverse Dynamics Based Contact Force Estimation, IEEE Conference on Control Applications, 1021–1026.
KLIMCHIK A., PASHKEVICH A., 2018, Robotic Manipulators with Double Encoders: Accuracy Improvement Based on Advanced Stiffness Modeling and Intelligent Control, IFAC-PapersOnLine, 11/51, 740–745.
KAMINAGA H., ODANAKA K., KAWAKAMI T., NAKAMURA Y., 2011, Measurement Crosstalk Elimination of Torque Encoder Using Selectively Compliant Suspension, IEEE International Conference on Robotics and Automation, 4774–4779.
YAMADA S., INUKAI K., FUJIMOTO H., 2015, Joint Torque Control for Two-Inertia System with Encoders on Drive and Load Sides, IEEE 13th International Conference on Industrial Informatics, 396–401.
HAN Z., YUAN J., GAO L., 2018, External Force Estimation Method for Robotic Manipulator Based on Double Encoders of Joints, IEEE International Conference on Robotics and Biomimetics, 1852–1857.
CORKE P., 2016, Robotics, Vision and Control – Fundamental Algorithms in MATLAB, Springer International Publishing AG, Cham, Switzerland.
KLIMCHIK A., 2011, Enhanced Stiffness Modelling of Serial and Parallel Manipulators for Robotic-Based Processing of High Performance Materials, PhD thesis, Ecole Centrale de Nantes.
BITTENCOURT A.C., WERNHOLT E., SANDER-TABALLAEY S., BORGARDH T., 2010, An Extended Friction Model to Capture Load and Temperature Effects in Robot Joints, IEEE/RSJ International Conference on Intelligent Robots and Systems, 6161–6167.
WU K., LI J., ZHAO H., ZHONG Y., 2022, Review of Industrial Robot Stiffness Identification and Modelling, Applied sciences, 12/8719, 1–24.
ABELE E., ROTHENBÜCHER S., WEIGOLD M., 2008, Cartesian Compliance Model for Industrial Robots Using Virtual Joints, Production Engineering – Research and Development, 2, 339–343.
SCHNEIDER U., MOMENI-K M., ANSALONI M., VERL A., 2014, Stiffness Modeling of Industrial Robots for Deformation Compensation in Machining, IEEE/RSJ International Conference on Intelligent Robots and Systems, 4464–4469.
RASMUSSEN C.E., WILLIAMS K.I., 2006, Gaussian Processes for Machine Learning, the MIT Press, Massachusetts.
BLUMBERG J., LI Z., BESONG L.I., POLTE M., BUHL J., UHLMANN E., BAMBACH M., 2021, Deformation Error Compensation of Industrial Robots in Single Point Incremental Forming by Mean of Data-Driven Stiffness Model, 26th International Conference on Automation and Computing, 1–6.
D’ERRICO J., 2023, SLM-Shape Language Modeling, MATLAB Central File Exchange.