O(N) Recursive Algorithm for the Operational Space Inertia Matrix of a Robot Manipulator

Abstract

The operational space inertia matrix reflects the dynamic properties of a robot manipulator to its tip. It mav be used to decouple force and/or motion control about the manipulator workspace axes, and it also plays an important role in the development of efficient algorithms for the dynamic simulation of closed-chain robotic mechanisms. The traditional approach for computing this matrix has a computational complexity of O(N3) for an N degree-of-freedom manipulator. This paper presents the development of a new recursive algorithm for the operational space inertia matrix which reduces the computational complexity to O(N) for any manipulator. The Hew algorithm is based on a single recursion which begins at the base of the manipulator and progresses out to the last link, and it is the most efficient method known for N ≥ 6. The numerical accuracy of the new algorithm is tested for a PUMA 560 robot with a fixed base.