Efficient O(N) recursive computation of the operational space inertia matrix

Abstract

The operational space inertia matrix Lambda reflects the dynamic properties of a robot manipulator to its tip. In the control domain, it may be used to decouple force and/or motion control about the manipulator workspace axes. The matrix Lambda also plays an important role in the development of efficient algorithms for the dynamic simulation of closed-chain robotic mechanisms, such as multiple manipulator systems and walking machines. This paper presents the development of a recursive algorithm for computing the operational space inertia matrix (OSIM) that reduces the computational complexity to O(N). This algorithm, the inertia propagation method, is based on a single recursion that begins at the base of the manipulator and progresses out to the last link. Also applicable to redundant systems and mechanisms with multiple-degree-of-freedom joints, the inertia propagation method is the most efficient method known for computing Lambda for N>or=6. The numerical accuracy of the algorithm is discussed for a PUMA 560 robot with a fixed base.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>