The constantly increasing congestion in the sea lanes and air traffic lanes raises the risk of ship collisions and aircraft collisions. This danger was tragically illustrated in a recent air disaster over Germany. This research seeks to reduce the collision risk via the development of a high-performance, robust, real-time collision avoidance algorithm. The research approach is based on the combination of an offline optimization algorithm generating the structure of the solution and an online algorithm approximating the solution in real time. The collision avoidance problem is formulated as a maximin problem of Chebyshev type: the objective is to maximize with respect to controls the timewise minimum distance between the host vehicle and an intruder. A multiple-subarc version of the sequential gradient-restoration algorithm is being developed to solve numerically the optimal control problem. Because it is not feasible to compute the optimal trajectory in real time, a collision avoidance guidance algorithm is being developed to approximate the optimal trajectory in real time. This algorithm partitions the collision avoidance maneuver into an avoidance phase and a recovery phase. For the avoidance phase, the time interval for which saturation control can be applied is determined so as to quickly escape from the collision danger. During the recovery phase, the host vehicle is maneuvered back to the assigned path via a feedback restoration algorithm. To rapidly disseminate the research results and foster education in the fields of optimization, guidance, and system safety, an online demonstration of the algorithm is being developed. This software will allow remote users to simulate ship/aircraft maneuvers with the aid of animated graphical displays and will help the development of collision avoidance instrumentation for ships and aircraft. The research results will also be relevant to the orbital debris avoidance for spacecraft.
