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FLoRa: Flight-Assisted Data Collection from Duty Cycling LoRa Nodes under Energy Constraints

Naresh Babu Kakarla, V. Mahendran

arXiv:2610.09226v1cs.NIcs.LG

TL;DR

UAV collection from duty-cycling LoRa nodes must balance energy-limited routing, hovering, uncertain probing, and decaying freshness. FLoRa combines SA, CMA-ES, and POMDPs, with VIP accounting for failed probes. It outperforms metaheuristic, greedy, and DRL baselines across expected VIP, coverage, and successful collections.

  • Problem

    Energy-limited UAV collection must select which duty-cycling LoRa nodes to visit despite uncertain availability and time-sensitive data.

    Source: §I · p. 1, A. Challenges addressed by FLoRa… · p. 2

  • Method

    FLoRa uses SA for routing, CMA-ES for hover positioning, and POMDPs for probing, with VIP valuing fresh data and penalizing failed probes.

    Source: §I · p. 1, §XII · p. 17

  • Results

    FLoRa gains 30.6%, 27.8%, and 15.2% in total expected VIP over metaheuristic, greedy, and DRL baselines, respectively, and improves coverage and successful collections across those baselines.

    Source: §XII · p. 17

  • Takeaways & Limitations

    FLoRa jointly optimizes path planning, hover positioning, and adaptive probing for fresh data collection in energy-constrained UAV-LoRa networks.

    Source: §XII · p. 17

Abstract

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Data collection using Unmanned Aerial Vehicles (UAVs) is challenging when LoRa IoT Devices (IoTDs) duty-cycle to conserve battery. Under energy constraints, a UAV must decide which IoTDs to visit, in what order, where to hover, and how many times to probe each node, while time-based data freshness decays. Tractably solving this problem requires a multi-level optimization architecture: discrete combinatorial optimization for routing, continuous global optimization for spatial positioning, and sequential decision-making under uncertainty. We propose FLoRa, a Flight-assisted LoRa data collection architecture using Simulated Annealing (SA) for path planning, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for hover positioning, and Partially Observable Markov Decision Processes (POMDPs) for probing IoTDs. To quantify collection utility from duty-cycling nodes, we introduce the Value of Information for Pull-based systems (VIP), a metric that rewards fresh data and penalizes failed probes, imposing well-posedness and preventing indefinite probing when an IoTD is off. Tracking hard battery constraints on every POMDP sample path requires state augmentation, worsening the curse of dimensionality. For tractability, SA and CMA-ES work on the hard battery constraints, while at the POMDP layer we relax them into soft average constraints via Lagrangian relaxation. Since solving the network-wide POMDP is computationally complex, we decompose it into node-level POMDPs by approximating inter-node time dependency using a forward-decomposition technique. Evaluation shows FLoRa outperforms metaheuristic, greedy, and deep reinforcement learning baselines by 30.6%, 27.8%, and 15.2% in total expected VIP, while increasing node coverage by 24.5%, 29.2%, and 8.8%, and successful collections by 24.3%, 25.6%, and 15.2%, respectively.

I. INTRODUCTION

FLoRa addresses UAV collection from duty-cycling LoRa nodes under energy constraints, where routing, hovering, probing, and data freshness interact. It combines methods for these decisions and introduces VIP to account for failed probes.

I. INTRODUCTION

  • VIP rewards fresh data and penalizes failed probes, making freshness utility well-posed when duty-cycling nodes are unavailable.The penalty prevents indefinite probing when an IoTD is off.Source: §I · p. 1
  • Energy-limited UAV tours may visit only a subset of IoTDs, while duty-cycling makes device availability uncertain and collection decisions time-dependent.Selecting a subset under battery constraints is an Orienteering Problem, which is NP-hard.Source: §I · pp. 1–2

A. Challenges addressed by FLoRa framework

  • FLoRa addresses combinatorial route selection, continuous hover positioning, and uncertain sequential probing as distinct optimization challenges.SF transitions make packet-success probability non-differentiable, while proximity, freshness, coverage, and collection probability trade off.Source: A. Challenges addressed by FLoRa… · p. 2

