13.2.1 Reducing Degree by Increasing Dimension

Taking into account constraints on higher order derivatives seems
substantially more complicated. This section explains a convenient
trick that converts constraints that have higher order derivatives
into a new set of constraints that has only first-order derivatives.
This involves the introduction of a *phase space*, which has
more dimensions than the original C-space. Thus, there is a trade-off
because the dimension is increased; however, it is widely accepted
that increasing the dimension of the space is often easier than
dealing with higher order derivatives. In general, the term *state space* will refer to either C-spaces or phase spaces derived
from them.

Steven M LaValle 2020-08-14