Nonholonomic Motion Planning: Steering Using Sinusoids

From Murray Wiki
Revision as of 06:20, 15 May 2016 by Murray (talk | contribs) (htdb2wiki: creating page for 1993d_ms93.html)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigationJump to search

Richard M. Murray and S. Shankar Sastry
IEEE T. Automatic Control, 38(5):700-716

In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives 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, we 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. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of two-input systems can be converted into this form.