{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T14:09:26Z","timestamp":1791814166260,"version":"4.3.4"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:00:00Z","timestamp":1559865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To protect operators and conform to safety standards for human\u2013machine interactions, the design of collaborative robot arms often incorporates flexible mechanisms and force sensors to detect and absorb external impact forces. However, this approach increases production costs, making the introduction of such robot arms into low-cost service applications difficult. This study proposes a low-cost, sensorless rigid robot arm design that employs a virtual force sensor and stiffness control to enable the safety collision detection and low-precision force control of robot arms. In this design, when a robot arm is subjected to an external force while in motion, the contact force observer estimates the external torques on each joint according to the motor electric current and calculation errors of the system model, which are then used to estimate the external contact force exerted on the robot arm\u2019s end-effector. Additionally, a torque saturation limiter is added to the servo drive for each axis to enable the real-time adjustment of joint torque output according to the estimated external force, regulation of system stiffness, and achievement of impedance control that can be applied in safety measures and force control. The design this study developed is a departure from the conventional multisensor flexible mechanism approach. Moreover, it is a low-cost and sensorless design that relies on model-based control for stiffness regulation, thereby improving the safety and force control in robot arm applications.<\/jats:p>","DOI":"10.3390\/s19112603","type":"journal-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T11:35:05Z","timestamp":1559907305000},"page":"2603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Development of a Virtual Force Sensor for a Low-Cost Collaborative Robot and Applications to Safety Control"],"prefix":"10.3390","volume":"19","author":[{"given":"Shih-Hsiang","family":"Yen","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pei-Chong","family":"Tang","sequence":"additional","affiliation":[{"name":"Ubiqelife Technology Corporation, Jhubei, Hsinchu 302, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan-Chiu","family":"Lin","sequence":"additional","affiliation":[{"name":"Ubiqelife Technology Corporation, Jhubei, Hsinchu 302, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8931-7650","authenticated-orcid":false,"given":"Chyi-Yeu","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan"},{"name":"Taiwan Building Technology Center, National Taiwan University of Science and Technology, Taipei 106, Taiwan"},{"name":"Center for Cyber-Physical System, National Taiwan University of Science and Technology, Taipei 106, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,7]]},"reference":[{"key":"ref_1","unstructured":"Matthias, B. 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