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Trajectory Design for Cellular-Connected UAV Under Outage Duration Constraint

Shuowen Zhang, Rui Zhang

TL;DR

This work tackles trajectory design for a cellular-connected UAV under a maximum outage duration constraint, aiming to minimize the mission time while maintaining QoS in the presence of outages. It reformulates the non-convex problem into a tractable sequence of representations based on GBS-UAV associations and connected-line-segment trajectories, enabling a convex optimization treatment of waypoint locations. The authors develop a graph-based feasibility check and propose both an optimal (exhaustive over associations) and a computationally efficient suboptimal solution, leveraging shortest-path graphs and SOCP/CVX. Numerical results show the proposed designs outperform DP-based methods in both performance and complexity, with the suboptimal approach closely matching the optimal performance and offering practical scalability to larger GBS sets.

Abstract

In this paper, we study the trajectory design for a cellular-connected unmanned aerial vehicle (UAV) with given initial and final locations, while communicating with the ground base stations (GBSs) along its flight. We consider delay-limited communications between the UAV and its associated GBSs, where a given signal-to-noise ratio (SNR) target needs to be satisfied at the receiver. However, in practice, due to various factors such as quality-of-service (QoS) requirement, GBSs' availability and UAV mobility constraints, the SNR target may not be met at certain time periods during the flight, each termed as an outage duration. In this paper, we aim to optimize the UAV trajectory to minimize its mission completion time, subject to a constraint on the maximum tolerable outage duration in its flight. To tackle this non-convex problem, we first transform it into a more tractable form and thereby reveal some useful properties of the optimal trajectory solution. Based on these properties, we then further simplify the problem and propose efficient algorithms to check the feasibility of the problem as well as to obtain its optimal and high-quality suboptimal solutions, by leveraging graph theory and convex optimization techniques. Numerical results show that our proposed trajectory designs outperform the conventional method based on dynamic programming, in terms of both performance and complexity.

Trajectory Design for Cellular-Connected UAV Under Outage Duration Constraint

TL;DR

This work tackles trajectory design for a cellular-connected UAV under a maximum outage duration constraint, aiming to minimize the mission time while maintaining QoS in the presence of outages. It reformulates the non-convex problem into a tractable sequence of representations based on GBS-UAV associations and connected-line-segment trajectories, enabling a convex optimization treatment of waypoint locations. The authors develop a graph-based feasibility check and propose both an optimal (exhaustive over associations) and a computationally efficient suboptimal solution, leveraging shortest-path graphs and SOCP/CVX. Numerical results show the proposed designs outperform DP-based methods in both performance and complexity, with the suboptimal approach closely matching the optimal performance and offering practical scalability to larger GBS sets.

Abstract

In this paper, we study the trajectory design for a cellular-connected unmanned aerial vehicle (UAV) with given initial and final locations, while communicating with the ground base stations (GBSs) along its flight. We consider delay-limited communications between the UAV and its associated GBSs, where a given signal-to-noise ratio (SNR) target needs to be satisfied at the receiver. However, in practice, due to various factors such as quality-of-service (QoS) requirement, GBSs' availability and UAV mobility constraints, the SNR target may not be met at certain time periods during the flight, each termed as an outage duration. In this paper, we aim to optimize the UAV trajectory to minimize its mission completion time, subject to a constraint on the maximum tolerable outage duration in its flight. To tackle this non-convex problem, we first transform it into a more tractable form and thereby reveal some useful properties of the optimal trajectory solution. Based on these properties, we then further simplify the problem and propose efficient algorithms to check the feasibility of the problem as well as to obtain its optimal and high-quality suboptimal solutions, by leveraging graph theory and convex optimization techniques. Numerical results show that our proposed trajectory designs outperform the conventional method based on dynamic programming, in terms of both performance and complexity.

Paper Structure

This paper contains 15 sections, 4 theorems, 22 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. Problem Reformulation and Optimal Solution Structure
  5. GBS-UAV Associations and Problem Reformulation
  6. Optimal Structure of UAV Trajectory
  7. Feasibility Check
  8. Proposed Solution to (P3)
  9. Optimal Solution
  10. Suboptimal Solution
  11. Numerical Examples
  12. Conclusion
  13. Proof of Proposition \ref{['prop_P1eq']}
  14. Proof of Proposition \ref{['prop_connected']}
  15. Proof of Lemma \ref{['prop_waypoint']}

Key Result

Proposition 1

(P1) is equivalent to the following problem:

Figures (6)

  • Figure 1: Illustration of trajectories without versus with communication outage.
  • Figure 2: Illustration of GBS-UAV associations with ${\hbox{\boldmath{$I$}}}=[m,n,l]^T$.
  • Figure 3: Illustration of maximum outage duration minimizing waypoint locations with ${\hbox{\boldmath{$I$}}}=[m,n,l]^T$.
  • Figure 4: Mission completion time $T$ versus $\bar{O}_{\mathrm{T}}$.
  • Figure 5: Trajectory comparison with $\bar{O}_{\mathrm{T}}=84.6124$ s.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2: Trajectory with Connected Line Segments
  • Lemma 1: Maximum Outage Duration Minimizing Waypoint Locations
  • Proposition 3