Stereographic projection for industrial manipulator tasks: Theory and experiments

In this paper, we present a solution and experimental results for real-time control of manipulation tasks considering the alignment of a robots end effector relative to some reference. The developed controller is applicable to industrial manipulators and is based on the pseudoinverse redundancy resolution method. The application considered is the employment of two industrial robots in an offshore remote inspection and maintenance system. A leader robot is controlled freely from onshore, and a follower robot uses an attached camera to provide the onshore operator with live video feed of the ongoing operation. Robot manipulators constitute flexible camera platforms, compared to e.g. simple pan/tilt units, for monitoring offshore operations. We develop a controller for the follower robot such that automatic camera tracking is achieved using pseudoinverse redundancy resolution control. A minimal task space parametrization relying on stereographic projection is constructed which achieves relative end effector alignment tracking without introducing representational or algorithmic singularities. It is shown that singular configurations will only in special cases affect the closed loop behavior. The controller is applicable to tasks such as spray painting or polishing on curved surfaces. The control approach is experimentally validated on two Kuka KR-16 industrial robot manipulators.