Efficient route planning for an unmanned air vehicle deployed on a moving carrier

Abstract

Vehicle routing problem (VRP) is a constrained extension of the well-known traveling salesman problem (TSP). Emerging from the current conceptual trends in operations field, a new constraint to be included to the existing VRP parameters is the depot mobility. A practical example of such a problem is planning a route for an Unmanned air vehicle (UAV) deployed on a mobile platform to visit fixed targets. Furthermore, the range constraint of the UAV becomes another constraint within this sample case as well. In this paper, we define new VRP variants by introducing depot mobility (Mobile Depot VRP: MoDVRP) and extending it with capacity constraint (Capacitated MoDVRP: C-MoDVRP). As a sample use case, we study route planning for a UAV deployed on a moving carrier. To deal with the C-MoDVRP, we propose a Genetic Algorithm that is adapted to satisfy the constraints of depot mobility and range, while maximizing the number of targets visited by the UAV. To examine the success of our approach, we compare the individual performances of our proposed genetic operators with conventional ones and the performance of our overall solution with the Nearest Neighbor and Hill Climbing heuristics, on some well-known TSP benchmark problems, and receive successful results.

Appendix: Inclusion of takeoff and landing points in the solution

1.1 A.1 Takeoff point calculation

Whenever the first target to be visited in a tour is changed by an operation, the takeoff point for that tour is re-assigned with the calculations explained in this section.

Since the carrier moves on a constant heading, the algorithm calculates the nearest takeoff locations for each tour depending on the first target to be visited in its itinerary. For this, a linear equation of point-slope form is used to calculate the shortest path between the target and the carrier route as depicted in Fig. 21. Here $P_\mathrm{t}$ represents the location of the first target in the given tour, $P_\text {0}$ and $P_\text {1}$ represent any two points belonging to the line of the carrier route ($d_\mathrm{c}$), and $P_\mathrm{T}$ represents the nearest takeoff location.

Fig. 21

Geometrical representation of nearest takeoff point calculation

1.2 A.2 Landing point prediction

For this task, the time that the last target visited by the UAV in a tour is taken as the start point ($t_{0}$) for calculation. Since the speeds of the carrier and UAV are constant, their movement axes are vectorized from this point on and a linear equation of point-slope form is used to calculate their nearest meeting, as shown in Fig. 22. Here $P_\mathrm{u}$ and $P_\mathrm{c}$, respectively, represent the locations of the carrier and the UAV, and $P_\mathrm{m}$ is the nearest meeting point.

Fig. 22

Geometrical representation of nearest landing point prediction

The time spent by the UAV to visit targets can be acquired using its speed and the distance it traveled before time ($t_{0}$), using the formula $t=d/v$. Then this time value and the speed of the carrier can be used in the same formula to acquire the distance it covered at the time of ($t_{0}$). The inclusion of this distance in the formulation gives the exact location of UAV’s landing on the carrier.