{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T10:11:02Z","timestamp":1767262262853,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T00:00:00Z","timestamp":1637107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In this work, we present methods allowing parallel, hybrid, and serial manipulators to be analyzed, calibrated, and controlled with the same analytical tools. We introduce a general approach to describe any robotic manipulator using established serial-link representations. We use this framework to generate analytical kinematic and calibration Jacobians for general manipulator constructions using null space constraints and extend the methods to hybrid manipulator types with complex geometry. We leverage the analytical Jacobians to develop detailed expressions for post-calibration pose uncertainties that are applied to describe the relationship between data set size and post-calibration uncertainty. We demonstrate the calibration of a hybrid manipulator assembled from high precision calibrated industrial components resulting in 91.1 \u03bcm RMS position error and 71.2 \u03bcrad RMS rotation error, representing a 46.7% reduction compared to the baseline calibration of assembly offsets.<\/jats:p>","DOI":"10.3390\/robotics10040124","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T21:32:07Z","timestamp":1637184727000},"page":"124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Unified Parameterization and Calibration of Serial, Parallel, and Hybrid Manipulators"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7996-7032","authenticated-orcid":false,"given":"Benjamin L.","family":"Moser","sequence":"first","affiliation":[{"name":"M3 Robotics Laboratory, Department of Mechanical Engineering, Colorado School of Mines, Golden, CO 80401, USA"}]},{"given":"Joshua A.","family":"Gordon","sequence":"additional","affiliation":[{"name":"National Institute of Standards and Technology, Boulder, CO 80305, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2070-4227","authenticated-orcid":false,"given":"Andrew J.","family":"Petruska","sequence":"additional","affiliation":[{"name":"M3 Robotics Laboratory, Department of Mechanical Engineering, Colorado School of Mines, Golden, CO 80401, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Campos, L., Bourbonnais, F., Bonev, I.A., and Bigras, P. 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