For the problem of stabilizing motion of an n-dimensional nonholonomic wheeled
system along a prescribed path, the concept of a canonical representation of the equations of
motion is introduced. The latter is defined to be a representation that can easily be reduced
to a linear system in stabilizable variables by means of an appropriate nonlinear feedback. In
the canonical representation, the path following problem is formulated as that of stabilizing the
zero solution of an (n−1)-dimensional subsystem of the canonical system. It is shown that, by
changing the independent variable, the construction of the canonical representation reduces to
finding the normal form of a stationary affine system. The canonical representation is shown to
be not unique and is determined by the choice of the independent variable. Three changes of
variables known from the literature, which were earlier used for synthesis of stabilizing controls
for wheeled robot models described by the third- and fourth-order systems of equations, are
shown to be canonical ones and can be generalized to the n-dimensional case. Advantages and
disadvantages of the linearizing control laws obtained by means of these changes of variables
are discussed.
