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