A plan generates *actions* that manipulate
the state. The terms *actions* and *operators* are common in
artificial intelligence; in control theory and robotics, the related
terms are *inputs* and *controls*. Somewhere in the planning
formulation, it must be specified how the state changes when actions
are applied. This may be expressed as a state-valued function for the
case of discrete time or as an ordinary differential equation for
continuous time. For most motion planning problems, explicit
reference to time is avoided by directly specifying a path through a
continuous state space. Such paths could be obtained as the integral
of differential equations, but this is not necessary. For some
problems, actions could be chosen by *nature*, which interfere
with the outcome and are not under the control of the decision maker.
This enables uncertainty in predictability to be introduced into the
planning problem; see Chapter 10.

Steven M LaValle
2012-04-20