Pose control of robot manipulators using different orientation representations: A comparative review

The pose of a rigid-body in 3-D space is described by a set of six independent variables, being three for position and three for orientation. In pose control tasks it is useful to define a pose error representing the deviation between the desired and actual pose of the body. Nevertheless, due to the peculiar properties of the orientation manifold, the orientation error is not well defined as a vector difference. This paper deals with some of those properties, and reviews various definitions of the orientation error found in the literature. Then, some simulations are carried out on a robotic spherical wrist in order to compare the performance of each approach in a simple orientation control task.