Alternate Formulations for the Manipulator Inertia Matrix

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Abstract
Four compact methods for computing the manipulator joint space inertia matrix are derived and compared. The deriva tion of the first, the Structurally Recursive Method, is based on the successive addition of single links to the free end of a serial manipulator. A general joint model allows multiple- degree-of-freedom joints to connect the links if desired, and the manipulator Jacobian matrix is a simultaneous result at no extra cost. The computational complexity of this new method is O(N3) for an N-link manipulator with revolute and/or prismatic joints. Derivation of the other methods fol lows from expanding the equations obtained in the structural recursion and examining the resulting terms. The second method, the Inertia Projection Method, defines a finite sum mation for each matrix component that has a form similar to that found in other work. This method is also O(N3), and once again, the Jacobian matrix is computed simultaneously. Through judicious use of the composite rigid body inertia concept, a third new and efficient algorithm, the Modified Composite Rigid Body Method, is developed with a compu tational complexity of O( N2). Additional manipulation leads to the O( N2) Spatial Composite Rigid Body Method, which is the most efficient for all N ≥ 6 but eliminates the simulta neous Jacobian computation. Thesefour methods are com pared with existing algorithms for computing the inertia matrix with respect to their computational complexities. The significance of the simultaneous Jacobian computation is demonstrated by a brief examination of the operational space inertia matrix.

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