Research Article

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

Table 1

Notation table.

SymbolDescription

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