Filming runners with drones is hard

TL;DR

This paper proves that the problem of optimization of drones for aerial photography and cinematography is NP-hard for the more realistic case in which the battery endurance of the drones is limited.

Abstract

The use of drones or Unmanned Aerial Vehicles (UAVs) for aerial photography and cinematography is becoming widespread. The following optimization problem has been recently considered. Let us imagine a sporting event where a group of runners are competing and a team of drones with cameras are used to cover the event. The media \emph{director} selects a set of \emph{filming scenes} (determined by locations and time intervals) and the goal is to maximize the total \emph{filming time} (the sum of recordings) achieved by the aerial cinematographers. Recently, it has been showed that this problem can be solved in polynomial time assuming the drones have unlimited battery endurance. In this paper, we prove that the problem is NP-hard for the more realistic case in which the battery endurance of the drones is limited.

Figures (3)

• Figure 1: Construction. The clause vertices $q_j$ are located at the exterior circle $D_1$ inside the arc $D_1'$. The gadgets are located at the inner circle $D_2$ inside the arc $D_2'$. The three directed edges correspond to the literals appearing in the clause $C_j$. Zoom: Variable Gadget. Auxiliaries vertices $y_{ij}$ and $w_{ij}$ are located in an alternating way in the gadget.
• Figure 2: The collision zone is the blue region of the annulus. The variable vertices are located at $D_2".$ The clause vertices are located at $D_1'$. Two intersecting segments connecting variable and clause vertices intersect inside the collision zone.
• Figure 3: Scenes and the flight plan.

Theorems & Definitions (7)

• Theorem 1
• Lemma 2
• Lemma 3
• proof
• Lemma 4
• proof
• Corollary 5