Data-Driven Dynamics Modeling of Miniature Robotic Blimps Using Neural ODEs With Parameter Auto-Tuning

TL;DR

This work tackles the challenge of accurately modeling the dynamics of miniature robotic blimps, where traditional first-principle models struggle with uncertain aerodynamics and high-order nonlinearities. It introduces ABNODE, a two-phase, physics-informed neural ODE that couples a first-principle blimp model with a neural residual and automatic tuning of aerodynamic parameters. Experimental validation on the RGBlimp prototype shows ABNODE achieving substantial improvements in prediction accuracy and generalization over baselines such as the purely first-principle model, SINDYc, BNODE, and KNODE, while demonstrating robustness to time-step variations and initial parameter perturbations. The approach provides a practical pathway for robust, data-driven dynamics modeling of lighter-than-air vehicles and lays groundwork for improved control design under complex aerodynamic conditions.

Abstract

Miniature robotic blimps, as one type of lighter-than-air aerial vehicles, have attracted increasing attention in the science and engineering community for their enhanced safety, extended endurance, and quieter operation compared to quadrotors. Accurately modeling the dynamics of these robotic blimps poses a significant challenge due to the complex aerodynamics stemming from their large lifting bodies. Traditional first-principle models have difficulty obtaining accurate aerodynamic parameters and often overlook high-order nonlinearities, thus coming to its limit in modeling the motion dynamics of miniature robotic blimps. To tackle this challenge, this letter proposes the Auto-tuning Blimp-oriented Neural Ordinary Differential Equation method (ABNODE), a data-driven approach that integrates first-principle and neural network modeling. Spiraling motion experiments of robotic blimps are conducted, comparing the ABNODE with first-principle and other data-driven benchmark models, the results of which demonstrate the effectiveness of the proposed method.

Figures (7)

• Figure 1: An overview of the two-phase ABNODE model training strategy. The first phase optimizes the physical parameters $\bm{\eta}$ of the first-principle model while the second phase focuses on network parameters $\bm{\theta}$.
• Figure 2: Illustration of the RGBlimp prototype and the testing environment. The dashed line represents the trajectory of spiraling motion within the motion capture arena.
• Figure 3: Heat maps of the prediction loss for the first-principle, SINDYc, NODE, KNODE, BNODE and ABNODE models, tested with spiral and linear trajectories featuring various motion configurations. The vertical axis represents different displacements $\Delta_{\overline{\bm{r}}_{x}}$ of the gondola on the slide. The left vertical axis corresponds to the left two columns, and the right vertical axis corresponds to the right five columns. The horizontal axis represents different configurations of the propulsion thrust $F_l$ and $F_r$.
• Figure 4: CMSE of a single test trajectory, demonstrating the changing total loss over time. (Inset) MSE distributions across the entire trajectory, with black dots indicating the average MSE of the entire test trajectory.
• Figure 5: Boxplot of the model prediction loss (Eq. \ref{['eq:allloss']}) across four comparison models. The box represents the interquartile range (IQR), spanning from the first quartile (Q1) to the third quartile (Q3). The line inside the box represents the median while the red diamond dot represents the mean. (Overlap) Beeswarm scatter plot of loss values. Black crosses represent the 48 sets of test results corresponding to each model. The horizontal axis employs a logarithmic scale.