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Laser-Tracker-Assisted Camera-to-Robot Calibration for Mobile Robots
Jan A. Rudolph, Öykü Kandemir, Markus Ulrich
TL;DR
Restricted mobile-robot motion can make conventional hand–eye calibration insufficient to constrain the camera-to-robot pose. The paper uses laser-tracker metrology and chained calibration targets to extend calibration to more camera orientations. All 120 Scene A evaluations were better than 1 cm, while the longer Scene B chain had lower precision and a systematic accuracy offset.
Problem
Mobile-robot motion may not provide the pose diversity needed for conventional hand–eye calibration to constrain all components of the camera-to-robot transformation.
Source: §1 · p. 2Method
The workflow combines laser-tracker metrology with camera-based target observations and chains calibration plates to transfer their spatial relation for camera-to-robot calibration.
Source: §1 · p. 3Results
All 120 Scene A evaluations were better than 1 cm, whereas the longer Scene B chain had lower precision and a systematic accuracy offset.
Source: §3.2 · p. 10, §4 · p. 11Takeaways & Limitations
The distance between reference and observed plates and the number of intermediate targets should be minimized to limit error accumulation.
Source: §4 · p. 11The accuracy evaluation assumes zero robot roll and pitch because the robot motion is planar.
Source: §3.2 · p. 9
Abstract
from arXiv · showhide
We present a laser-tracker-assisted hand-eye calibration method for camera-equipped mobile robots. The method combines laser-tracker-based 3D metrology with camera-based 2D observations. Building on our previous laser-tracker-assisted camera-to-robot calibration method for ground-observing mobile robots, we present a generalized formulation for calibrating the camera pose in the coordinate system of tracker-localized mobile robots. The new approach relaxes assumptions of our previous method on robot and camera configuration by chaining multiple calibration targets resulting in a more general approach supporting various camera-equipped mobile robot systems.
1 Motivation
Mobile-robot motion may not provide the pose diversity conventional hand–eye calibration needs to constrain the camera-to-robot transformation. This work generalizes a laser-tracker-assisted, plate-based workflow to more camera configurations.
1 Motivation
- Restricted mobile-robot motion can leave components of the camera-to-robot transformation insufficiently constrained for conventional hand–eye calibration.For RITA, motion is approximately planar; the SCARA height workaround is not applicable because it requires vertical motion and physical access to the robot-coordinate-system center.Source: §1 · p. 2
- Successive calibration-target links remove the need for a dedicated combined plate while retaining the characterized reference plate as a tracker anchor.The focus is a practical procedure for laser-tracker-localized mobile robots rather than manipulator kinematics or SCARA-like configurations.Source: §1 · p. 3
- The method extends the prior nadir-camera workflow to more general camera mounting configurations using laser-tracker metrology and image-based target observations.It evaluates transformation precision and absolute accuracy against manual laser-tracker ground-truth measurements.Source: §1 · pp. 2–3
2 Method
The method separates the tracker reference plate from the plate observed by the robot, enabling calibration with cameras in arbitrary orientations. A chain of target observations transfers their spatial relation before the camera-to-robot pose is composed.
2 Method
- Separating the reference plate from the robot-observed plate allows the observed plate to be positioned for the robot camera, supporting cameras in arbitrary orientations.The earlier arrangement used a common-plane plate directly observed by a nadir camera.Source: §2 · p. 3
2.1 Calibration Object
- When both plates cannot be imaged together, adjacent auxiliary-camera images link calibration plates through a shared fixed target.Both targets in each image must be correctly distinguished and identified.Source: §2.1 · p. 4, Figure 2 · p. 4
- Combining the two detected plate poses in each image yields adjacent relative transforms, which are multiplied to connect reference plate PCS0 to robot-observed plate PCSn.Figure 3 illustrates a two-pose chain through intermediate plate PCS1.Source: §2.1 · p. 4, Figure 3 · p. 5
- Three tracker-measured reflector centers are matched to their known positions on the reference plate to estimate the reference-plate-to-tracker pose [1, Eq. (13)].The calibration object can then be used to calibrate a series of robots.Source: §2.1 · p. 5, Figure 4 · p. 5
2.2 Camera–Robot Calibration
- The robot camera observes PCSn to obtain its pose relative to the camera, and the target-chain relation transfers that pose to PCS0 for camera-to-robot pose composition.The robot pose is obtained from laser-tracker reflector measurements and inertial measurement information.Source: §2.2 · p. 6
3 Results
The results compare precision across two calibration-chain configurations and add absolute-accuracy evaluation using tracker-measured reference points, enabled by the outward-facing camera’s larger workspace.
3.1 Precision
- Precision was tested over eight calibrations: four Scene A runs used n=2 across about 0.9 m, while four Scene B runs used n=3 across about 1.3 m.Scene A used two chain images; Scene B used three.Source: §3.1 · p. 6
- Scene B had lower precision than Scene A; its greater plate separation required an extra intermediate target, and z precision was worse than lateral precision.The authors state that minimizing chain length helps avoid error accumulation.Source: §3.1 · pp. 6, 8, Figure 6 · p. 8
3.2 Accuracy
- Absolute accuracy was evaluated by measuring a reference point with a laser tracker and comparing it with the camera’s line of sight using orthogonal distance and reprojection error.The camera image point defines the 3D line of sight.Source: §3.2 · p. 9
- All 120 Scene A accuracy evaluations were better than 1 cm, while Scene B showed worse results with a significant systematic offset.Table 2 summarizes the absolute errors for the two scenes.Source: §3.2 · p. 10, Table 2 · p. 10
4 Conclusion
The method extends nadir-camera calibration to arbitrarily oriented cameras by chaining tracker-referenced and robot-observed calibration plates. Experiments show sub-centimeter precision and accuracy in Scene A, while the longer Scene B chain had lower precision and a systematic accuracy offset.
4 Conclusion
- The method connects tracker-referenced and robot-observed calibration plates through a chain of targets, extending nadir-camera calibration to arbitrarily oriented cameras.Source: §4 · p. 10
- All 120 Scene A evaluations had precision and accuracy better than 1 cm, while the longer Scene B chain had lower precision and a systematic accuracy offset.The conclusion says chain design is critical.Source: §4 · p. 11
- To limit error accumulation, minimize the distance between reference and observed plates and the number of intermediate calibration targets.Future work will isolate translation and orientation components of robot and target poses, as well as setup stability, to help optimize target arrangements and methodology.Source: §4 · p. 11