Mathematical Model of Horizontal Track Conflict Prevention Algorithm in Detect-and-Avoid Framework

With the proliferation of Unmanned Aerial Vehicle (UAV) technology, the demand for effective collision avoidance technology has intensified. The DAIDALUS algorithm, devised by NASA Langley Research Center under the Detect-and-Avoid (DAA) framework, provides conflict prevention bands for remotely piloted UAVs navigating in intricate airspace. The algorithm computes the bands in two distinct phases: Conflict and Recovery. The formal model for both phases has been established and implemented through iterative programming approaches. However, the mathematical model remains incomplete. Therefore, based on the model, this paper proposes the mathematical model for the two phases of the horizontal track conflict prevention algorithm. Firstly, Cauchy’s inequality is proposed to formulate the model that addresses trajectory conflicts considering the UAV non-instantaneous maneuvering dynamics model, and then a prudent maneuvering strategy is designed to optimize the model for the recovery phase. Finally, the execution procedure of the algorithm within the two-stage mathematical model is also detailed. The results demonstrate that the proposed model achieves a higher precision in the preventive bands, implements an effective collision avoidance strategy, and consistently aligns with the DAIDALUS model while offering a larger buffer time or distance. This work theoretically validates the formal model of the DAIDLAUS algorithm and provides insights for further refinement.