B. Positioning against the state-of-the-art

  • Prior UAV data-collection approaches make assumptions such as always-on or scheduled devices, sufficient battery, fixed probe counts, or no freshness objective.The paper positions FLoRa as jointly addressing energy constraints, duty cycling, freshness, path planning, hovering, and probabilistic probing.Source: B. Positioning against the… · p. 2

C. FLoRa design principles

  • FLoRa assigns path planning to SA, hover positioning to CMA-ES, and probing to POMDPs, with the spatial and temporal layers interacting hierarchically.Hard battery constraints apply to SA and CMA-ES; POMDP probing uses Lagrangian relaxation to impose average energy constraints and avoid state augmentation.Source: C. FLoRa design principles · pp. 2–3
  • Forward decomposition approximates inter-node time dependency using preceding nodes’ expected time and total flight time, enabling sequential node-level POMDP solutions.The node-level expected reward also serves as a scoring function for the heuristic layer.Source: C. FLoRa design principles · p. 3

II. RELATED WORK

Prior UAV data-collection work addresses energy-constrained paths, freshness, and LoRa-specific challenges. FLoRa is set in a pull-based system where a battery-limited UAV selects and orders a subset of IoTDs.

A. Path-Planning with Energy Constraints

  • Earlier path-planning studies optimize trajectories and, in later work, also consider hover positions and energy constraints.The section also notes that many UAV path-planning approaches assume push-based collection, whereas FLoRa uses pull-based probing without prior synchronization.Source: A. Path-Planning with Energy Constraints · p. 4

B. Freshness-Aware Data Collection

  • Freshness-aware studies use AoI or deadline-based metrics such as UoI and VoI, but these assume devices are on and do not handle repeated unanswered probes.FLoRa introduces VIP for pull-based systems with duty-cycling devices.Source: B. Freshness-Aware Data Collection · pp. 4–5

C. LoRa-Based Data Collection

  • LoRa data-collection studies address transmission settings, proximity, trajectory, and freshness, while much of the cited work assumes scheduled duty-cycling or always-on nodes.FLoRa instead considers random duty-cycling.Source: C. LoRa-Based Data Collection · p. 5

III. SYSTEM MODEL

  • Finite battery limits the UAV to selecting and ordering a subset of IoTDs for its tour.The tour starts and ends at the home station.Source: §III · p. 5

A. Data Generation Model

The model represents uncertain LoRa node availability, distance-dependent communication, UAV flight and hover costs, and time-decaying data value. VIP extends deadline-based freshness accounting to failed pull-based probes.

A. Data Generation Model

  • Each IoTD has a mission-level latent availability A_k drawn from Bernoulli(a_k), with known a_k derived from the sensor network's delivery statistics.Availability is treated as relatively static during the UAV tour.Source: A. Data Generation Model · p. 5

B. Communication Model

  • The UAV may hover anywhere within an IoTD's coverage neighborhood, and packet-reception probability decreases with distance under the stated channel model.The hover location l_i is constrained by d_i = ||l_i − c_i|| ≤ d_max.Source: B. Communication Model · pp. 5–6

C. UAV Energy Consumption Model

  • UAV energy use comprises flight between nodes and hovering during data transfer, with node-wise costs accounting for reaching and probing a node.The model also accounts for the return-flight energy from the last IoTD to home.Source: C. UAV Energy Consumption Model · p. 6

D. Data Freshness Model

  • Collected data has time-varying value that decays toward a common deadline and becomes worthless after it.Tour time at each visit includes both flight from the preceding position and hover time.Source: D. Data Freshness Model · p. 6, §IV · p. 6

IV. PROPOSING VIP METRIC: VALUE OF INFORMATION FOR PULL-BASED SYSTEMS

  • VIP assigns positive utility to successfully collected fresh data and a time-based penalty to failed probes, accounting for unsuccessful attempts in pull-based collection.The penalty is intended to discourage excessive probing at low-probability locations or after residual freshness is depleted.Source: §IV · p. 6

V. PROPOSED FLORA FRAMEWORK FOR FRESH DATA COLLECTION

FLoRa formulates fresh UAV data collection as a coupled optimization of visits, hover positions, and probing under an energy budget. Its hierarchical solver addresses the distinct structures of these decisions.

