An interesting extension of the simple car can be made by attaching
one or more trailers. You may have seen a train of luggage carts on
the tarmac at airports. There are many subtle issues for modeling the
constraints for these models. The form of equations is very sensitive
to the precise point at which the trailer is attached and also on the
choice of body frames. One possibility for expressing the kinematics
is to use the expressions in Section 3.3; however, these
may lead to complications when analyzing the constraints. It is
somewhat of an art to find a simple expression of the constraints.
The model given here is adapted from [727].^{13.4}

Consider a simple car that pulls trailers as shown in Figure
13.6. Each trailer is attached to the center of the rear
axle of the body in front of it. The important new parameter is the
*hitch length* which is the distance from the center of
the rear axle of trailer to the point at which the trailer is
hitched to the next body. Using concepts from Section
3.3.1, the car itself contributes
to
, and each trailer contributes an
component to . The
dimension of is therefore . Let denote the
orientation of the th trailer, expressed with respect to the
world frame.

The configuration transition equation is

An interesting variation of this model is to allow the trailer wheels to be steered. For a single trailer, this leads to a model that resembles a

Steven M LaValle 2020-08-14