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QIEN: Quantum-Inspired Energy-Neutral UAV Trajectory for WPT-Enabled Industrial HRLLC

Ali Ranjha, Georges Kaddoum, Halim Yanikomeroglu

arXiv:2610.23524v1eess.SYcs.SY

TL;DR

Autonomous mining robots need reliable, low-latency communication where terrain and disaster damage can disrupt links, while their UAV relay must also sustain energy and robot power delivery. QIEN jointly optimizes trajectory and communication and power resources with a heterogeneous quantum-behaved swarm. The paper reports benchmark outperformance while maintaining energy-neutral operation and continuous WPT.

  • Problem

    Mining robots require short-packet, low-latency links with stringent reliability, while conventional Shannon-capacity designs do not capture finite-blocklength operation.

    Source: §I · p. 1

  • Method

    QIEN formulates joint trajectory and resource allocation as an HRLLC-constrained MINLP and applies a hybrid cooperative quantum-behaved PSO.

    Source: 4) Algorithmic Positioning and… · p. 2, B. Novelty and Contributions · p. 2, §V · p. 11

  • Results

    Simulations report that QIEN outperforms classical benchmarks while converging, maintaining a sustainable energy margin, and delivering continuous wireless power to the robot.

    Source: B. Novelty and Contributions · p. 3

  • Takeaways & Limitations

    The simulations support QIEN’s operation in the modeled mission while maintaining energy sustainability and continuous robot power delivery.

    Source: B. Novelty and Contributions · p. 3, §V · p. 11

    Classical PSO is limited in this setting: interacting energy, WPT, and mobility constraints create narrow, disconnected feasible regions that velocity updates can overshoot.

    Source: A. Classical PSO Limitations · p. 5

Abstract

from arXiv · show

This paper introduces Quantum-Inspired Energy-Neutral (QIEN) UAV Trajectory for WPT-Enabled Industrial HRLLC, a novel framework for mobility-integrated trajectory and resource optimization in solar-powered uncrewed aerial vehicle (UAV) relay systems supporting autonomous mining robots in post-disaster environments. We formulate a mixed-integer nonlinear program (MINLP) that jointly optimizes UAV trajectory, finite blocklength allocation, transmit power, and wireless power transfer (WPT) over discrete time horizons to maximize aggregate data throughput. The system operates under strict extreme hyper-reliable low-latency communication (HRLLC) constraints, energy sustainability requirements via solar harvesting, and continuous robot power delivery. To solve this large-scale optimization problem, QIEN employs a hybrid Cooperative Quantum-behaved Particle Swarm Optimization (Co-QPSO) algorithm using quantum tunneling mechanisms and a heterogeneous swarm architecture. Our simulation results demonstrate that the proposed QIEN framework significantly outperforms benchmark algorithms, achieving successful convergence while maintaining energy-neutral operation and satisfying all reliability, power, and mobility constraints.

I. INTRODUCTION

UAV relays address obstructed or compromised mining communications, where robots need short-packet, low-latency links with stringent reliability. QIEN combines energy-aware trajectory and resource optimization with a heterogeneous quantum-behaved swarm to address the coupled constraints.

I. INTRODUCTION

  • Mining robots operate in hazardous areas where terrain can obstruct line-of-sight links and post-disaster terrestrial networks may be compromised.HRLLC supports real-time closed-loop control, while FBL models short control packets with stringent latency and reliability requirements.Source: §I · p. 1

1) UAV Channel Modeling and Airborne Networks:

  • Prior UAV channel studies describe propagation challenges across high-altitude, air-to-ground, and air-to-air links.The cited review and network studies emphasize channel behavior beyond traditional terrestrial assumptions.Source: 1) UAV Channel Modeling and Airborne… · p. 1

2) Trajectory Optimization under Energy and WPT Constraints:

  • Prior energy-aware UAV work addresses wireless charging, SWIPT, and propulsion-energy constraints in trajectory design.The cited studies include charging towers, signal-based energy harvesting, and relay power dynamics.Source: 2) Trajectory Optimization under… · pp. 1–2

3) HRLLC and FBL Regimes:

  • FBL and URLLC studies address short-packet reliability, transmission power, and energy use in UAV and integrated networks.The cited work includes a UAV relay reliability result and optimization under imperfect channel state information.Source: 3) HRLLC and FBL Regimes · p. 2

4) Algorithmic Positioning and Metaheuristic Optimization:

  • Classical PSO and related methods face disconnected feasible regions when reliability, WPT, and energy constraints interact.The related-work discussion identifies an “invisible wall” challenge for standard PSO and DRL in this setting.Source: 4) Algorithmic Positioning and… · p. 2

