Wake Up to the Past: Using Memory to Model Fluid Wake Effects on Robots

Abstract

Autonomous aerial and aquatic robots that attain mobility by perturbing their medium, such as multicopters and torpedoes, produce wake effects that act as disturbances for adjacent robots. Wake effects are hard to model and predict due to the chaotic spatio-temporal dynamics of the fluid, entangled with the physical geometry of the robots and their complex motion patterns. Data-driven approaches using neural networks typically learn a memory-less function that maps the current states of the two robots to a force observed by the "sufferer" robot. Such models often perform poorly in agile scenarios: since the wake effect has a finite propagation time, the disturbance observed by a sufferer robot is some function of relative states in the past. In this work, we present an empirical study of the properties a wake-effect predictor must satisfy to accurately model the interactions between two robots mediated by a fluid. We explore seven data-driven models designed to capture the spatio-temporal evolution of fluid wake effects in four different media. This allows us to introspect the models and analyze the reasons why certain features enable improved accuracy in prediction across predictors and fluids. As experimental validation, we develop a planar rectilinear gantry for two spinning monocopters to test in real-world data with feedback control. The conclusion is that support of history of previous states as input and transport delay prediction substantially helps to learn an accurate wake-effect predictor.

Figures (6)

• Figure 1: Comparing models with and without memory: we study the influence of modeling temporal context in the prediction of fluid wake effects in four domains, including aerial and aquatic scenarios. In dynamic regimes, data-driven predictors must support history and learn the transport delay from the medium. Illustrations of the experimental domains in the third and fourth column are extracted from kharitenko2025spatiotemporal and das2025fish.
• Figure 2: Performance comparison of each of the methods on the four domains. (left) A CFD dataset for two quadrotors kharitenko2025spatiotemporal. (center left) A numerical model of ship-ship interactions varyani2002. (center right) A dataset that captures hydrodynamic interactions between two fish swimming in line das2025fish. (right) Closed-loop tracking on a custom 2D downwash simulator.
• Figure 3: Fish schooling analysis. (left) Scatter plot of true vs. predicted disturbances. The memoryless MLP ($R^2 = 0.57$) exhibits two distinct modes, failing to distinguish periodic phases, while the GRU achieves accurate, unbiased predictions. (right) Convergence basin of the Delay Embedding model. Depending on the random initialisation of $\mu$, the model converges to either the true physical delay (0.33 s, higher $R^2$) or an alias peak (0.148 s, lower $R^2$).
• Figure 4: (left) Average attention weights of the Cross-Attention model over all episodes in the 2D downwash simulator. The profile shows a clear peak near the true physical delay (red dashed line at 0.38s), demonstrating that the model attends to the correct time lag. (right) Learned versus physical delay for the Delay Embedding model across five values of $\Delta z$.
• Figure 5: Out-of-distribution closed-loop ablation on the 2D downwash simulator. Models are trained with physics parameters sampled at $\pm 10\%$ of their nominal values and evaluated at $\pm 10\%$, $\pm 50\%$, and $\pm 75\%$ perturbation levels. Red lines denote the baseline closed-loop RMSE from a 3-seed evaluation trained and evaluated at the nominal (unperturbed) conditions. Degradation preserves the relative ranking across conditions.