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In this paper various control representations selected from a family of harmonic controls were examined for the task of locally
optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state
space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and
simulation results are presented for two inputs and three dimensional state space and some hints for higher dimensional state spaces were
given. Results of the paper are important for designers of motion planning algorithms not only to preserve controllability of the systems but
also to optimize their motion.
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