B. Novelty and Contributions

  • QIEN formulates throughput maximization as a MINLP enforcing HRLLC error, integer blocklength, and energy-neutrality constraints.Its system model couples finite-blocklength signaling, solar harvesting, and WPT.Source: B. Novelty and Contributions · p. 2
  • Co-QPSO separates Safety exploitation from Hunter exploration, using heavy-tailed sampling to help Hunters bypass constraint barriers.This architecture targets premature convergence and momentum-trapping problems in constrained search.Source: B. Novelty and Contributions · pp. 2–3
  • QIEN simulations report benchmark outperformance, convergence, a sustainable energy margin, and continuous wireless power delivery to the robot.The UAV relay supports autonomous mining robots in post-disaster environments.Source: B. Novelty and Contributions · p. 3

II. SYSTEM MODEL AND PROBLEM FORMULATION

The model considers a solar-powered UAV relaying data from a ground station to a mobile robot while supplying the robot with wireless power. It discretizes the mission and constrains mobility and communication geometry to keep trajectories operational and links within the modeled line-of-sight regime.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The UAV relays information and concurrently transfers power to a robot following a prescribed circular surveillance path.The architecture is framed for autonomous operation in hazardous or infrastructure-denied environments.Source: §II · p. 3
  • Data communication and WPT use separate bands and independent robot hardware, avoiding the rate-energy trade-offs of single-RF SWIPT receivers.The UAV uses an information receiver path and a dedicated rectenna-based energy-harvesting path at the robot.Source: §II · p. 3

A. Time Discretization and Mobility Model

  • The mission is discretized into uniform time steps, with time-varying system quantities evaluated at those discrete instances.The mission duration is defined by the number of intervals and their spacing.Source: A. Time Discretization and Mobility… · p. 3
  • The model uses free-space channel gains and represents the robot’s surveillance path as a circle with specified center, radius, angular velocity, and initial angle.The UAV-to-robot distance depends on both agents’ positions.Source: A. Time Discretization and Mobility… · p. 3
  • The UAV is constrained by horizontal operating radius, altitude bounds, and a minimum elevation angle for ground-station line of sight.A bounded large-scale channel model uses a geometric elevation constraint to remain in the dominant LoS regime rather than embedding probabilistic blockage functions in the FBL rates.Source: A. Time Discretization and Mobility… · pp. 3–4
  • Horizontal and vertical UAV velocities have independent operational limits, reflecting different rotary-wing flight constraints.The text describes vertical maneuvers as thrust-limited and horizontal cruising as governed by pitch dynamics.Source: A. Time Discretization and Mobility… · p. 4
  • The model also bounds total 3D speed through orthogonal mobility constraints and requires minimum separation from the ground station.These conditions are described as supporting physically executable trajectories and operational safety.Source: A. Time Discretization and Mobility… · p. 4

B. Finite Blocklength Communication Model

The communication model allocates finite channel uses and transmit power across two links, then evaluates achievable rates with finite-blocklength effects. It constrains the combined decoding error to meet an HRLLC target and aggregates rates over the mission.

B. Finite Blocklength Communication Model

  • The two links share N channel uses per time step, with integer allocations summing to N and transmit powers bounded between Pmin and Pmax.The allocation vector assigns n1 and n2 channel uses to the respective links.Source: B. Finite Blocklength Communication… · p. 4
  • Finite-blocklength achievable rates account for channel dispersion and target error probability rather than relying only on Shannon capacity.The text attributes the approximation to Polyanskiy’s finite-blocklength theory.Source: B. Finite Blocklength Communication… · p. 4
  • The sum of the two link decoding errors must be at most 10^-9 at every time step, and aggregate throughput integrates the sum rate over the mission.The error bound is the stated HRLLC constraint.Source: B. Finite Blocklength Communication… · p. 4

C. Energy Harvesting and Power Consumption Model

The energy model combines altitude-dependent solar harvesting with propulsion, communication, WPT, and circuit power consumption. A separate WPT model constrains received robot power to support operation without exceeding its stated upper bound.

