A reduced-order recursive algorithm for the computation of the operational-space inertia matrix
Date
2012
Authors
Wensing, Patrick
Featherstone, Roy
Orin, David
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IEEE Robotics and Automation Society
Abstract
This paper provides a reduced-order algorithm, the Extended-Force- Propagator Algorithm (EFPA), for the computation of operational-space inertia matrices in branched kinematic trees. The algorithm accommodates an operational space of multiple end-effectors, and is the lowest-order algorithm published to date for this computation. The key feature of this algorithm is the explicit calculation and use of matrices that propagate a force across a span of several links in a single operation. This approach allows the algorithm to achieve a computational complexity of O(N +md+m2) where N is the number of bodies, m is the number of end-effectors, and d is the depth of the system's connectivity tree. A detailed cost comparison is provided to the propagation algorithms of Rodriguez et al. (complexity O(N + dm2)) and to the sparse factorization methods of Featherstone (complexity O(nd2 + md2 + m2d)). For the majority of examples considered, our algorithm outperforms the previous best recursive algorithm, and demonstrates efficiency gains over sparse methods for some topologies.
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Keywords: Cost comparisons; Efficiency gain; Factorization methods; Inertia matrix; Key feature; Kinematic tree; Operational space; Propagation algorithm; Recursive algorithms; Reduced order; Sparse methods; Algorithms; Forestry; Matrix algebra; Robotics; Trees (ma
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2037-12-31
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