Fast conflict detection using probability flow

Probabilistic conflict detection has recently attracted much attention from researchers due to its importance in safe automated transport systems; however, current methods struggle to accurately calculate in real-time the probability of conflict for complex vehicle maneuvers in cluttered environments. We present a formulation for the general probabilistic conflict detection problem using the flow rate of conflict probability at the boundary of a conflict zone. For Gaussian distributed vehicle states, we then derive a tight upper bound for the probability of conflict over a time period, which can be calculated in real-time using adaptive numerical integration techniques. We present two examples to illustrate the performance of this method: the first example shows that this method is very efficient for simple environments and the second example shows that this method can calculate the conflict probability upper bound in real-time even for complex vehicle maneuvers in cluttered environments.