Estimation of Cartesian Space Robot Trajectories Using Unit Quaternion Space

The ability to estimate Cartesian space trajectories that include orientation is of great importance for many practical applications. While it is becoming easier to acquire trajectory data by computer vision methods, data measured by general-purpose vision or depth sensors are often rather noisy. Appropriate smoothing methods are thus needed in order to reconstruct smooth Cartesian space trajectories given noisy measurements. In this paper, we propose an optimality criterion for the problem of the smooth estimation of Cartesian space trajectories that include the end-effector orientation. Based on this criterion, we develop an optimization method for trajectory estimation which takes into account the special properties of the orientation space, which we represent by unit quaternions. The efficiency of the developed approach is discussed and experimental results are presented.