Modeling and Calculating the Collision Risk for Air Vehicles

This paper deals with collision risk modeling and assessment for autonomous air vehicles. The suggested approach simplifies the problem by resolving the workspace into horizontal and vertical planes. Collision in 3-D corresponds to simultaneous collisions in the horizontal and vertical planes. Collision conditions are first derived for the deterministic case and then discussed in the presence of uncertainties. The collision conditions are expressed as inequalities in terms of the time rates of the bearing and the collision cone angles. This formulation brings important simplifications since it does not explicitly use speed and orientation information. Monte Carlo simulation is used to calculate the probability of collision in the presence of uncertainties. An important advantage of Monte Carlo methods is their ability to deal with uncertainty propagation in nonlinear systems with non-Gaussian noise. The simplicity of the collision inequalities allows for fast implementation of the Monte Carlo algorithm. Results are illustrated using simulation.