Capturing an Omnidirectional Evader in Convex Environments Using a Differential Drive Robot

We study the problem of capturing an omnidirectional evader in convex environments using a differential drive robot (DDR). The DDR wins the game if at any time instant it captures (collides with) the evader. The evader wins if it can avoid capture forever. Both players are unit disks with the same maximum (bounded) speed, but the DDR can only change its motion direction at a bounded rate. We show that despite this limitation, the DDR can capture the evader.