Mathematical metrology for evaluating a 6DOF visual servoing system

In this paper we develop a homogeneous matrix transformation to fit two streams of dynamic six degree of freedom (6DOF) data for evaluating perception systems using ground truth. In particular, we compare object position and orientation results from a 6DOF laser tracker that we consider to be ground truth with results from a real-time visual servoing system from the Purdue Robot Vision Lab. A problem that arises when comparing these two data streams is that they are not necessarily in the same coordinate system. Therefore, a method to transform one coordinate system to the other is needed. We solve this problem by developing an optimization problem that minimizes the space between each coordinate system. In other words, we construct a rotation and translation which best transforms one coordinate space to the other.