Black-box simulators

For some problems, a state transition equation might not be available; however, it is still possible to compute future states given a current state and an action trajectory. This might occur, for example, in a complex software system that simulates the dynamics of a automobile or a collection of parts that bounce around on a table. In computer graphics applications, simulations may arise from motion capture data. Some simulators may even work internally with implicit differential constraints of the form $g_i(x,{\dot x},u) = 0$, instead of ${\dot x}= f(x,u)$. In such situations, many sampling-based planners can be applied because they rely only on the existence of the system simulator. The planning algorithm is thus shielded from the particular details of how the system is represented and integrated.