PaperlayerView exact revision on arXiv

Source-linked AI summary

FlapKAD: A Simulation Dataset of Coupled Wing Kinematics and Aerodynamic Dynamics for Flapping-Wing Aerial Vehicles

Haichuan Li

arXiv:2609.38719v1cs.RO

TL;DR

Flapping-wing research lacks large-scale records that align wing kinematics, aerodynamic responses, and flight states in time. FlapKAD provides a synchronized simulation dataset and shared forward-and-inverse sequence benchmark; inverse model performance varies with prediction horizon, and twist-angle errors can exceed flap-angle errors.

  • Problem

    Large-scale records aligning rapidly varying wing kinematics, aerodynamic responses, and flight states are scarce, and experimental measurements can be noisy or temporally misaligned.

    Source: Introduction · p. 1

  • Method

    FlapKAD provides synchronized episode-level simulation records and a shared benchmark evaluating eight time-series architectures in forward and inverse prediction directions.

    Source: Introduction · pp. 1–2

  • Results

    Inverse model performance depends on prediction horizon, and channel-wise evaluation shows twist-angle error can be substantially larger than flap-angle error.

    Source: Results · pp. 6–7

  • Takeaways & Limitations

    FlapKAD provides a reproducible foundation for developing, screening, and comparing sequence-learning methods before physical FWAV testing.

    Source: Conclusion · p. 7

    Reported inference measurements cover model-forward execution, not complete closed-loop control latency including sensing, communication, command generation, scheduling, and actuator delays.

    Source: Inference Efficiency · p. 17

Abstract

from arXiv · show

Experimental investigation and modeling of flapping-wing aerial vehicles are limited by the scarcity of large-scale records that temporally align wing kinematics, aerodynamic responses, and flight states. Existing datasets are often limited in scale and affected by measurement noise and temporal misalignment between rapidly varying wing motion and the associated dynamic response, particularly during high-frequency flapping. We introduce FlapKAD, an episode-structured simulation dataset comprising 2,000 rigid-wing flight episodes and 720,152 valid time steps, with bilateral wing kinematics, aerodynamic responses, and flight states recorded synchronously within a common clock. FlapKAD supports a unified bidirectional sequence-prediction benchmark constructed from the same temporally aligned episodes. The forward task predicts future vertical force coefficients and body vertical velocity from histories of realized flap and twist angles, whereas the inverse task reconstructs future flap- and twist-angle trajectories from the corresponding response histories. A benchmark of eight representative time-series architectures across multiple prediction horizons reveals direction- and horizon-dependent model behavior, systematically higher reconstruction errors for twist angle than for flap angle, and no consistent advantage from increased architectural complexity. FlapKAD provides a reproducible dataset and benchmark for studying coupled wing-kinematic, aerodynamic, and flight-state dynamics in flapping-wing aerial vehicles.

Introduction

Flapping-wing modeling requires temporally aligned records because aerodynamic loading depends nonlinearly on motion history, while rapid flapping makes experimental alignment difficult. FlapKAD pairs synchronized simulation episodes with a common forward-and-inverse benchmark.

Introduction

  • Wing kinematics and aerodynamic loading are nonlinear, temporally structured, and difficult to represent with static models; experimental records are scarce and can suffer noise and temporal misalignment.These issues are particularly challenging during rapid flapping, where acquisition, calibration, and alignment requirements complicate measurement.Source: Introduction · p. 1
  • The benchmark uses shared episodes and protocols for both directions: predicting future aerodynamic responses from realized wing-motion histories and reconstructing future wing motion from response histories.The forward targets include vertical force coefficients and body vertical velocity; inverse targets are realized flap- and twist-angle trajectories.Source: Introduction · pp. 1–2
  • FlapKAD contains 2,000 rigid-wing flight episodes and 720,152 retained simulator observations pairing bilateral kinematics, aerodynamic responses, and flight states.The records are synchronized within a common episode structure.Source: Introduction · pp. 1–2
  • Eight representative time-series architectures are evaluated in both directions at short, intermediate, and long prediction horizons using common partitions, preprocessing, model selection, and metrics.Evaluation includes aggregate and channel-wise errors, parameter counts, and inference efficiency.Source: Introduction · p. 2

Related Work

Prior work learns temporal relationships in flapping-wing aerodynamics and provides valuable experimental datasets, but resources and evaluation protocols are generally organized around particular tasks. FlapKAD adds a shared simulation benchmark for both prediction directions and multiple architecture families.