C. Energy Harvesting and Power Consumption Model

  • Solar harvesting varies with UAV altitude through an elevation factor and a piecewise cloud-attenuation model.The text defines the elevation-factor parameters and cloud-layer boundaries and attenuation coefficient.Source: C. Energy Harvesting and Power… · p. 4
  • The UAV’s propulsion power is modeled as altitude-dependent, with coefficients P0, P1, and P2.The passage attributes the increase with altitude to varying air density.Source: C. Energy Harvesting and Power… · p. 4
  • The energy-causality model reserves an Energy Safety Margin instead of requiring consumption to equal all harvested energy.Total consumption includes propulsion, communication and WPT transmission, and circuit processing power.Source: C. Energy Harvesting and Power… · p. 4

D. Wireless Power Transfer Model

  • Received robot power depends on WPT transmit power, channel gain, and RF-to-DC efficiency, and must stay between the robot’s operating requirement and a maximum bound.The minimum requirement combines robot circuit and locomotion power; the upper bound protects its harvesting circuitry.Source: D. Wireless Power Transfer Model · p. 5

E. Problem Formulation

Problem P1 maximizes aggregate mission throughput across time while jointly handling discrete allocation and continuous operating constraints. Its scale and non-convexity motivate a quantum-inspired metaheuristic, while classical PSO can struggle in the constrained feasible region.

E. Problem Formulation

  • The objective is to maximize aggregate data throughput over the entire mission.The formulation is described as mobility-integrated trajectory optimization.Source: E. Problem Formulation · p. 5
  • Problem P1 has 9K decision variables—7K continuous and 2K integer—and severe non-convexity from integer, channel, finite-blocklength, WPT, and mobility terms.The inverse Q-function in the finite-blocklength rate formula is one stated source of non-convexity.Source: E. Problem Formulation · p. 5
  • Classical gradient methods fail, while global optimization faces the curse of dimensionality as K grows and an “invisible wall” phenomenon.These difficulties motivate the quantum-inspired metaheuristic approach.Source: E. Problem Formulation · p. 5

A. Classical PSO Limitations

  • Classical PSO updates each particle’s position and velocity, using personal-best and global-best positions in its update.The supplied passage identifies inertia, cognitive, and social coefficients, plus random parameters, in the update.Source: A. Classical PSO Limitations · p. 5
  • When energy sustainability, WPT, and mobility constraints are concurrently active, classical PSO can overshoot and remain infeasible in a narrow, disconnected feasible region.The passage attributes this behavior to accumulated velocity and insufficient penalty-gradient guidance for returning to feasibility.Source: A. Classical PSO Limitations · p. 5

B. Quantum-Behaved PSO Foundation

QPSO replaces velocity-based motion with probabilistic position updates, while Co-QPSO adds cooperative particle roles to balance exploration and exploitation. A targeted local search refines feasible solutions.

B. Quantum-Behaved PSO Foundation

  • QPSO eliminates the velocity term and updates probabilistic particle positions using a local attractor based on personal and global bests.A random convex combination balances the two best positions; quantum uncertainty informs the update.Source: B. Quantum-Behaved PSO Foundation · pp. 5–6
  • The logarithmic term models quantum tunneling, allowing occasional large jumps across infeasible barriers and away from local optima.The approach is described as quantum-inspired, not dependent on quantum-computing hardware; its sampling uses a heavy-tailed Laplace distribution.Source: B. Quantum-Behaved PSO Foundation · p. 6

C. Cooperative Swarm Architecture

  • Co-QPSO partitions the swarm into safety particles that exploit and hunter particles that continue aggressive exploration.Safety particles use an adaptive coefficient and a smoothing transformation; hunter particles use fixed αhunter = 0.7 and fully random attractor weights.Source: C. Cooperative Swarm Architecture · p. 6
  • When the global best enters the feasible region, Co-QPSO perturbs two randomly selected dimensions to refine the solution.The perturbation ratio is ρ = 0.05, and its magnitude decreases over iterations for coarse-to-fine adjustment.Source: C. Cooperative Swarm Architecture · p. 6

D. Fitness Function, Constraint Handling, and Quantum Terminology

The fitness function converts throughput maximization into minimization and separates feasible from infeasible solutions through penalties. Co-QPSO’s “quantum” terminology refers to its classical stochastic search mechanism.

Fitness and constraint handling

  • Feasible solutions receive fitness equal to negative aggregate sum rate; infeasible solutions receive a large penalty base plus accumulated constraint violations.The evaluated violations include energy, robot power delivery, mobility, spatial boundaries, and ground-station safety distance.Source: D. Fitness Function, Constraint… · p. 6
  • Penalty weights reflect constraint criticality, with energy sustainability and robot power delivery receiving the highest stated weights.Spatial and mobility violations receive moderate weights to guide search without overwhelming objective improvement.Source: D. Fitness Function, Constraint… · pp. 6–7

Quantum terminology

  • Co-QPSO is a classical metaheuristic whose quantum-inspired terminology refers to wavefunction-based modeling and heavy-tailed Laplace sampling, not quantum hardware.The text calls the resulting stochastic exploration and escape from local optima “quantum tunneling.”Source: D. Fitness Function, Constraint… · p. 7

IV. SIMULATION RESULTS

The simulations evaluate a 100-second surveillance mission and test Co-QPSO’s sensitivity to custom hyperparameters. Every tested parameter combination found a feasible trajectory, with throughput varying by at most 2.51%.

