{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:34:11Z","timestamp":1767987251371,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T00:00:00Z","timestamp":1696032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"AI Research Institutes program supported by NSF and USDA-NIFA under the AI Institute: Agricultural AI for Transforming Workforce and Decision Support (AgAID)","award":["2021-67021-35344"],"award-info":[{"award-number":["2021-67021-35344"]}]},{"name":"AI Research Institutes program supported by NSF and USDA-NIFA under the AI Institute: Agricultural AI for Transforming Workforce and Decision Support (AgAID)","award":["11972070"],"award-info":[{"award-number":["11972070"]}]},{"name":"National Natural Science Foundation of China","award":["2021-67021-35344"],"award-info":[{"award-number":["2021-67021-35344"]}]},{"name":"National Natural Science Foundation of China","award":["11972070"],"award-info":[{"award-number":["11972070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>The Delta robot is a parallel robot that is over-actuated and has a highly nonlinear dynamic model, which poses a significant challenge to its control design. The inverse kinematics that maps the motor angles to the position of the end effector is highly nonlinear and extremely important for the control design of the Delta robot. It has been experimentally shown that geometry-based inverse kinematics is not accurate enough to capture the dynamics of the Delta robot due to manufacturing component errors, measurement errors, joint flexibility, backlash, friction, etc. To address this issue, we propose a neural network model to approximate the inverse kinematics of the Delta robot with stepper motors. The neural network model is trained with randomly sampled experimental data and implemented on the hardware in an open-loop control for trajectory tracking. Extensive experimental results show that the neural network model achieves excellent performance in terms of the trajectory tracking of the Delta robot under different operation conditions, and outperforms the geometry-based inverse kinematics model. A critical numerical observation indicates that neural networks trained with the specific trajectory data fall short of anticipated performance due to a lack of data. Conversely, neural networks trained on random experimental data capture the rich dynamics of the Delta robot and are quite robust to model uncertainties compared to geometry-based inverse kinematics.<\/jats:p>","DOI":"10.3390\/robotics12050135","type":"journal-article","created":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T16:57:06Z","timestamp":1696179426000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Data-Driven Inverse Kinematics Approximation of a Delta Robot with Stepper Motors"],"prefix":"10.3390","volume":"12","author":[{"given":"Anni","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Merced, CA 95343, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3305-6126","authenticated-orcid":false,"given":"Arash","family":"Toudeshki","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Merced, CA 95343, USA"}]},{"given":"Reza","family":"Ehsani","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Merced, CA 95343, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5441-7982","authenticated-orcid":false,"given":"Jian-Qiao","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of California, Merced, CA 95343, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,30]]},"reference":[{"key":"ref_1","first-page":"1387","article-title":"Robust trajectory tracking of a Delta robot through adaptive active disturbance rejection control","volume":"23","author":"Chairez","year":"2014","journal-title":"IEEE Trans. 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