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arxiv: 1906.09520 · v1 · pith:3QVK4YZ2new · submitted 2019-06-22 · 📡 eess.SP · cs.NI

Power Efficient Trajectory Optimization for the Cellular-Connected Aerial Vehicles

Behzad Khamidehi , Elvino S. Sousa This is my paper

Pith reviewed 2026-05-25 17:44 UTC · model grok-4.3

classification 📡 eess.SP cs.NI
keywords trajectory optimizationaerial vehiclespower minimizationcellular connectivitysuccessive convex approximationmixed integer nonlinear programmingpropulsion powerground base stations
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The pith

An iterative algorithm using successive convex approximation solves for power-minimizing trajectories of aerial vehicles that maintain cellular connectivity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Aerial vehicles need paths that keep propulsion power low while preserving a reliable link to ground base stations for command and control. The paper casts this requirement as a non-convex mixed-integer nonlinear optimization problem that is hard to solve directly. It first relaxes and reformulates the problem, then applies successive convex approximation to generate a sequence of convex subproblems solved iteratively. Readers care because limited onboard energy determines how long such vehicles can operate, and loss of connectivity can terminate a mission. If the approach succeeds, mission planners gain a practical way to extend flight time without dropping the cellular link.

Core claim

The paper claims that the trajectory optimization problem of minimizing total propulsion-related power consumption subject to a cellular-connectivity constraint throughout the flight can be relaxed and reformulated into a tractable form; successive convex approximation then converts the problem into an efficiently solvable sequence of convex problems.

What carries the argument

successive convex approximation applied after relaxation and reformulation of the mixed-integer nonlinear program

If this is right

  • The total propulsion power consumption of the aerial vehicle is minimized while the connectivity constraint is enforced.
  • The algorithm produces a solution by iteratively solving a sequence of convex problems.
  • Command and control data flows remain supported throughout the entire flight.
  • The method handles the non-convexity that arises from the power model and the distance-dependent link quality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same relaxation-plus-SCA pipeline could be tested on fleets of multiple aerial vehicles whose links share the same ground stations.
  • Adding wind or time-varying channel effects would reveal whether the computed trajectories stay robust in realistic conditions.
  • The formulation might transfer directly to ground robots that must stay connected while minimizing energy on battery-powered routes.

Load-bearing premise

The initial relaxation and reformulation produces solutions that remain feasible and near-optimal for the original connectivity and power objectives.

What would settle it

A numerical check on a small instance showing that the trajectory returned by the algorithm violates the minimum received signal strength requirement at any point along the path would falsify the claim.

Figures

Figures reproduced from arXiv: 1906.09520 by Behzad Khamidehi, Elvino S. Sousa.

Figure 1
Figure 1. Figure 1: An aerial user flying from an initial location to its destination. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of the proposed algorithm when [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Trajectory of the aerial vehicle for map 1. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Trajectory of the aerial vehicle for map 2. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Aerial vehicles have recently attracted significant attention in a variety of commercial and civilian applications due to their high mobility, flexible deployment and cost-effectiveness. To leverage these promising features, the aerial users have to satisfy two critical requirements: First, they have to maintain a reliable communication link to the ground base stations (GBSs) throughout their flights, to support command and control data flows. Second, the aerial vehicles have to minimize their propulsion power consumption to remain functional until the end of their mission. In this paper, we study the trajectory optimization problem for an aerial user flying over an area including a set of GBSs. The objective of this problem is to find the trajectory of the aerial user so that the total propulsion-related power consumption of the aerial user is minimized while a cellular-connectivity constraint is satisfied. This problem is a non-convex mixed integer non-linear problem and hence, it is challenging to find the solution. To deal with, first, the problem is relaxed and reformulated to a more mathematically tractable form. Then, using successive convex approximation (SCA) technique, an iterative algorithm is proposed to convert the problem into a sequence of convex problems which can be solved efficiently.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper formulates a trajectory optimization problem for an aerial vehicle that minimizes total propulsion power consumption subject to a cellular-connectivity constraint (minimum rate/SINR to ground base stations at every time slot). The resulting non-convex mixed-integer nonlinear program is first relaxed by replacing binary GBS-association variables with continuous [0,1] variables and then solved via an iterative successive convex approximation (SCA) procedure that produces a sequence of convex subproblems.

