SIAM Journal on Control and Optimization, Vol.48, No.2, 812-838, 2009
A PROBLEM OF GUARDING LINE SEGMENT
A line segment on the plane is guarded by n defenders. One invader wants to pass through the line segment, but he has to keep the distance from each defender no less than a given constant. All defenders can move along a straight line only with maximal speed 1. The invader can move on the whole plane with maximal speed greater than 1. Other than this, no kinematic or dynamic constraints are imposed on the defenders' and the invader's motions. The maximal length of the line segment which can be guarded by defenders is established in this paper.