Path Planning for Aerial Relays via Probabilistic Roadmaps

TL;DR

The paper tackles relay path planning for multiple UAVs under arbitrary flight constraints and channel models by discretizing space and employing a tailored probabilistic roadmap (PR) approach. It introduces PR with feasible initialization (PRFI), which seeds the PR graph with a heuristic, feasible tentative path and augments it with random samples to balance optimality and tractability. The framework supports both static and moving UEs, and scales to multiple UAVs and UEs, with theoretical guarantees under a tomographic channel model and practical complexity advantages over existing methods. Numerical experiments demonstrate that PRFI achieves faster connectivity, lower outage, and higher total data transfer than benchmarks, highlighting its potential for robust, scalable aerial-relay deployments.

Abstract

Autonomous unmanned aerial vehicles (UAVs) can be utilized as aerial relays to serve users far from terrestrial infrastructure. Unfortunately, existing algorithms for aerial relay path planning cannot accommodate general flight constraints or channel models. This is required in practice due to connectivity constraints, the presence of obstacles (e.g., buildings), and regulations. This paper proposes a framework that overcomes these limitations by spatially discretizing the flight region. To cope with the resulting exponential growth in complexity, the framework adopts a probabilistic roadmap approach, where a shortest path is found through a graph of randomly generated states. To attain high optimality with affordable complexity, the probability distribution used to generate these states is designed based on heuristic path planners with theoretical guarantees. The algorithms derived in this framework not only overcome the main limitations of existing schemes but also entail smaller computational complexity. Extensive theoretical and numerical results corroborate the merits of the proposed approach.

Figures (15)

• Figure 1: Trajectories of two relay UAVs obtained with the proposed algorithm. Red/blue boxes represent buildings. The flight grid points are represented as blue dots. The green and yellow lines denote the trajectories of the UAVs.
• Figure 2: Top view of an example case where no path through adjacent points exists that allows UAV-1 to serve UAV-2 throughout the path of the latter. At some point, UAV-2 may need to wait so that UAV-1 can gain altitude. Grey boxes represent buildings and dots are grid points.
• Figure 3: Expected UE rate $\mathbb{E}[\textcolor{black}{r}_{\text{UE}}(\textcolor{black}{\bm Q}(\textcolor{black}{t}))]$ vs. $\textcolor{black}{t}$. The proposed algorithm is the first to attain the target rate $\textcolor{black}{r}_{\text{UE}}^{\text{min}}$ ($\textcolor{black}{r}_{\text{UE}}^{\text{min}} = 90$ Mbps, $[\check {{\textcolor{black}{d}}}_{\text{BS}}^{\text{UE}},\hat{{\textcolor{black}{d}}}_{\text{BS}}^{\text{UE}}]=[150,250]$ m).
• Figure 4: $\textcolor{black}{\bar{T}}_{\text{c}}$ and $\textcolor{black}{P}_{\text{f}}$ vs. $\textcolor{black}{r}_{\text{UE}}^{\text{min}}$. Some benchmarks achieve a smaller mean connection time because they only succeed in the easiest MC realizations.
• Figure 5: $\textcolor{black}{\bar{T}}_{\text{c}}$ and $\textcolor{black}{P}_{\text{f}}$ vs. mean $\|\textcolor{black}{\bm q}_{\text{UE}}-\textcolor{black}{\bm q}_{\text{BS}}\|$ ($\textcolor{black}{r}_{\text{UE}}^{\text{min}}$ = 90 Mbps).

Theorems & Definitions (8)

• Proposition 1
• proof
• Theorem 1
• Theorem 2
• proof
• Theorem 3
• proof
• Lemma 1