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Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. R.W. Brockett (1981) derived the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their (first-order) Lie brackets. Using Brockett's result as motivation, the authors derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. Examples and simulation results are presented.>
Murray et al. (Mon,) studied this question.