Inverse, forward and other dynamic computations computationally optimized with sparse matrix factorizations
This work addresses computational efficiency in robotics and simulation for researchers and engineers, but it is incremental as it builds on existing dynamic computation methods with optimization improvements.
The paper tackles the problem of computing dynamics for articulated rigid-bodies by proposing an algorithm that uses off-line sparse matrix factorizations to reduce computational complexity, showing a reduction in floating point operations compared to standard methods like recursive Newton-Euler and articulated body algorithm.
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational complexity of the underlying solution. This optimisation step consists in formulating the dynamic computations as a system of linear equations. The computational complexity of computing the associated solution is reduced by performing a permuted LU-factorisation with off-line optimised permutations. We apply our algorithm to solve classical dynamic problems: inverse and forward dynamics. The computational complexity of the proposed solution is compared to `gold standard' algorithms: recursive Newton-Euler and articulated body algorithm. It is shown that our algorithm reduces the number of floating point operations with respect to previous approaches. We also evaluate the numerical complexity of our algorithm by performing tests on dynamic computations for which no gold standard is available.