Incorporating Stochastics into Optimal Collision Avoidance Problems Using Superquadrics

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Collision avoidance modeling methods vary between nonoptimal deterministic approaches to more challenging optimal probabilistic approaches [1]. To efficiently “model” these time-varying probability regions for use in an optimal control problem, this paper applies a novel approach using superquadrics. This paper determines optimal flight paths for the ownship, such as minimum flight path deviation, given different time-varying 3D uncertainty regions placed around the ownship and multiple intruder aircraft. Previous research demonstrated methods to 1) keep the ownship away from an ellipsoidal probability region around an intruder, and 2) keep the intruder away from a cylinder-shaped horizontal or vertical keep-out region around the ownship [2,3]. The problem considered herein determines the point of closest approach between multiple moving arbitrarily shaped superquadrics representing uncertainty regions in a nonlinear programming (NLP) framework to ensure collision-free operation while minimizing flight path deviations. Formulating this problem is challenging due to the necessity of constructing a smooth everywhere differentiable function that models the gradient of the closest point of approach of these surfaces as they move relative to one another at different aspect angles. This paper demonstrates the proposed approach by solving a challenging multiple-intruder collision avoidance problem. In this scenario, the ownship is assumed to be equipped with an onboard sensor with a 1 Hz update rate and iteratively solves the optimal control problem over a fixed 30 s receding time horizon.


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Journal of Air Transportation