Abstract
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 μm RMS position error and 71.2 μrad RMS rotation error, representing a 46.7% reduction compared to the baseline calibration of assembly offsets.
Highlights
Kinematic calibration is the process in which a parameterized mathematical model used in planning and control operations is adjusted to minimize pose-error
In the case of the simulated data without measurement uncertainty, it is noted that the pose-error falls significantly below this mark, indicating that the calibration procedure is capable of reducing error below the measurable threshold
This process cannot impact the pose uncertainty caused by discrete encoder counts, it minimizes the uncertainty added by physical phenomenon such as gravitational loading and bending effects that are captured in pose measurements
Summary
Kinematic calibration is the process in which a parameterized mathematical model used in planning and control operations is adjusted to minimize pose-error. The majority of the parallel mechanisms in the literature incorporate coincident passive joints in the form of universal or spherical joints at the top and bottom of a prismatic leg similar to the popular 6 DoF Stewart–Gough configuration [7,8], recent work has modified the design to use offset universal joints to increase stiffness and reduce manufacturing constraints [9] This 6-RRRPRR parallel manipulator configuration with offset R-R joints, with individual parallel members constructed of rotary (R) and prismatic (P) joints listed in order, requires more general kinematic and calibration approaches than typically used with Stewart Platform designs due to the removal of the geometric simplifications permitted by the coincident passive joints and is of particular interest within this work.
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