Reach-Avoid Games with a Time Limit and Detection Range: A Geometric Approach

Table 1

Notation table.

Symbol	Description
	Game domain
	The position of at time
	The state of the game
	The set of the game’s terminal states
	The barrier of the game with a time limit and detection range
	The maximum operating time of
	The maximum range of
	The point where enters the detection range
	The polar coordinate of
	The left one of the intersection points of -based Apollonian circle and
	The target line
	The position of at time
	Speed ratio
	The set of the game’s neutral terminal states
	The barrier of the game with a time limit only
	The radius of the defender’s detection range
	The -coordinate of the defender’s initial position
	The point where reaches the boundary of the detection range for the first time
	The polar coordinate of
	The -coordinate of the point