Related Work

  • Flapping-wing aerodynamic studies use data-driven and reduced-order approaches for load prediction, transient-response estimation, and kinematic optimization, but task definitions and data organization generally target one modeling direction.The cited work includes Bayiz and Cheng 2021b; Pereira et al. 2023; Lan et al. 2022; and Corban, Bauerheim, and Jardin 2023.Source: Related Work · p. 2
  • Open experimental datasets provide synchronized motion and force measurements for forward modeling (Bayiz and Cheng 2021b,a) and inverse mapping (Sharvit, Karl, and Beatus 2025).FlapKAD complements these resources with a larger, repeatable simulation dataset, though the supplied passage does not state a size comparison value.Source: Related Work · p. 2
  • Figure 2 summarizes retained episode lengths and episode-level feature structure; the first two principal components explain 70.4% of episode-level variance.The figure separates early-terminated episodes from those reaching maximum length and shows feature loadings.Source: Figure 2 · p. 3
  • FlapKAD derives forward and inverse benchmarks from the same episode records and evaluates them with common partitions, preprocessing, and metrics.This episode-level organization supports reuse across task directions.Source: Related Work · p. 3
  • The benchmark covers recurrent, convolutional, linear, decomposition-based, patch-based, variable-centered attention, and periodicity-aware model families under a common bidirectional, multi-horizon protocol.Their comparative behavior on flap, twist, aerodynamic-response, and flight-state trajectories is described as less well characterized.Source: Related Work · p. 3

Methodology

FlapKAD preserves synchronized episode records and defines forward and inverse tasks by selecting inputs and targets from shared kinematic, aerodynamic, and flight-state variables. Its representation retains episode boundaries and supports validity-aware sequence construction.

Simulation and Aerodynamic Validation

  • The simulator evaluates left- and right-wing aerodynamic forces independently, using local flow components for angle of attack and relative-flow magnitude for dynamic pressure before applying forces to the vehicle body.Recorded aerodynamic outputs include vertical force components for the two wings and their aggregate.Source: Methodology · p. 3

Dataset Representation and Quality Control

  • Benchmark kinematics are realized left-wing flap and twist angles; response channels are left-wing, right-wing, and aggregate vertical force coefficients plus body vertical velocity.The response vector is specified as four channels in the recorded sequence representation.Source: Methodology · pp. 3–4

Simulation and Aerodynamic Validation

  • The recorded aggregate vertical load is compared with bilateral loads, while Figure 4 also presents phase-resolved loading, bilateral imbalance, and load variation with angle of attack.Its panels include a closure comparison between aggregate load and the sum of left- and right-wing loads.Source: Figure 4 · p. 4

Dataset Representation and Quality Control

  • FlapKAD preserves 2,000 episode boundaries through preprocessing, splitting, and sequence construction, preventing temporal windows from crossing between independent episodes.Figure 3 depicts forward and inverse mappings built from shared episodes, splits, normalization, model interfaces, and metrics.Source: Figure 3 · p. 3, Methodology · p. 4
  • After sign alignment, realized left-wing flap and twist angles represent the benchmark kinematics, consistent with the prescribed bilateral mirror convention for flap and same-sign convention for twist.Figure 5 depicts bilateral trajectories, shared twist kinematics, command tracking, and the joint flap-angle distribution.Source: Methodology · p. 4, Figure 5 · p. 4
  • Stored episodes use 470-sample sequences and a binary validity mask; shorter episodes retain their physical observations and repeat the final valid observation for padding.The mask excludes padded positions from benchmark samples and normalization statistics, while quality control removes episodes failing validity, duration, wing-speed, or aggregate-load criteria.Source: Methodology · p. 4

Kinematic and Multivariate Consistency

  • Figure 6 reports Pearson correlations among kinematic, aerodynamic, and state variables; the matrix is descriptive because Pearson correlation captures only linear association, not causal or complete dynamical dependence.Right-wing flap angle is sign-aligned with the left-wing convention before calculating correlations.Source: Methodology · p. 4, Figure 6 · p. 5

Unified Forward and Inverse Tasks

  • For input length L and horizon H, each task predicts the subsequent H observations from the L observations ending at time t, with forward and inverse mappings exchanging kinematic and response channels.The same released episodes support both directions; task direction depends on input and target selection rather than separate dataset construction.Source: Methodology · pp. 4–5

Experiments

The experiments evaluate forward and inverse sequence prediction across horizons and target variables using a common benchmark protocol. Episode-level sequences support flexible task and temporal configurations while preventing windows from crossing episode boundaries.

