Tractable Conflict Risk Accumulation in Quadratic Space for Autonomous Vehicles

Recent developments have shown that conflict avoidance may be cast as a probabilistic state-space problem. The probabilistic accumulation of risk because of exposure to a hazard over a period of time is an essential and often neglected and misunderstood aspect of the process of conflict risk calculation. How such risk accumulation may be accurately approximated in real time is demonstrated. The research reverts to theoretical basics and illustrates how risk accumulation for a one- and two-vehicle scenario is a first passage time problem. It is illustrated how exact quadratic state-order reduction may be combined with simple and accurate first passage time approximations. In this way, a tractable and accurate receding horizon solution is provided with the recognition of the time dependence of risk accumulation. The solution algorithm is implemented as a relatively straight-forward four-step discrete-time propagation and accumulation of risk. Small calculation errors are characterized to first order-second moment and always lead to a slight upper-bound solution, thereby improving safety. Simulation results indicate a high degree of risk calculation accuracy, calculable in real time.