Abstract-Multi-agent differential games are important and useful tools for analyzing many practical problems. With the recent surge of interest in using UAVs for civil purposes, the importance and urgency of developing tractable multiagent analysis techniques that provide safety and performance guarantees is at an all-time high. Hamilton-Jacobi (HJ) reachability has successfully provided safety guarantees to smallscale systems and is flexible in terms of system dynamics. However, the exponential complexity scaling of HJ reachability prevents its direct application to large scale problems when the number of vehicles is greater than two. In this paper, we overcome the scalability limitations of HJ reachability by using a mixed integer program that exploits the properties of HJ solutions to provide higher-level control logic. Our proposed method provides safety guarantee for three-vehicle systemsa previously intractable task for HJ reachability -without incurring significant additional computation cost. Furthermore, our method is scalable beyond three vehicles and performs significantly better by several metrics than an extension of pairwise collision avoidance to multi-vehicle collision avoidance. We demonstrate our proposed method in simulations.

CL impairs emmetropization. Specifically, it disrupts compensation to lens-imposed hyperopia but not imposed myopia. However, CL eyes are able to recover from lens-induced hyperopia, suggesting that the mechanisms underlying the compensatory responses to defocusing lenses are different from those involved in recovery responses. The ocular growth effects of CL on young eyes are reversible under NL.

With the recent surge of interest in UAVs for civilian services, the importance of developing tractable multiagent analysis techniques that provide safety and performance guarantees has drastically increased. Hamilton-Jacobi (HJ) reachability has successfully provided these guarantees to smallscale systems and is flexible in terms of system dynamics. However, the exponential complexity scaling of HJ reachability with respect to system dimension prevents its direct application to larger-scale problems where the number of vehicles is greater than two. In this paper, we propose a collision avoidance algorithm using a hybrid framework for N + 1 vehicles through higher-level control logic given any N -vehicle collision avoidance algorithm. Our algorithm conservatively approximates a guaranteed-safe region in the joint state space of the N + 1 vehicles and produces a safety-preserving controller. In addition, our algorithm does not incur significant additional computation cost. We demonstrate our proposed method in simulation.

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