Experimental Scope

  • The evaluation examines both task directions, horizon-dependent accuracy, variable-specific errors, and the relationship between accuracy and computational efficiency.Complete efficiency results are reported in the supplementary material.Source: Experiments · p. 5

Benchmark Protocol

  • The benchmark constructs forward and inverse samples from synchronized episode sequences using L = 256, H ∈ {1, 16, 32}, and stride one.The same episodes support different temporal configurations and task directions.Source: Experiments · p. 5
  • Windows are constructed only within valid episode lengths, and all windows from an episode remain in the same train, validation, or test partition.The 2,000 episodes are split into 1,600 training, 200 validation, and 200 test episodes before window construction.Source: Experiments · p. 5

Training and Evaluation

  • Eight representative architectures share a forecasting interface, with task-specific output adapters where required.The best checkpoint for each model, task direction, and horizon is selected using validation MSE and evaluated on the held-out test partition.Source: Experiments · p. 6
  • Performance is evaluated in normalized target space using MSE, MAE, and the 95th percentile of absolute error.Channel-wise MSE and MAE are also reported; standardization statistics use valid training observations only and are applied unchanged to validation and testing.Source: Experiments · p. 6

Results

Across 48 model–task–horizon configurations, architecture rankings vary by task direction and horizon, with no single model winning every setting. Inverse prediction is more horizon-dependent, and twist-angle errors consistently exceed flap-angle errors.

Overall Benchmark Performance

  • Forward rankings are relatively stable and inverse rankings substantially more horizon-dependent; no architecture achieves the lowest MSE in every evaluated setting.Performance is compared separately within each task direction and horizon.Source: Results · p. 6

Flap- and Twist-Angle Prediction

  • Twist-angle MSE exceeds flap-angle MSE across evaluated models and horizons, including the best aggregate model at each horizon.The reported flap/twist MSE pairs are 0.011/0.092 for GRU at H = 1, 0.020/0.137 for TCN at H = 16, and 0.024/0.132 for PatchTST at H = 32.Source: Results · pp. 6–7

Forward Prediction

  • TCN achieves the lowest forward MSE at all three horizons, with small margins over close competitors; at H = 1, its MSE is 0.734 versus GRU’s 0.741.At H = 32, TCN also leads in MAE and E95, with values 0.584 and 1.580, respectively.Source: Results · p. 6, Table 1 · p. 7

Inverse Prediction

  • Inverse winners change with horizon: GRU leads at H = 1, TCN at H = 16, and PatchTST at H = 32.At H = 1, GRU’s MSE, MAE, and E95 are 0.052, 0.127, and 0.473; at H = 32, PatchTST’s are 0.078, 0.169, and 0.566.Source: Results · p. 6, Table 2 · p. 7

Flap- and Twist-Angle Prediction

  • The benchmark does not isolate why twist-angle errors are larger, so aggregate inverse errors should be considered alongside channel-wise results.The authors identify target dynamics, observability, and aerodynamic sensitivity as possible contributing factors, not isolated causes.Source: Results · p. 7

Conclusion

FlapKAD is an episode-level simulation dataset and benchmark that preserves synchronized wing-kinematic, aerodynamic, and flight-state sequences. It supports flexible forward and inverse prediction tasks, and the benchmark highlights the value of evaluating multiple horizons and both aggregate and channel-wise performance.

Conclusion

  • FlapKAD provides a reproducible foundation for developing, screening, and comparing sequence-learning methods before physical FWAV testing.Physical testing complicates precise acquisition of rapidly varying kinematic and aerodynamic quantities through sensor payload or apparatus intrusion, calibration, measurement noise, and temporal synchronization.Source: Conclusion · p. 7

Simulation and Aerodynamic Validation Simulation and Data Acquisition

FlapKAD couples rigid-body simulation, bilateral aerodynamics, and synchronized episode logging. Validation checks the consistency of bilateral and aggregate loads and examines how loading varies across wing phase and angle of attack.

Simulation and Aerodynamic Validation

  • Aerodynamic forces are estimated independently for each wing from local relative flow, which sets angle of attack and dynamic pressure before forces are applied to the rigid body.The moving sampling point’s flow is resolved along local chordwise, surface-normal, and spanwise directions.Source: Simulation and Aerodynamic Validation… · p. 9

Simulation and Data Acquisition

  • Each episode resets and settles before acquisition, then synchronously logs wing kinematics, aerodynamic quantities, and vehicle states until duration or validity limits terminate it.Reset transients are excluded by suspending rigid-body motion and aerodynamic-force application during settling.Source: Simulation and Aerodynamic Validation… · p. 9

Simulation and Aerodynamic Validation

  • The reference dynamic pressure uses the average of left- and right-wing relative-flow speeds, and aggregate vertical load combines the two wing-specific vertical components.Vertical components are expressed along the Unity world-frame y-axis.Source: Simulation and Aerodynamic Validation… · p. 9

Aerodynamic Validation

  • Phase-resolved loads show similar left- and right-wing patterns, while normalized imbalance varies near zero across episodes and angle of attack has a nonlinear relationship with vertical loading.The angle-of-attack analysis also notes dispersion consistent with variation in relative-flow speed, dynamic pressure, flap phase, and other time-varying conditions.Source: Simulation and Aerodynamic Validation… · p. 9

Simulation and Aerodynamic Validation

  • The recorded aggregate load is numerically consistent with the sum of the two wing-specific contributions.The force-closure residual is evaluated using the aggregate channel and the valid evaluated time steps.Source: Simulation and Aerodynamic Validation… · pp. 9–10

Against Real-World Experimental Data Cross-Dataset Evaluation Protocol

The cross-dataset evaluation finds stronger architecture-ranking agreement for forward and short-horizon inverse prediction than for longer-horizon inverse prediction. It compares independently prepared synthetic and real-world benchmarks, so its evidence concerns learning-pattern transfer rather than direct physical-error equivalence.

