A fast, robust solution to the Stewart platform forward kinematics

The Stewart platform is a six degree-of-freedom fully-in-parallel linkage well-suited to robotic tasks where structural rigidity and high small motion bandwidth are required. In this article we describe an approach for computing the forward kinematics of this device that is both fast and robust. Our solution is based on the simultaneous solution of three constraint equations using a Newton-Raphson scheme. A well-known property of Newton-Raphson is its tendency to fail when the constraint equations become poorly conditioned, and the main contribution of this article is the development of two algorithms for overcoming this limitation and hence for providing robustness. Certain other matters, such as the singular configurations of the Stewart platform and its assembly modes, are touched upon.