An Adaptive <i>p</i> -Norms-Based Kinematic Calibration Model for Industrial Robot Positioning Accuracy Promotion
Tinghui Chen, Weiyi Yang, Shuai Li, Xin Luo
Abstract
Industrial robots inevitably incur kinematic errors in the advanced manufacturing and assembly processes, resulting in the severe reduction of the absolute positioning accuracy (APA). Kinematic calibration (KC) is well-known as a vital technique in APA-promoting tasks. However, existing KC models generally adopt a single distance-oriented Loss, e.g., an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> norm-oriented one that neglects the featured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> norms. In response to this critical issue, this study presents an Adaptive p-norms-oriented Kinematic Calibration (ApKC) model on the basis of threefold ideas: 1) studying the effects of diversified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> norms on the industrial robot calibration performance; 2) combining multiple <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> norms to obtain the aggregated loss with the hybrid effects by different norms; and 3) implementing the weight adaptation on the norm components of the aggregated loss, and rigorously prove its ensemble capability benefiting the calibration performance. Afterwards, a novel Newton interpolated Adaptive Differential Evolution (NADE) algorithm is further proposed to optimize the ApKC model. Empirical studies on an HRS JR680 industrial robot demonstrate that the achieved ApKC-NADE calibrator can significantly reduce the robot’s maximum positioning error from 4.610 to 0.856 mm. It can vigorously support the high-accuracy application of industrial robots.