Geometric Algebra-Based Robust Calibration Method of Robot Base Coordinate System Using Camera Sensor

One essential problem encountered in base coordinate system calibration is the unknown initial transformation relationship between the manipulator and external measuring sensor. Conventional pose description solutions, i.e., vector algebra-based methods, handle transformation parameters separately, destroying the uniformity of 3-D motion and increasing the computational complexity. Moreover, conventional calibration methods are often susceptible to the measurement noise, inevitably undermining both the accuracy and robustness of the calibration process. This article presents the geometric algebra-based pose relationship calibration approach between the robotic manipulator and external measuring sensor. Using the transformation primitive of characteristic straight lines, we construct the pose configuration to obtain the coordinate transformation within the motor algebra (MA) framework. This approach can conveniently represent the arbitrary transformation comprising rotation and translation, which helps reduce the number of representation parameters. In addition, the robust M-estimation algorithm is used to mitigate the impacts of actual measurement noise on the candidate calibration solution by applying different weights to different residuals. Subsequently, multiple numerical simulations and practical experiments are implemented to assess the calibration accuracy and algorithm robustness for the geometric algebra-based robust calibration method under varying noise levels, with evaluation results demonstrating that the robust calibration approach outperforms traditional solutions regarding calibration accuracy, robustness, and performance with small sample sizes.