Uncertainty estimation and multi sensor fusion for kinematic laser tracker measurements

Laser trackers are widely used to measure kinematic tasks such as tracking robot movements. Common methods to evaluate the uncertainty in the kinematic measurement include approximations specified by the manufacturers, various analytical adjustment methods and the Kalman filter. In this paper a new, real-time technique is proposed, which estimates the 4D-path (3D-position + time) uncertainty of an arbitrary path in space. Here a hybrid system estimator is applied in conjunction with the kinematic measurement model. This method can be applied to processes, which include various types of kinematic behaviour, constant velocity, variable acceleration or variable turn rates. The new approach is compared with the Kalman filter and a manufacturer's approximations. The comparison was made using data obtained by tracking an industrial robot's tool centre point with a Leica laser tracker AT901 and a Leica laser tracker LTD500. It shows that the new approach is more appropriate to analysing kinematic processes than the Kalman filter, as it reduces overshoots and decreases the estimated variance. In comparison with the manufacturer's approximations, the new approach takes account of kinematic behaviour with an improved description of the real measurement process and a reduction in estimated variance. This approach is therefore well suited to the analysis of kinematic processes with unknown changes in kinematic behaviour as well as the fusion among laser trackers.