Sampling-Based Roadmap Methods for a Visual Reconnaissance UAV*

Abstract

This article considers a path planning problem for a single fixed-wing aircraft performing a reconnaissance mission using EO (Electro-Optical) camera(s). A mathematical formulation of the general aircraft visual reconnaissance problem for static ground targets in terrain is given and it is shown, under simplifying assumptions, that it can be reduced to what we call the PVDTSP (Polygon-Visiting Dubins Traveling Salesman Problem), a variation of the famous TSP (Traveling Salesman Problem). Two algorithms are developed to solve the PVDTSP. They fall into the class of algorithms known as sampling-based roadmap methods because they operate by sampling a finite set of points from a continuous state space in order to reduce a continuous motion planning problem to planning on a finite discrete graph. The first method is resolution complete, which means it provably converges to a nonisolated global optimum as the number of samples grows. The second method achieves slightly shorter computation times by using approximate dynamic programming, but consequently is only guaranteed to converge to a nonisolated global optimum modulo target order. Numerical experiments indicate that, for up to about 20 targets, both methods deliver good solutions suitably quickly for online purposes. Additionally, both algorithms allow trade-off of computation time for solution quality and are shown extensible to handle wind, airspace constraints, any vehicle dynamics, and open-path (vs. closed-tour) problems.

Unsupervised learning‐based flexible framework for surveillance planning with aerial vehicles

“…Even though the LKH algorithm is one of the most powerful heuristics for the TSP, due to the samples and transformation, the final problem has many nodes. The reported computational times for problems with 20 targets and 1,500 random samples are several hundreds of seconds (Obermeyer et al, ), which is reported to be faster than the genetic algorithm for the DTSPN proposed by the same authors in Obermeyer (), but still far from our needs and expectations.…”

Algorithms for the traveling Salesman Problem with Neighborhoods involving a dubins vehicle

“…This algorithm samples the regions and then relies on the Noon and Bean tranformation [18] for overlapping nodesets to transorm the problem to an ATSP. We show that for the same set of samples this method will produce a tour that is no longer than that of [16], and presented numerical results that show performance improvement when there is overlap in the regions of interest.…”

“…Many researchers have addressed this problem with various regions, but most have used the Euclidean distance as the cost function [12], [13], [14]. Obermeyer was the first to tackle the TSPN with Dubins vehicle dynamics in [15] using a genetic algorithm approach, then later in [16] by using a sampling based roadmap method which we will call RCM that is proven to be resolution complete. In the latter method, the DTSPN is transformed to a General Traveling Salesman Problem (GTSP) with non-overlapping nodesets and then to an Asymmetric Traveling Salesmen Problem (ATSP) through a version of the Noon and Bean transformation [17].…”

“…The second algorithm addresses the case in which the regions intersect frequently. In this case, we propose a sampling based roadmap algorithm similar to that of [16], but use a more general version of the Noon and Bean transformation [18] in which the GTSP can contain overlapping nodesets. We show that for the same set of samples this method will produce a tour that is no longer than that of RCM from [16] and performs significantly better when the regions overlap.…”

Multiple event localization in a sparse acoustic sensor network using UAVs as data mules

“…The DTSPN for the data mule UAV seeks to combine the Dubins Traveling Salesman Problem [8] with the Traveling Salesman with Neighborhoods Problem [9]. The path planning algorithm used to address the DTSPN for the UAV data mule is most similar to the sampling based method from [10].…”