A. FLoRa: Problem Formulation

  • FLoRa maximizes total expected VIP across visited IoTDs while respecting the UAV's hard battery budget, choosing a tour, hover positions, and probe counts.The formulation includes return-flight energy in its total-energy constraint.Source: A. FLoRa: Problem Formulation · p. 7

1) Problem Characteristics:

  • Tour selection is combinatorial, hover positions are continuous, and probe counts are integer-valued, yielding a non-convex, non-differentiable mixed-integer nonlinear program.Step-like spreading-factor transitions in packet-success probability preclude gradient-based methods.Source: 1) Problem Characteristics · p. 7

2) Multi-Objective Nature:

  • The objective balances coverage, freshness, and collection probability: closer hovering improves packet success but costs flight time and reduces freshness available to later nodes.Maximizing coverage can reduce per-node data-collection probability.Source: 2) Multi-Objective Nature · p. 7

3) Computational Complexity:

V. PROPOSED FLORA FRAMEWORK FOR FRESH DATA COLLECTION

  • FLoRa decomposes the problem into tour, hover-position, and probing levels, assigning SA, CMA-ES, and POMDP methods to their respective subproblems.Each level optimizes one decision variable while treating the others as fixed parameters.Source: 3) Computational Complexity · p. 7

VI. HIERARCHICAL SOLUTION FRAMEWORK OF FLORA

FLoRa nests probing optimization within hover-position search and tour planning. Simulated Annealing explores tours, while CMA-ES searches for hover positions without requiring gradients.

VI. HIERARCHICAL SOLUTION FRAMEWORK OF FLORA

  • The hierarchy optimizes tours with SA, hover positions with CMA-ES for each candidate tour, and probing with POMDP for each candidate hover vector.The decomposition matches each decision level to its distinct optimization structure.Source: §VI · pp. 7–8

VII. P1: SOLVING PATH PLANNING USING SIMULATED ANNEALING ALGORITHM

  • SA searches the NP-hard tour space using swap, shift, insert, and delete perturbations, accepting worse candidates probabilistically to escape local minima.Its temperature cools geometrically, reducing acceptance of inferior solutions as the search progresses.Source: §VII · p. 8

VIII. P2: SOLVING POSITIONING PROBLEM USING CMA-ES ALGORITHM

  • CMA-ES samples hover vectors from an adaptive multivariate Gaussian and updates its mean and covariance using top-scoring candidates, without gradients.Its covariance adapts to the objective landscape; the search is suited to narrow ridges associated with spreading-factor transitions.Source: §VIII · p. 9

IX. P3: FINDING OPTIMAL NUMBER OF PROBES USING POMDP APPROACH

P3 chooses how many times to probe each selected IoTD while respecting the remaining UAV battery budget. Lagrangian relaxation replaces sample-path hard battery tracking with an expected constraint and a shadow price.

IX. P3: FINDING OPTIMAL NUMBER OF PROBES USING POMDP APPROACH

  • P3 relaxes the remaining hard battery constraint into an expected constraint because tracking continuous battery levels on every POMDP sample path is computationally intractable.The upper SA and CMA-ES layers retain the hard battery constraint.Source: §IX · p. 9
  • The POMDP maximizes expected VIP across the tour’s nodes subject to expected probe battery use not exceeding the budget remaining after flight.The probe-count tuple determines each node’s VIP and hovering battery consumption.Source: §IX · p. 10, A. Lagrangian Approximation 1 · p. 10

A. Lagrangian Approximation 1

  • Lagrangian relaxation converts the expected-battery constrained problem into an unconstrained objective using multiplier λ.λ acts as a shadow price converting battery use into VIP reward units.Source: A. Lagrangian Approximation 1 · p. 10
  • The method finds the optimal multiplier by bisection, then uses it to compute the optimal probe count at each IoTD.The bisection procedure returns λ*; the probe-count optimization uses that value.Source: A. Lagrangian Approximation 1 · p. 10

B. Forward-Decomposition Approximation 2

The network-wide probing POMDP is approximated by sequential node-level problems, using expected prior-node hover times to represent shared time dependence. Each node’s policy probes while its belief-based threshold holds, then terminates.