Cross-Dataset Evaluation Protocol

  • Both datasets use matched channel definitions, model implementations, horizons, and normalized-space evaluation, with a 256-sample input history and episode-level windows.Each dataset is partitioned and standardized independently using its own training episodes; the cross-dataset ranking includes seven shared model families.Source: Against Real-World Experimental Data… · p. 10

Against Real-World Experimental Data

Overall Agreement Between Our Synthetic and Real-World Benchmarks

  • Rank correlations of 0.857–0.893 with complete Top-2 overlap characterize inverse H = 1 and forward H ∈{1, 16}; inverse H = 16 and H = 32 have correlations of 0.536 and 0.286 with no shared Top-2 architectures.The weaker agreement is concentrated in medium- and long-horizon inverse prediction.Source: Against Real-World Experimental Data… · pp. 10–11

Architecture-Ranking Transfer and Horizon-Dependent Gap

  • For inverse prediction, leading architectures diverge with horizon: PatchTST moves from first on synthetic data to fifth on real-world data at H = 32, while GRU moves from fifth to first.TimesNet also improves from fourth to second, and the datasets differ in long-horizon error growth and leading models.Source: Against Real-World Experimental Data… · p. 11

Against Real-World Experimental Data

Interpretation and Scope of the External Validation

  • The comparison uses independent datasets without matched trials, wing geometry, or operating conditions, and does not establish simulator fidelity or zero-shot simulation-to-real transfer.Similar normalized errors should not be interpreted as equal physical prediction error; the comparison instead identifies architecture- and task-level patterns and a remaining long-horizon inverse gap.Source: Against Real-World Experimental Data… · p. 12

Representation

FlapKAD’s episode-based representation supports consistent forward and inverse benchmarks, while its architecture rankings vary by prediction direction and horizon. Efficiency and consistency analyses show trade-offs among model speed, predictive performance, and realized wing motion.

Representation

  • Episode-level quality screening excludes records with non-finite variables or failures in duration, wing-speed, or aggregate-load criteria; compact episodes use 470-sample storage with masks for padding.Short episodes retain their physical sequence and repeat the final valid observation to fill storage positions; padded positions are excluded from benchmark samples and statistics.Source: Representation · pp. 12–13
  • Synthetic-to-real ranking agreement is strongest for inverse prediction at H = 1 and forward prediction at H = 1 and H = 16; inverse Top-2 overlap is absent at H = 16 and H = 32.The comparison covers seven model families evaluated on both datasets.Source: Figure 8 · p. 13, Table 7 · p. 13
  • A fixed episode manifest assigns 1,600, 200, and 200 episodes to training, validation, and testing, and channel standardization uses training observations only.Windows remain within one episode and partition, and fitted transformations are applied unchanged to validation and test data.Source: Episode Splits, Window Counts, and… · pp. 14–15

Kinematic and Multivariate Consistency Bilateral Kinematic Consistency and Command

  • After sign alignment, bilateral flap and twist trajectories agree closely, supporting realized left-wing flap and twist angles as representative benchmark variables.Commanded-versus-realized flap values cluster near identity, while flap–twist phase portraits show coupled cyclic motion varying across episodes.Source: Kinematic and Multivariate Consistency… · p. 16

Model and Training Configurations

  • The final benchmark settings are drawn from saved run metadata, with architecture-specific hyperparameters reported only when used by the corresponding implementation.Optimization, model-selection, architecture, and execution settings are summarized in Tables 11–13.Source: Model and Training Configurations · p. 16

Metric Implementation Details

  • Aggregate errors pool scalar targets across test batches, prediction steps, and channels, while channel-wise metrics are reported separately for each predicted variable.Metrics are evaluated in normalized target space, with forward and inverse tasks evaluated independently.Source: Metric Implementation Details · p. 16

Additional Benchmark Visualizations

Inference Efficiency

  • TCN balances accuracy and cost across tasks, while PatchTST leads long-horizon inverse prediction; Autoformer is slowest without a corresponding accuracy advantage.NLinear and DLinear are fastest but have larger errors, particularly for inverse prediction; GRU is slow despite its one-step inverse lead.Source: Inference Efficiency · pp. 15–17, Table 9 · p. 17, Table 10 · p. 17

Related papers

Loading 2609.38719v1…