The interactive decision-making in multi-agent autonomous racing offers insights valuable beyond the domain of self-driving cars. Mapless online path planning is particularly of practical appeal but poses a challenge for safely overtaking opponents due to the limited planning horizon. Accordingly, this paper introduces RaceMOP, a novel method for mapless online path planning designed for multi-agent racing of F1TENTH cars. Unlike classical planners that depend on predefined racing lines, RaceMOP operates without a map, relying solely on local observations to overtake other race cars at high speed. Our approach combines an artificial potential field method as a base policy with residual policy learning to introduce long-horizon planning capabilities. We advance the field by introducing a novel approach for policy fusion with the residual policy directly in probability space. Our experiments for twelve simulated racetracks validate that RaceMOP is capable of long-horizon decision-making with robust collision avoidance during overtaking maneuvers. RaceMOP demonstrates superior handling over existing mapless planners while generalizing to unknown racetracks, paving the way for further use of our method in robotics. We make the open-source code for RaceMOP available at http://github.com/raphajaner/racemop.

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