B. Forward-Decomposition Approximation 2

  • The formulation makes the hard shared energy constraint a soft expected constraint through Lagrangian relaxation.The node-level reward prices hover energy; flight energy is accounted for in the upper SA/CMA-ES layers.Source: B. Forward-Decomposition Approximation 2 · pp. 10–11
  • Forward decomposition replaces previous nodes’ random hover times with their expectations, allowing each subsequent node to use prior expected time incrementally.This approximation decouples the global shared-time dependence that otherwise requires tracking total time in the POMDP state.Source: B. Forward-Decomposition Approximation 2 · pp. 10–11
  • Each node-level POMDP tracks the posterior probability that the IoTD is available and chooses among idle, probe, or terminate actions.Successful collection requires both device availability and successful channel reception.Source: B. Forward-Decomposition Approximation 2 · p. 11
  • The optimal node policy probes consecutively until its threshold condition fails, then terminates; idle is dominated.The threshold depends on the node’s availability belief and remains unchanged across its probe slots.Source: B. Forward-Decomposition Approximation 2 · pp. 11–12
  • The forward algorithm processes nodes in tour order, debiting expected hover time from the time remaining for successor nodes.It computes the expected probe count from the absorbing chain induced by the consecutive-probe policy.Source: Computing E[ni] · p. 12
  • The authors state that unknown IoTD-level POMDP parameters can be learned feasibly and optimally.Their proposition relaxes the assumption that initial device-availability probabilities are known.Source: Computing E[ni] · p. 12

X. WELL-POSEDNESS OF FLORA FRAMEWORK

The framework uses regularization at several layers to address discontinuities, coupled VIP objectives, repeated failed probes, and rigid energy limits.

X. WELL-POSEDNESS OF FLORA FRAMEWORK

  • CMA-ES smooths abrupt LoRa channel changes at spreading-factor boundaries through Gaussian location selection and weight-based rank estimators.The passage describes this as approximate smoothing of SNR discontinuities.Source: §X · p. 13
  • Unweighted linear scalarization maximizes summed VIP across nodes to handle the multi-objective trade-off under mild convexity assumptions.VIP at each node depends on common residual time, so increasing one node’s VIP can decrease a subsequent node’s utility.Source: §X · p. 13
  • VIP’s delay penalty discourages repeated probes of an inactive node after failed attempts, supporting well-posedness.Without the delay tax, the POMDP would chase an inactive node with repeated probes yielding zero reward or cost.Source: §X · p. 13
  • Lagrangian relaxation converts the rigid global hard energy limit into a soft constraint met in expectation.The passage presents this as regularization of the energy constraint.Source: §X · p. 13

5) Structural regularization using Bi-level energy optimization:

FLoRa separates hard flight-energy management in upper optimization layers from node-level optimization of hovering energy.

5) Structural regularization using Bi-level energy optimization:

  • SA/CMA-ES manage hard flight energy as leaders, while POMDP followers treat flight energy as fixed and optimize hovering energy.CMA-ES uses the POMDP solver as its scoring function, and the layers interact iteratively.Source: 5) Structural regularization using… · p. 13

A. Simulation Setup

FLoRa is evaluated across two spatial scales, two node densities, and multiple UAV battery budgets against greedy, metaheuristic, and learning-based baselines. It leads the reported VIP and collection metrics, with component comparisons showing the benefits of close-enough hovering and global path planning.

