[Solved] Nonlinear-control Homework4 -Accessibility of the N-trailer system

In some special coordinates, the kinematic model of the N-trailer system is described by

We computed dimH2 = n2 so that H2 = span{₁,₂, ,_n2}. The two first basis vectors were computed as well as

₁ = x₃dx₁ + dx₂

and

₂ = x₄dx₁ + dx₃

1. Compute the ] [ H2 in the form of row vectors ]

0 0 . Write the corre-

sponding 1-forms 3 and n2.

2. Check whether ₁ H2
3. Check whether ₂ H2
4. Check whether n2 H2
5. Write a basis for H3