Perimeter Surveillance Based on Set-Invariance

A solution to the perimeter surveillance problem for one intruder and multiple surveillance robots based on set-invariance is presented. The surveillance robots, constrained to move on the perimeter of a polygonal region, intercept the intruders as they cross the perimeter. The proposed closed-form control laws only depend on the maximum speed of the robots and their distances to the endpoints of the line segments that make the sides of the polygon. The presented results allow for groups of robots with members of different characteristics, such as size and maximum speed, to defend polygonal regions. Simulations are used to show the application and effectiveness of the theoretical results.