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The control of complex non-linear systems can be aided by modeling each system as a collection of simplified hybrid modes, with each mode representing a particular operating regime defined by the system dynamics or by a region of the state space in which the system operates. Guarantees on the safety and performance of such hybrid systems can still be challenging to generate, however. Reachability analysis using a dynamic game formulation with Hamilton-Jacobi methods provides a useful way to generate these types of guarantees, and the technique is flexible enough to analyze a wide variety of systems. This paper presents two applications of reachable sets, both focused on guaranteeing the safety and performance of robotic aerial vehicles. In the first example, reachable sets are used to design and implement a backflip maneuver for a quadrotor helicopter. In the second, reachability analysis is used to design a decentralized collision avoidance algorithm for multiple quadrotors. The theory for both examples is explained, and successful experimental results are presented from flight tests on the STARMAC quadrotor helicopter platform.

This work considers a pursuit-evasion game in which a number of pursuers are attempting to capture a single evader. Cooperation among multiple agents can be difficult to achieve, as it may require the selection of actions in the joint input space of all agents. This work presents a decentralized, real-time algorithm for cooperative pursuit of a single evader by multiple pursuers in bounded, simply-connected planar domains. The algorithm is based on minimizing the area of the generalized Voronoi partition of the evader. The pursuers share state information but compute their inputs independently. No assumptions are made about the evader's control strategies other than requiring the evader control inputs to conform to a speed limit. Proof of guaranteed capture is shown when the domain is convex and the players' motion models are kinematic. Simulation results are presented showing the efficiency and effectiveness of this strategy.