Significance. If the relaxed SCA iterates converge to a point that remains feasible for the original connectivity constraint and yields lower power than standard baselines, the work would supply a computationally tractable design tool for energy-efficient cellular-connected UAV flights. The approach relies on well-known relaxation and SCA steps rather than novel parameter-free derivations or machine-checked proofs.

major comments (3)
  1. [Abstract] Abstract and method description: the central claim that the relaxed SCA procedure solves the original MINLP requires a feasibility-recovery argument or a bound showing that the final trajectory satisfies the original non-convex rate constraint at every time slot; no such argument or recovery step is supplied.
  2. [Abstract] Abstract: the manuscript states that the sequence of convex problems 'can be solved efficiently' yet provides neither convergence analysis of the SCA iterates nor any numerical evidence (objective values, feasibility rates, or runtime) that the returned trajectory meets the connectivity requirement after rounding.
  3. [Proposed solution approach] Method outline: the initial relaxation of binary association variables to [0,1] together with convex upper/lower bounds on the rate expressions can produce limit points that violate the original SINR constraint once the continuous solution is rounded; the paper does not quantify or control this gap.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it explicitly named the propulsion power model and the precise form of the connectivity constraint (e.g., minimum SINR threshold).

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments correctly identify areas where the presentation of the relaxation and SCA approach could be strengthened with additional clarification and evidence. We address each major comment below and commit to revisions that improve rigor without overstating the current results.

read point-by-point responses

  1. Referee: [Abstract] Abstract and method description: the central claim that the relaxed SCA procedure solves the original MINLP requires a feasibility-recovery argument or a bound showing that the final trajectory satisfies the original non-convex rate constraint at every time slot; no such argument or recovery step is supplied.

    Authors: We agree that the abstract phrasing could imply a stronger guarantee than is formally established. The algorithm is developed for the continuous relaxation of the MINLP, and the manuscript does not supply a recovery argument or bound ensuring the rounded solution satisfies the original non-convex SINR constraint at every slot. In the revised manuscript we will explicitly state that the procedure solves the relaxed problem, add a brief discussion of the potential feasibility gap after rounding, and include a simple post-processing recovery step (e.g., a local adjustment of the trajectory or re-association) when minor violations occur. revision: yes

  2. Referee: [Abstract] Abstract: the manuscript states that the sequence of convex problems 'can be solved efficiently' yet provides neither convergence analysis of the SCA iterates nor any numerical evidence (objective values, feasibility rates, or runtime) that the returned trajectory meets the connectivity requirement after rounding.

    Authors: The phrase 'can be solved efficiently' is intended to indicate that each subproblem is convex and therefore amenable to standard interior-point solvers. We acknowledge that neither a convergence proof for the SCA sequence nor supporting numerical statistics appear in the abstract (or are highlighted in the provided summary). The full manuscript contains simulation results, but to directly address the concern we will augment the abstract and add a dedicated subsection reporting iteration counts, objective-value convergence, post-rounding feasibility rates, and runtimes on the tested instances. revision: yes

  3. Referee: [Proposed solution approach] Method outline: the initial relaxation of binary association variables to [0,1] together with convex upper/lower bounds on the rate expressions can produce limit points that violate the original SINR constraint once the continuous solution is rounded; the paper does not quantify or control this gap.

    Authors: The referee correctly notes that the combination of continuous relaxation and convex approximations on the rate function does not automatically guarantee that the rounded solution remains feasible for the original non-convex constraint. The manuscript relies on the standard practice of solving the relaxed problem but does not quantify the resulting gap or provide a control mechanism. In the revision we will add an analysis of the relaxation tightness (including numerical evaluation of SINR violation after rounding) and describe a lightweight recovery procedure to restore feasibility when needed. revision: yes

Circularity Check

0 steps flagged

No circularity in SCA-based MINLP relaxation for trajectory optimization

full rationale

The paper applies standard relaxation of binary association variables to [0,1] followed by successive convex approximation (SCA) to generate a sequence of convex subproblems. This is a conventional algorithmic technique relying on external convex solvers; no parameter is fitted to data and then relabeled as a prediction, no self-citation chain supplies a load-bearing uniqueness result, and no ansatz or known empirical pattern is smuggled in via prior work by the same authors. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the relaxed problem yields useful trajectories for the original non-convex instance; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The original non-convex mixed-integer problem can be relaxed and reformulated into a more tractable form whose solutions remain relevant to the original objectives.
    Explicitly stated as the first step after problem formulation.

pith-pipeline@v0.9.0 · 5741 in / 1003 out tokens · 24301 ms · 2026-05-25T17:44:01.162361+00:00 · methodology

discussion (0)

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Reference graph

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