Minimum time-error planning horizon for plan updating triggered by Poisson random events

Trajectory planning is essential in many applications, such as search and track missions by unmanned aerial vehicles (UAV). In a dynamic situation, events that call for a plan change may occur. Such events include the arrival of a new command or intelligence, detection of a new target, loss of a UAV, a sudden change of weather, etc. Therefore, a plan update is necessary and an appropriate time horizon for re-planning must be determined. If it is too long or too short, the updated plan may be poor. Unfortunately, there is little research in the selection of a planning horizon. This work presents a planning horizon that is optimal in the sense of minimizing errors in planning time. It is intended for use in mission planning but has many other applications. We model the rate of interrupting events as Poisson distributed with a known rate parameter. This paper shows the relationship between the optimal planning horizon and this rate parameter. To test the proposed planning horizon, a predator-prey scenario is simulated to compare different planning horizons. Simulation results are encouraging. While the proposed horizon is optimal in minimizing planning time errors, it is also near optimal in minimizing the average time needed to capture the prey.