Robot calibration is an effectively way to increase the absolutely accuracy, which is of vital importance for robot applications in the manufacturing industries. Product of exponentials (POE) model based kinematic calibration algorithms are praised for the simple coordinate frame setup and elimination of parameter discontinuity inherent in the Denavit-Hartenberg (DH) parameter based methods. However, the joint twist coordinate in the POE model is not a minimal parameterization and must be normalized during identification process. Moreover, differentiation of a parameter-varying matrix exponential exists in several POE-based calibration algorithms which is computationally intensive. In this thesis, we show that by respecting the nonlinear geometry of the joint axis configuration space (ACS...[ Read more ]

Robot calibration is an effectively way to increase the absolutely accuracy, which is of vital importance for robot applications in the manufacturing industries. Product of exponentials (POE) model based kinematic calibration algorithms are praised for the simple coordinate frame setup and elimination of parameter discontinuity inherent in the Denavit-Hartenberg (DH) parameter based methods. However, the joint twist coordinate in the POE model is not a minimal parameterization and must be normalized during identification process. Moreover, differentiation of a parameter-varying matrix exponential exists in several POE-based calibration algorithms which is computationally intensive. In this thesis, we show that by respecting the nonlinear geometry of the joint axis configuration space (ACS) as a differentiable manifold, these two disadvantages can be elegantly removed. This geometric ACS model naturally leads to a multiplicative error of the twist coordinates in the form of Adjoint transformations, hereafter referred to as the Adjoint error. We propose a new calibration algorithm based on the geometric ACS model and Adjoint error update which has the following advantages over existing approaches: (1) the ACS model illustrates intuitively the discontinuity and redundancy of both DH parameters and twist coordinates; (2) the proposed algorithm is computationally efficient with a well-structured error Jacobian matrix; (3) parameter redundancy of the joint twist coordinate can be easily removed; (4) the kinematic model and parameter update of various calibration algorithms can be conveniently transformed into our framework for a consistent comparative study.

The Adjoint error approach addresses the calibration problem of robot joint axis configurations, and in this thesis we expand our algorithm to include more kinematic parameters and factors. We show that the imprecise joint pitches, reduction ratios and coupling coefficients can be successfully identified, which forms a complete robot kinematic calibration method. Additional geometry assumptions on joint relations can also be well handled by carefully manipulating the basis matrix, with which we can not only ease the error compensation in most commercial robot controllers, but also improve the calibration performance if we have good prior information.

Robot works cooperatively with accessory facilities in the work cell, which usually consists of multiple positioning modules and dedicated machines. In this thesis, we put forward the calibration method to identify the displacements of the positioning modules as external axes and the machines represented by feature points relatively to the robot. Sensor installed on the robot end-effector is used to observe the work cell. Workpiece can be located using a similar setup at the same time the robot parameters are also calibrated. Simulations and experiments are presented to show the robot and system accuracy enhancement through calibration, and illustrate the convergence, reliability and efficiency of our algorithm.