A. Simulation Setup

  • The evaluation uses compact 3 km urban and wide-area 12 km rural scenarios, each with N ∈ {20, 40} IoTDs and swept UAV battery budgets.The node layout is scaled fourfold between scenarios; results are averaged over 20 seeds, with 95% confidence intervals.Source: A. Simulation Setup · p. 13

B. Baseline Approaches

  • Five baselines vary path planning and hovering: SSA, GU, GUHO, ACO, and PPO; performance is assessed by total expected VIP, Node Coverage, and expected successful collections.PPO is trained from scratch for each fixed topology, while GUHO adds CMA-ES hover optimization to greedy planning.Source: B. Baseline Approaches · pp. 13–14

C. Total Expected VIP Performance

  • At 642 kJ in the 12 km scenario, FLoRa collects 469 (N = 20) and 955 (N = 40) VIP units while SSA, GU, and ACO collect zero.CMA-ES places the UAV at the nearest node’s coverage boundary; the marginal packet-success reduction is outweighed by lower flight cost.Source: C. Total Expected VIP Performance · p. 14
  • 15.2% average total expected VIP gain over PPO; FLoRa also leads at every battery budget in both scenarios and densities.Across battery levels, FLoRa gains 15.9% (3 km) and 38.9% (12 km) VIP over SSA, and 24.7% (3 km) and 18.3% (12 km) over GUHO.Source: C. Total Expected VIP Performance · p. 14, Figure 6 · p. 15, Figure 7 · p. 15

D. Node Coverage Analysis

  • FLoRa improves Node Coverage over GUHO by 35.3% (3 km) and 17.7% (12 km), and over SSA by 14.6% (3 km) and 29.7% (12 km).At maximum budget, coverage reaches 9.8 nodes (3 km, N = 20) and 6.6 nodes (12 km, N = 20). GUHO can occasionally exceed FLoRa in coverage at 2568 kJ (12 km) despite trailing in VIP.Source: D. Node Coverage Analysis · p. 14, Figure 8 · p. 15, Figure 9 · p. 16

E. Expected successful collections Analysis

F. Sensitivity Analysis

The sensitivity studies assess SA cooling and forward-decomposition accuracy, while runtime analysis and the conclusion report planning cost and benchmark gains.

F. Sensitivity Analysis

  • FLoRa’s total expected VIP reaches a stable maximum for α ∈ [0.99, 0.995] across N = 20 and N = 40; α = 0.995 is adopted.At α = 0.998, VIP declines modestly under the fixed Kmax = 2000 iteration budget because the schedule under-anneals; α = 0.995 has the lowest variance on the stable plateau.Source: F. Sensitivity Analysis · p. 16, Figure 12 · p. 17

G. Sensitivity Analysis of Forward Decomposition Approximation

  • Forward-decomposition approximation loss stayed below 3% for fixed tours of length 5–9, assessed on a few-node network because the coupled POMDP is analytically complex.The deployed policy’s Monte Carlo mean stayed close to exact DP at every tour length, with the exact value inside or at the edge of the 95% confidence interval.Source: G. Sensitivity Analysis of Forward… · p. 17, Figure 13 · p. 17

H. Runtime Analysis

  • FLoRa’s mean offline planning time was ∼12.1 min, about 2.3× PPO’s ∼5.1 min on the representative N=40, 12 km instance.The reported mean averages 20 seeds; offline planning precomputes the tour, hover positions, and threshold policy, so online execution has no real-time planning burden.Source: Table VII · p. 17, H. Runtime Analysis · p. 17

XII. CONCLUSION

  • 30.6%, 27.8%, and 15.2% are FLoRa’s average total expected VIP gains over metaheuristic, greedy, and strongest DRL baselines, respectively.Node coverage improves by 24.5%, 29.2%, and 8.8%, and expected successful collections by 24.3%, 25.6%, and 15.2%, over those respective baseline categories.Source: §XII · p. 17

APPENDIX A PROOFS OF LEMMA 1 AND LEMMA 2

The proofs show that an optimal node-level probing policy can probe consecutively before terminating, and that belief does not increase over time.

APPENDIX A PROOFS OF LEMMA 1 AND LEMMA 2

  • Removing idle slots before later probes preserves expected VIP while reducing costs, so an optimal policy can use consecutive probes followed by termination.The reduced policy space therefore contains an optimal policy, and the per-slot decision reduces to probe versus terminate.Source: Appendix A · p. 18
  • The belief state is nonincreasing over time: xt+1 ≤ xt.Source: Appendix A · p. 18

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