POE-based kinematic calibration for serial robots using left-invariant error representation and decomposed iterative method

Abstract

Most kinematic calibration algorithms overlook the impact of the pose error representation of the robot end-effector on calibration accuracy. In this paper, we demonstrate that the left-invariant error representation (LIEP) provides better pose accuracy than the right-invariant error representation (RIEP) in robot kinematic calibration. Standard product-of-exponentials (POE) kinematic calibration algorithms naturally satisfy the continuity and completeness of the error parameters but lack minimality. We introduce a novel minimal parameterization for the error parameters by analyzing the ineffective error updates during iteration. The number of identifiable parameters is determined as $4r+2p+6$, where $r$ and $p$ represent the number of revolute and prismatic joints, respectively. In addition, we propose a decomposed iterative method to address the issue of the condition number in the identification Jacobian matrix being affected by the position data, thereby improving the convergence and robustness of algorithm. Finally, we present a POE-based calibration algorithm using the left-invariant error representation and decomposed iterative method, which satisfies completeness, continuity, and minimality. Several factors affecting calibration accuracy in POE-based kinematic calibration algorithms are discussed through simulations and experiments. Both simulations and experiments support our claims, showing that our algorithm outperforms existing methods in terms of orientation and position accuracy.