| Summary: | With the dramatic development of small unmanned aircraft systems (sUAS), how to ensure sUAS safety operation has been a growing concern. This article proposes a fast probabilistic collision detection method for sUAS based on probability density function approximations. Firstly, cylindrical collision zones for sUAS and obstacles are established by geometrical methods for simplifying collision modeling, and instantaneous collision probability for sUAS is expressed by a triple integral. Secondly, a rapid estimation algorithm is derived for instantaneous collision probability, and then the predicted collision probability in probabilistic collision detection can be obtained by the maximum of instantaneous collision probabilities during the encounter. Randomized tests indicate that the average computation time of the proposed algorithm is less than 0.001s, and the Mean Absolute Error (MAE) is less than 0.01 and the Root Mean Squared Error (RMSE) is less than 0.02. Finally, numerical simulations are carried out to analyze the influence of parameters, including crossing angle, predicted separation at the closest point of approach (CPA), and predicted time to CPA, on collision probabilities. The optimal detection time for collision detection is also discussed in the different types of encounters. The collision detection method proposed in this article can provide support for real-time collision avoidance and the definition of dynamic safety bounds for sUAS.
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