| Abstract: |
| We study the singularities of differentially flat systems, in the
perspective of providing global or semi-global motion planning solutions for
such systems: flat outputs may fail to be globally defined, thus potentially
preventing from planning trajectories leaving their domain of definition, the
complement of which we call singular. Such singular subsets are classified into
two types: apparent and intrinsic. A rigorous definition of these singularities
is introduced in terms of atlas and local charts in the framework of the
differential geometry of jets of infinite order and Lie-Backlund isomorphisms.
We then give an inclusion result allowing to effectively compute all or part
of the intrinsic singularities. Finally, we show how our results apply to the
case of n-dimensional affine systems with n-1 commands. |
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