IV. SIMULATION RESULTS

  • The 100-second mission used 11 time steps, yielding 77 optimization variables, with a 150-channel-use blocklength per time step and an HRLLC error constraint of 10^-9.The robot followed a circular perimeter-surveillance trajectory.Source: §IV · p. 7

A. Hyperparameters and Sensitivity Analysis

  • The Safety-particle contraction-expansion coefficient α(i) decreased linearly from 1.0 to 0.5, while the Hunter coefficient was empirically selected as 0.7 and perturbation ratio ρ was maintained at 0.08.The Safety schedule was directly adopted from foundational QPSO global convergence theory; heterogeneous roles and custom parameters were novel to the framework.Source: A. Hyperparameters and Sensitivity… · p. 7
  • Sensitivity testing averaged independent randomized-seed trials across a 5 × 5 grid of α_hunter values from 0.5 to 0.9 and ρ values from 0.01 to 0.10.The custom hyperparameters were tested to assess robustness and reduce deterministic bias.Source: A. Hyperparameters and Sensitivity… · p. 7
  • Every tested hyperparameter combination found a feasible trajectory, with average final throughput ranging from 186.92 Mb to 191.72 Mb and maximum variance of 2.51%.The authors attribute this stability to the cooperative architecture rather than brittle parameter tuning.Source: A. Hyperparameters and Sensitivity… · p. 7
  • The Hunter contraction coefficient α_hunter governs global convergence, while perturbation ratio ρ acts as a fail-safe when suboptimal α_hunter values lead the swarm into local minima.When optimal α_hunter values prevent stagnation, ρ remains inactive and yields flat ridges.Source: A. Hyperparameters and Sensitivity… · pp. 7–8

B. Baseline Comparisons and Complexity Analysis

Co-QPSO is compared with classical optimization baselines and analyzed against relaxed upper bounds. It achieves higher aggregate throughput than the baselines and reaches 98.04% of the tightest theoretical bound.

1) Gradient Trapping in SCA:

  • SCA found an early feasible solution by iteration 200 but then flatlined at 179.24 Mb, which the authors attribute to becoming trapped in a local optimum.The paper links the stagnation to severe MINLP non-convexity and the absence of a stochastic broad-exploration mechanism.Source: 1) Gradient Trapping in SCA · p. 9

2) Delayed Feasibility in Standard Metaheuristics:

  • GA and SA spent 400 iterations navigating infeasible regions, while DE found no valid trajectory until iteration 600 and reached 157.36 Mb.The authors connect delayed feasibility to disconnected feasible regions formed by coupled WPT and energy constraints.Source: 2) Delayed Feasibility in Standard… · p. 9

3) Advantages of the Proposed Co-QPSO:

  • 190.06 Mb: Co-QPSO’s maximum aggregate throughput, with classical baselines yielding a 5.3% to 17.2% lower sum-rate; the solution satisfies HRLLC and energy-neutrality requirements.The heterogeneous swarm pairs global exploration by Hunter particles with local exploitation by Safety particles.Source: 3) Advantages of the Proposed Co-QPSO · p. 9
  • Population-based Co-QPSO, GA, DE, and SA have worst-case time complexity O(N_p · T_max · K), while finite-difference SCA scales as O(T_max · K^2).The paper notes that SCA’s quadratic dependence on time steps makes it more computationally burdensome as mission duration or discretization density increases.Source: 3) Advantages of the Proposed Co-QPSO · p. 9

C. Optimality Analysis

  • The analysis defines UB-Shannon as an infinite-blocklength, mobility-relaxed ceiling and UB-FBL as a tighter bound restoring FBL rates while retaining relaxed mobility constraints.The achieved Co-QPSO solution enforces integer blocklengths and physical UAV trajectory and velocity limits.Source: C. Optimality Analysis · p. 9
  • 98.04%: Co-QPSO achieved this fraction of the realistic UB-FBL bound, leaving a 1.96% algorithmic optimality gap; its throughput was 87.89% of idealized Shannon capacity.The comparison separates the FBL overhead from the gap between UB-FBL and the achieved solution.Source: Figure 5 · p. 9, C. Optimality Analysis · pp. 9–10, Figure 6 · p. 10

D. Robustness Analysis

QIEN's Co-QPSO remains feasible as energy margins tighten and mission size grows, while benchmark methods struggle with extended missions. The optimized trajectory balances solar harvesting, communication, and continuous robot power delivery under energy-neutral operation.

