Kinematic Calibration of a 5-DoF Parallel Machining Robot with a Novel Adaptive and Weighted Identification Method Based on Generalized Cross Validation

Abstract

Accurate kinematic calibration is the very foundation for robots’ application in industry demanding high precision such as machining. Considering the complex error characteristic and severe ill-posed identification issues of a 5-DoF parallel machining robot, this paper proposes an adaptive and weighted identification method to achieve high-precision kinematic calibration while maintaining reliable stability. First, a kinematic error propagation mechanism model considering the non-ideal constraints and the screw self-rotation is formulated by incorporating the intricate structure of multiple chains and a unique driven screw arrangement of the robot. To address the challenge of accurately identifying such a sophisticated error model, a novel adaptive and weighted identification method based on generalized cross validation (GCV) is proposed. Specifically, this approach innovatively introduces Gauss-Markov estimation into the GCV algorithm and utilizes prior physical information to construct both a weighted identification model and a weighted cross-validation function, thus eliminating the inaccuracy caused by significant differences in dimensional magnitudes of pose errors and achieving accurate identification with flexible numerical stability. Finally, the kinematic calibration experiment is conducted. The comparative experimental results demonstrate that the presented approach is effective and has enhanced accuracy performance over typical least squares methods, with maximum position and orientation errors reduced from 2.279 mm to 0.028 mm and from 0.206° to 0.017°, respectively.

1. Introduction

Over the past years, the landscape of robotic applications in precision-demanding fields such as manufacturing and medical tasks has witnessed significant evolution [1–5]. One of the notable examples is the promotion of parallel robots in machining fields [6–9]. Characterized by the unique architectures involving multiple sub-chains and closed loops, the parallel robots are usually featured with larger stiffness-to-mass and payload-to-weight ratios, faster dynamic response, and much higher repeatability compared with traditional serial-type robots [10]. These properties enable parallel robots to have the potential of achieving exceptional absolute positioning accuracy. On this account, modeling and enhancing the positioning accuracy of parallel robots is critically important for optimally exploiting their performance advantages and further expanding their applications in precision engineering.

Generally, geometric errors arising from manufacturing, assembly, and wear are the primary sources of robot positioning errors [11]. To address this issue, the robot’s pose accuracy can be improved by increasing its manufacturing and assembly accuracy during the design phase, but the cost is high, and residual errors may still exist after assembly [12]. Kinematic calibration serves as an economical and effective technique to enhance the positioning accuracy of robots in the post-assembly phase by identifying and compensating for these geometric errors. The main sequential steps of kinematic calibration include error modeling, error measurement, parameter identification, and compensation.

Initially, the error model describes the mechanisms through which geometric errors in a robot affect its positioning errors, forming the theoretical foundation for establishing calibration algorithms. Accurate error modeling of parallel robots is often difficult due to their complex geometries and nonlinear coupled kinematics [13]. In past studies, researchers have proposed effective error modeling methods around the goals of solving computational singularities and achieving completeness. Among the methods, the D-H method [14–16] is widely used for its intuitive modeling, though it necessitates careful handling of parameter singularities. The CPC and POE methods [17–20] introduce redundant parameters to maintain error model integrity and continuity, showing its advantages for serial robots. For parallel robots, target poses need to be modified suitably fo