A reduced-order recursive algorithm for the computation of the operational-space inertia matrix

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.