Observability index selection for robot calibration

This paper relates 5 observability indexes for robot calibration to the "alphabet optimalities" from the experimental design literature. These 5 observability indexes are shown to be the upper and lower bounds of one another. All observability indexes are proved to be equivalent when the design is optimal after a perfect column scaling. It is shown that when the goal is to minimize the variance of the parameters, D-optimality is the best criterion. When the goal is to minimize the uncertainty of the end-effector position, E-optimality is the best criterion. It is proved that G-optimality is equivalent to E-optimality for exact design.