Autonomous overtaking at high speeds is a challenging multi-agent robotics research problem. The high-speed and close proximity situations that arise in multi-agent autonomous racing require designing algorithms that trade off aggressive overtaking maneuvers and minimize the risk of collision with the opponent. In this paper, we study a special case of multi-agent autonomous race, called the head-to-head autonomous race, that requires two racecars with similar performance envelopes. We present a mathematical formulation of an overtake and position defense in this head-to-head autonomous racing scenario, and we introduce the Automaton Referencing Guided Overtake System (ARGOS) framework that supervises the execution of an overtake or position defense maneuver depending on the current role of the racecar. The ARGOS framework works by decomposing complex overtake and position-defense maneuvers into sequential and temporal submaneuvers that are individually managed and supervised by a network of automatons. We verify the properties of the ARGOS framework using model-checking and demonstrate results from multiple simulations, which show that the framework meets the desired specifications. The ARGOS framework performs similar to what can be observed from real-world human-driven motor sport racing.

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