Abstract: The tailless configuration design and reduced aerodynamic control surface moment arms of tailless aircraft raise con-cerns about their maneuverability, necessitating control allocation algorithms that can effectively coordinate control sur-faces to fully exploit the vehicle's maneuver potential. The nonlinear attainable moment set accurately characterizes the maneuver capability space, while the incremental nonlinear attainable moment set enables precise identification of resid-ual maneuver capabilities during controlled operations. The incremental nonlinear attainable moment set serves as a lo-calized expression of the nonlinear attainable moment set under constraints of limited effector deflection angles and angu-lar velocities. A novel geometric control allocation algorithm is proposed based on the incremental nonlinear attainable moment set, achieving efficient allocation under nonlinear aerodynamic conditions through an enhanced surface search method and geometric projection technique. First，the intersection point between the desired moment and the surface of attainable moment set is calculated by an improved surface search method. Second，the specific surface of attainable moment set where the intersection point resides is identified，and the projection point of the desired moment onto this surface is determined through geometric methods. Subsequently，combining the spatial relationship between the desired moment and attainable moment set，the corresponding effector deflection vector under nonlinear aerodynamics is com-puted based on the intersection or projection point. This allocation solution aims to minimize allocation errors while satis-fying the desired moment requirements. Finally，comparative simulations of the control allocation algorithm are conduct-ed under open-loop snake-shaped maneuvers and closed-loop Herbst maneuvers to verify its feasibility and analyze its characteristics.

Key words: tailless aircraft, control allocation, attainable moment set, nonlinearity, increment