[Paper Review] UAV Trajectory and Communication Co-design: Flexible Path Discretization and Path Compression

Yijun Guo, Changsheng You+2 more|arXiv (Cornell University)|Oct 14, 2020

UAV Applications and Optimization28 references4 citations

TL;DR

This paper proposes a flexible path discretization (FPD) and path compression (PC) framework to reduce computational complexity in UAV trajectory and communication co-design. By optimizing only a subset of waypoints (designable waypoints) and using basis paths to compress the trajectory representation, the method achieves near-optimal rate performance with significantly reduced design variables, outperforming conventional time and path discretization schemes.

ABSTRACT

The performance optimization of UAV communication systems requires the joint design of UAV trajectory and communication efficiently. To tackle the challenge of infinite design variables arising from the continuous-time UAV trajectory optimization, a commonly adopted approach is by approximating the UAV trajectory with piecewise-linear path segments in three-dimensional (3D) space. However, this approach may still incur prohibitive computational complexity in practice when the UAV flight period/distance becomes long, as the distance between consecutive waypoints needs to be kept sufficiently small to retain high approximation accuracy. To resolve this fundamental issue, we propose in this paper a new and general framework for UAV trajectory and communication co-design. First, we propose a flexible path discretization scheme that optimizes only a number of selected waypoints (designable waypoints) along the UAV path for complexity reduction, while all the designable and non-designable waypoints are used in calculating the approximated communication utility along the UAV trajectory for ensuring high trajectory discretization accuracy. Next, given any number of designable waypoints, we propose a novel path compression scheme where the UAV 3D path is first decomposed into three one-dimensional (1D) sub-paths and each sub-path is then approximated by superimposing a number of selected basis paths weighted by their corresponding path coefficients, thus further reducing the path design complexity. Finally, we provide a case study on UAV trajectory design for aerial data harvesting from distributed ground sensors, and numerically show that the proposed schemes can significantly reduce the UAV trajectory design complexity yet achieve favorable rate performance as compared to conventional path/time discretization schemes.

Motivation & Objective

• To address the high computational complexity of UAV trajectory optimization due to infinite design variables in continuous-time trajectories.
• To reduce the number of optimized waypoints in 3D UAV path discretization without sacrificing communication accuracy.
• To develop a path compression scheme that further reduces design variables by representing trajectories as weighted superpositions of basis paths.
• To enable efficient joint optimization of UAV trajectory and communication under realistic channel models.
• To demonstrate superior performance-complexity trade-offs compared to conventional time and path discretization methods.

Proposed method

• Proposes flexible path discretization (FPD) that optimizes only a selected subset of waypoints (designable waypoints) while using all waypoints to compute communication utility for accuracy.
• Introduces a path compression (PC) scheme that decomposes the 3D UAV path into three 1D sub-paths and approximates each using a superposition of selected basis paths weighted by optimized coefficients.
• Uses a basis path selection strategy to minimize the number of path coefficients, reducing the number of design variables below the number of designable waypoints.
• Applies the block coordinate descent (BCD) method to iteratively optimize UAV trajectory and communication parameters under the new discretization and compression framework.
• Employs a finite-sum approximation error bound to ensure high trajectory discretization accuracy, derived using the gradient of the utility function and Lipschitz continuity.
• Validates the framework on a UAV data harvesting scenario with a probabilistic LoS channel model, using numerical simulations to compare performance and complexity.

Experimental results

Research questions

• RQ1 Can a flexible path discretization scheme reduce the number of optimized waypoints while maintaining high trajectory discretization accuracy?
• RQ2 Can path compression via basis path superposition further reduce the number of design variables in UAV trajectory optimization?
• RQ3 How does the proposed FPD-PC framework compare to conventional time discretization (TD) and conventional path discretization (CPD) in terms of rate performance and computational complexity?
• RQ4 What is the optimal trade-off between the number of designable waypoints and the number of basis paths for balancing complexity and performance?
• RQ5 Does the proposed framework maintain high communication utility despite reducing the number of design variables?

Key findings

• The proposed FPD-PC scheme achieves near-optimal rate performance with significantly reduced computational complexity compared to conventional TD and CPD schemes.
• With only 4 designable waypoints and 4 basis paths, the FPD-PC scheme achieves a 60% reduction in design variables compared to CPD with 10 waypoints.
• The finite-sum approximation error is bounded by $\frac{1}{2}D_u\Delta_{\text{max}}^U T$, ensuring high trajectory discretization accuracy.
• Numerical results show that setting too few designable waypoints (e.g., $J=2$) causes significant rate loss, while too many (e.g., $J=10$) limits degrees of freedom.
• The path compression scheme effectively reduces the number of path coefficients below the number of designable waypoints, enabling efficient trajectory representation.
• The framework is general and applicable to various UAV communication scenarios under different channel models, including probabilistic LoS and Rician fading.