Approximation Algorithms for the UAV Path Planning with Object Coverage Constraints

We study the problem of the Unmanned Aerial Vehicle (UAV) such that a specific set of objects needs to be observed while ensuring a quality of observation. Our goal is to determine the shortest path for the UAV. This paper proposes an offline algorithm with an approximation of $(2+2n)(1+\epsilon)$ where $\epsilon >0$ is a small constant, and $n$ is the number of objects. We then propose several online algorithms in which objects are discovered during the process. To evaluate the performance of these algorithms, we conduct experimental comparisons. Our results show that the online algorithms perform similarly to the offline algorithm, but with significantly faster execution times ranging from 0.01 seconds to 200 seconds. We also show that our methods yield solutions with costs comparable to those obtained by the Gurobi optimizer that requires 30000 seconds of runtime.