D. Robustness Analysis

  • A 15% safety margin reduces maximum throughput by 5.60%, from 190.06 Mb at 0% margin to 179.42 Mb.Intermediate results are 186.35 Mb at 5% and 182.96 Mb at 10%.Source: D. Robustness Analysis · p. 10

E. Scalability Analysis

F. Convergence Analysis

  • Co-QPSO reaches a high-throughput feasible solution by iteration 400, satisfying εtot(tk) ≤ 10^-9 hundreds of iterations faster than the benchmarks.PSO remains in penalty regions for most of the search, while standard QPSO takes significant iterations to escape infeasibility.Source: F. Convergence Analysis · p. 11

G. Trajectory Optimization

  • The optimized UAV dynamically varies its altitude, coordinating movement with the ground robot while maintaining the required station safety distance.Its starting and ending altitudes are near 1055 meters.Source: G. Trajectory Optimization · p. 11

H. Energy and WPT Performance

  • Co-QPSO balances solar harvesting and power consumption while keeping robot WPT between the 2.0 W minimum and 2.5 W maximum throughout the mission.The power allocation adjusts with UAV–robot distance, and energy neutrality is maintained at each time step without surplus.Source: H. Energy and WPT Performance · p. 11

V. CONCLUSION

  • 190 Mb throughput, energy-neutral operation, and continuous 2–2.2 W robot power delivery summarize QIEN's mission-level result, while classical PSO and QPSO fail to find feasible solutions for large problems.The conclusion reports a 0 W surplus margin at every time step and HRLLC reliability of εtot(tk) ≤ 10^-9.Source: §V · p. 11

APPENDIX A CONCAVO-CONVEX ANALYSIS

The appendix establishes that the joint objective and feasible region are non-convex. Discrete blocklengths, energy and WPT constraints, and time-coupled mobility decisions contribute to this structure.

APPENDIX A CONCAVO-CONVEX ANALYSIS

  • Integer blocklengths make the FBL problem mixed-integer: the discrete domain of n_i breaks the continuity needed for convexity.The continuous relaxation is concave for εtarget < 0.5, but n_i is constrained to Z+.Source: Appendix A · p. 12

P WPT

  • Energy sustainability and WPT constraints also create non-convex feasible regions through altitude-dependent harvesting and power–distance coupling.The energy constraint includes a nonlinear elevation factor, while the intersection of WPT and upper-bound power constraints is non-convex.Source: Appendix A · p. 12, P WPT · p. 12
  • Problem P1 is fundamentally non-convex because its objective has an indefinite Hessian and its constraints combine non-convex functions with integer variables.Mobility constraints couple decisions across time steps and propagate power–distance coupling through the mission horizon.Source: P WPT · p. 12, Appendix A · p. 12

APPENDIX B ALGORITHM JUSTIFICATION

The appendix argues that Co-QPSO fits QIEN's discrete-continuous, tightly constrained trajectory problem better than several alternative optimization approaches. Its rationale centers on native integer handling, whole-horizon decisions, and heavy-tailed exploration.

A. Theoretical Justification for Algorithm Selection

  • QIEN's coupled, discrete-continuous search motivates a heavy-tailed metaheuristic rather than gradient-based or classical evolutionary alternatives.The appendix theoretically justifies this selection against those approaches.Source: A. Theoretical Justification for… · p. 12

1) Limitations of Convex Approximations (SCA/BCD):

  • SCA and BCD relax integer blocklengths, but rounding relaxed FBL solutions can violate the 10^-9 reliability constraint; Co-QPSO handles blocklengths natively as discrete variables.The passage attributes rounding risk to the high sensitivity of Q^-1(·) in the FBL regime.Source: 1) Limitations of Convex… · p. 12

2) Structural Incompatibility with DRL and Lyapunov Optimization:

  • The appendix argues that DRL's local updates and soft constraint penalties cannot guarantee 10^-9 reliability, while Lyapunov's per-slot decisions miss whole-horizon mobility coupling.Co-QPSO treats the K-step trajectory as one decision vector, preserving early harvested energy for later WPT needs.Source: 2) Structural Incompatibility with DRL… · pp. 12–13

3) Probabilistic Superiority over GA and DE:

  • GA's Gaussian jumps become unlikely over large distances and DE loses exploration as its population clusters, whereas QPSO's Laplace steps have heavier tails for tunneling through infeasible regions.The appendix presents this as a probabilistic rationale for exploration in the constrained MINLP.Source: 3) Probabilistic Superiority over GA… · p. 13
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