We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the target perimeter without being captured by the defender, while the defender's goal is to capture as many intruders as possible. After one intruder breaches or is captured, the next appears randomly on a fixed circle surrounding the target. Therefore, the defender's final position in one game becomes its starting position for the next. We divide an intruder-defender engagement into two phases, partial information and full information, depending on the information available to the players. We address the capturability of an intruder by the defender using the notions of Dubins path and guarding arc. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders. Finally, the theoretical results are verified through numerical examples using Monte-Carlo-type random trials of experiments.

In strategy games, one of the most important aspects of game design is maintaining a sense of challenge for players. Many mobile titles feature quick gameplay loops that allow players to progress steadily, requiring an abundance of levels and puzzles to prevent them from reaching the end too quickly. As with any content creation, testing and validation are essential to ensure engaging gameplay mechanics, enjoyable game assets, and playable levels. In this paper, we propose an automated approach that can be leveraged for gameplay testing and validation that combines traditional scripted methods with reinforcement learning, reaping the benefits of both approaches while adapting to new situations similarly to how a human player would. We test our solution on a popular tower defense game, Plants vs. Zombies. The results show that combining a learned approach, such as reinforcement learning, with a scripted AI produces a higher-performing and more robust agent than using only heuristic AI, achieving a 57.12% success rate compared to 47.95% in a set of 40 levels. Moreover, the results demonstrate the difficulty of training a general agent for this type of puzzle-like game.

Previous studies in the perimeter defense game have largely focused on the fully observable setting where the true player states are known to all players. However, this is unrealistic for practical implementation since defenders may have to perceive the intruders and estimate their states. In this work, we study the perimeter defense game in a photo-realistic simulator and the real world, requiring defenders to estimate intruder states from vision. We train a deep machine learning-based system for intruder pose detection with domain randomization that aggregates multiple views to reduce state estimation errors and adapt the defensive strategy to account for this. We newly introduce performance metrics to evaluate the vision-based perimeter defense. Through extensive experiments, we show that our approach improves state estimation, and eventually, perimeter defense performance in both 1-defender-vs-1-intruder games, and 2-defenders-vs-1-intruder games.