UAV Trajectory Planning for Delay Tolerant Communications

Abstract

In this paper, we address the problem of optimizing a communication-aware trajectory for a quadrotor that must transfer periodically (with fixed period T) a maximum amount of data from a source node (SN) to a destination node (DN). The communications aspect is mathematically stated by linking the bit rate to the channel capacity concept from information theory. The trajectory is optimized using a parametric approach using Fourier series in order to reduce the computational load of the optimization process. We show that the proposed trajectory results in a large increase of the amount of transferred data, and can be easily tracked by the quadrotor. Index Terms-Trajectory planning, data ferry, delay tolerant communications. NOTATION A zero dimension subspace is denoted by {0}, and the identity operator is denoted by I, or In when its size, n×n, is specified. For a full row (column) rank matrix X ∈ R n×m , its right (left) inverses are denoted by X r (X), i.e. XX r = In (X X = Im). If X is square and invertible, its inverse is denoted by X −1. x T stands for the transpose of the matrix (or vector) x. s stands for the complex variable of Laplace transform. Given a pair of mappings (A, B), such that A : R n → R n and B : R m → R n , C (A, B) stands for the controllability matrix C (A, B) = B A B • • • A (n−1) B. Ψm(ξ) ∈ R n•m×m [ξ] stands for: Imξ Imξ 2 • • • Imξ n T. Further, c(ϑ) and s(ϑ) stand for cosine and sine of a given angle ϑ, respectively; and s −1 (ϑ) stands for arcsin(ϑ). The ceiling and the floor functions are denoted as • and • respectively.x stands for the estimate of the variable x; E[•] stands for the statistical expectation operator. A vector function f (ε, t) ∈ R n is said to be O(ε) over an interval [t1, t2] if there exist positive constants K and ε * such that f (ε, t) ≤ Kε for all ε ∈ [0, ε * ] and for all t ∈ [t1, t2], see [4]. CONFIDENTIAL. Limited circulation. For review only.

Optimum Trajectory Planning for Multi-Rotor UAV Relays with Tilt and Antenna Orientation Variations

“…In [12], the authors consider a UAV relay between ground users, but the effect of the antenna radiation pattern is overlooked. In [4], [13], we considered scenarios where the multi-rotor UAV communicates while moving; we considered more realistic dynamic models for the multi-rotor UAVs, but we disregarded the antenna radiation pattern.…”