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.

To enhance path planning efficiency in unmanned aerial vehicle (UAV) search missions in complex environments, this paper proposes a coverage path planning (CPP) algorithm for a UAV that integrates the deep Q-network (DQN) with the A* algorithm (DQN-A*). In the proposed DQN-A* algorithm, a dual-driven reward mechanism is established, comprising a probability-weighted reward and a step-dependent reward, steering the UAV toward high-probability regions. Furthermore, to handle previously unknown obstacles in real time, the algorithm employs a multi-stage obstacle-identification strategy, enabling the UAV to improve coverage of traversable cells by dynamically adjusting its local path when newly detected obstacles are encountered. A theoretical analysis derives a principled recommended range for the UAV positional identifier based on statistical feature analysis; this range is then validated through extensive simulations. Additionally, Hamiltonian path pre-training is introduced to accelerate convergence. Comparative simulations demonstrate that the proposed DQN-A* algorithm achieves higher area-coverage and target-detection probabilities than benchmark algorithms in environments with unknown obstacles, offering valuable insights for positional encoding in deep reinforcement learning (DRL)-based robotic coverage problems.