Algorithm to Express Lie Monomials in Ph. Hall Basis and Its Practical Applications

摘要

In this paper an algorithm is presented to expand any Lie monomial in the Ph. Hall basis. The algorithm exploits an algorithm for the optimal generation of Ph. Hall basis and it can be used to express log(exp X · exp Y) in this basis. An explicit formula for the logarithm includes the Ph. Hall elements up to the 7th degree. The Ph. Hall expansion is useful in the theory of Lie algebras and in robotics for nonholo-nomic motion planning.