  The perimeter defense game has received interest in recent years as a variant
of the pursuit-evasion game. A number of previous works have solved this game
to obtain the optimal strategies for defender and intruder, but the derived
theory considers the players as point particles with first-order assumptions.
In this work, we aim to apply the theory derived from the perimeter defense
problem to robots with realistic models of actuation and sensing and observe
performance discrepancy in relaxing the first-order assumptions. In particular,
we focus on the hemisphere perimeter defense problem where a ground intruder
tries to reach the base of a hemisphere while an aerial defender constrained to
move on the hemisphere aims to capture the intruder. The transition from theory
to practice is detailed, and the designed system is simulated in Gazebo. Two
metrics for parametric analysis and comparative study are proposed to evaluate
the performance discrepancy.
