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Unified Parameterization and Calibration of Serial, Parallel, and Hybrid Manipulators



Josh Gordon, Benjamin Moser, Ben Moser, Andrew Petruska


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 um RMS position error and 71.2 urad RMS rotation error, representing a 46.7% reduction compared to the baseline calibration of assembly offsets.
International Journal of Robotics Research


kinematics, robotics, metrology, optimization, laser tracker


Gordon, J. , Moser, B. , Moser, B. and Petruska, A. (2021), Unified Parameterization and Calibration of Serial, Parallel, and Hybrid Manipulators, International Journal of Robotics Research, [online],, (Accessed June 23, 2024)


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Created November 17, 2021, Updated October 6, 2023