EFFICIENT O(N) RECURSIVE COMPUTATION OF THE OPERATIONAL SPACE INERTIA MATRIX

The operational space inertia matrix A 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 A also plays an important role in the development of efficient algorithms for the dynamic simulation of closed-chain robotic mechanisms, including simple closed-chain mechanisms such as multiple manipulator systems and walking machines. The traditional approach used to compute A has a computational complexity of O(N3) for an N degree-of-freedom manipulator. 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 A for N greater-than-or-equal-to 6. The numerical accuracy of the algorithm is discussed for a PUMA 560 robot with a fixed base.