Geometric Robot Calibration Using a Calibration Plate

TL;DR

This work tackles geometric calibration of gantry machines by replacing costly absolute measurement systems with a calibration plate that encodes precisely known inter-point distances. By extending forward kinematics to account for laser-beam extensions and transforming plate measurements into the end-effector frame, the method derives a parameter vector $\mathbf{p}_{id}$ representing geometric errors via two routes: a linearized least-squares approach and a constrained nonlinear optimization implemented with CasADI and IPOPT. The plate design uses four-quadrant diodes and a laser pointer to yield recoverable pose information, enabling both intrinsic and pose-specific extrinsic parameter estimation. Experimental results on a three-axis laser-cutting setup show substantial xy-error reductions (mean and max) compared with uncalibrated data and comparable performance to laser-tracker-based calibration, highlighting the plate as a cost-effective, portable alternative with practical impact for initial calibration and post-crash recalibration of gantry systems, with future work extending to industrial robots and orientation estimation.

Abstract

In this paper a new method for geometric robot calibration is introduced, which uses a calibration plate with precisely known distances between its measuring points. The relative measurement between two points on the calibration plate is used to determine predefined error parameters of the system. In comparison to conventional measurement methods, like laser tracker or motion capture systems, the calibration plate provides a more mechanically robust and cheaper alternative, which is furthermore easier to transport due to its small size. The calibration method, the plate design, the mathematical description of the error system as well as the identification of the parameters are described in detail. For identifying the error parameters, the least squares method and a constrained optimization problem are used. The functionality of this method was demonstrated in experiments that led to promising results, correlated with one of a laser tracker calibration. The modeling and identification of the error parameters is done for a gantry machine, but is not restricted to that type of robot.

Figures (3)

• Figure 1: Geometric calibration concept using a calibration plate (gantry figure Festo2023)
• Figure 2: Calibration plate setup with four measuring points
• Figure 3: Absolute error between reference measurement and forward kinematics