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Navigation function : ウィキペディア英語版
Navigation function
Navigation function usually refers to a function of position, velocity, acceleration and time which is used to plan robot trajectories through the environment. Generally, the goal of a navigation function is to create feasible, safe paths that avoid obstacles while allowing a robot to move from its starting configuration to its goal configuration.
== Potential functions as navigation functions ==

Potential functions assume that the environment or work space is known. Obstacles are assigned a high potential value, and the goal position is assigned a low potential. To reach the goal position, a robot only needs to follow the negative gradient of the surface.
We can formalize this concept mathematically as following: Let X be the state space of all possible configurations of a robot. Let X_g \subset X denote the goal region of the state space.
Then a potential function \phi(x) is called a (feasible) navigation function if 〔Lavalle, Steven, (Planning Algorithms Chapter 8 )〕
#\phi(x)=0\ \forall x \in X_g
# \phi(x) = \infty if and only if no point in }, the local operator produces a state x' for which \phi(x') < \phi(x).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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