Alternate formulations for the manipulator inertia matrix
- Ohio State Univ., Columbus (United States)
Four compact methods for computing the manipulator joint space inertia matrix are derived and compared. The derivation 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(N{sup 3}) for an N-link manipulator with revolute and/or prismatic joints. Derivation of the other methods follows from expanding the equations obtained in the structural recursion and examining the resulting terms. The second method, the Inertia Projection Method, defines a finite summation for each matrix component that has a form similar to that found in other work. this method is also O(N{sup 3}), 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 computational complexity of O(N{sup 2}). Additional manipulation leads to the O(N{sup 2}) Spatial Composite Rigid Body Methods, which is the most efficient for all N {ge} 6 but eliminates the simultaneous Jacobian computation. These four methods are compared 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.
- OSTI ID:
- 5569175
- Journal Information:
- International Journal of Robotics Research; (United States), Journal Name: International Journal of Robotics Research; (United States) Vol. 10:1; ISSN 0278-3649; ISSN IJRRE
- Country of Publication:
- United States
- Language:
- English
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