The general n-trailer problem: conversion into chained form

The chained form is a useful canonical form to deal with systems with nonholonomic constraints. A typical example of a system that can be converted into chained form is the n-trailer problem, i.e. a car pulling n trailers. Here, we extend the class of n-trailer systems that can be transform into chained form in order to include the so-called general n-trailer problem in which one or more of the trailers have kingpin hitching. We show that a passive steering wheel can be placed in any of the off-hitching joints with the steering input calculated via nonlinear feedback from the configuration state. This is sufficient to assert that the general n-trailer problem can be converted into a multi-input chained form, with the new inputs obtained from the aforementioned feedback.