Organizations: The authors are with the Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing, 100871, China
Winged blimps operate across distinct aerodynamic regimes that cannot be adequately captured by a single model. At high speeds and small angles of attack, their dynamics exhibit strong coupling between lift and attitude, resembling fixed-wing aircraft behavior. At low speeds or large angles of attack, viscous effects and flow separation dominate, leading to drag-driven and damping-dominated dynamics. Accurately representing transitions between these regimes remains a fundamental challenge. This paper presents a hybrid aerodynamic modeling framework that integrates a fixed-wing Aerodynamic Coupling Model (ACM) and a Generalized Drag Model (GDM) using a learned neural network mixer with explicit physics-based regularization. The mixer enables smooth transitions between regimes while retaining explicit, physics-based aerodynamic representation. Model parameters are identified through a structured three-phase pipeline tailored for hybrid aerodynamic modeling. The proposed approach is validated on the RGBlimp platform through a large-scale experimental campaign comprising 1,320 real-world flight trajectories across 330 thruster and moving mass configurations, spanning a wide range of speeds and angles of attack. Experimental results demonstrate that the proposed hybrid model consistently outperforms single-model and predefined-mixer baselines, establishing a practical and robust aerodynamic modeling solution for winged blimps.
Figures & tables
Fig. 1 : Overview of the ACM–GDM hybrid aerodynamic model for winged blimps. Using RGBlimp as an example, the Aerodynamic Coupling Model (ACM) captures lift-drag coupling and angle-dependent moments in the high-speed, small-angle-of-attack flight regime, while the Generalized Drag Model (GDM) represents drag-dominated, viscous effects in the low-speed, large-angle-of-attack operating regime. A neural-network mixer provides a smooth, physically regularized transition between the two regimes. The resulting hybrid model reproduces the dominant aerodynamic behaviors of winged blimps across their full operating envelopes, offering a unified and interpretable modeling framework.
Fig. 2 : Illustration of the RGBlimp prototype and schematic representation of its ACM and GDM dynamic models. (a) RGBlimp prototype illustrating the winged envelope and suspended gondola with two thrusters. (b) Side-view diagram demonstrating the mass distribution. (c) Schematic of ACM, capturing lift–drag interactions and angle-dependent moments. (d) Schematic of GDM, representing drag-dominated, viscous effects.
Fig. 3 : Three-phase identification pipeline of the ACM–GDM hybrid model. The flight envelope is partitioned by α1 , α2 , V1 , V2 into ACM, GDM, and transition regions. Phase 1 sets the mixing coefficient λ=0 and uses ACM region data to identify ACM parameters φACM∗ . Phase 2 sets λ=1 and uses GDM region data to identify GDM parameters φGDM∗ , yielding the complete set of physical parameters φ∗ . Phase 3 fixes φ=φ∗ and trains the neural network λ=λ(α,V;ξ) on transition-region data to obtain the network parameters ξ∗ . The procedure produces the identified physical parameters φ∗ and the learned transition parameters ξ∗ .
Fig. 4 : Snapshots of RGBlimp flight experiments illustrating a variety of trajectories, angles of attack, and speeds. (a) Straight upward flight with input (Fl,Fr,Δrˉx)=(4.59gf,4.59gf,−5cm) . (b) Straight downward flight with input (Fl,Fr,Δrˉx)=(1.13gf,1.13gf,0cm) . (c) Spiral upward flight with input (Fl,Fr,Δrˉx)=(7.57gf,3.24gf,0cm) . (d) Spiral downward flight with input (Fl,Fr,Δrˉx)=(3.24gf,2.06gf,0cm) . Each snapshot includes an inset showing the time traces of α and V , along with their instantaneous values at the displayed frame.
Fig. 5 : Steady-state flight data fitted using ordinary least squares to identify the model switching points α∗ and V∗ . (a) Fitted surface of the sideslip coefficient CS as a function of angle of attack α and sideslip angle β in the ACM region. (b) Fitted surface of the lift coefficient CL as a function of α and β in the ACM region. (c) Fitted relation of the yaw drag moment Dψ versus yaw rate r in the GDM region.
Fig. 6 : Learned mixing function λ(α,V) produced by the neural network. (a) Three-dimensional surface of λ(α,V) . (b) Two-dimensional heatmap of λ(α,V) . At the operating point (α∗,V∗)=(0.40rad,0.45m/s) the network outputs λ≈0.678 , indicating that the learned mixing is not strictly symmetric in α and V .
Fig. 7 : Heatmaps of the prediction loss Lmodel for ACM-only, GDM-only, ACM–GDM (hard) and ACM–GDM (NN) evaluated on the test set of 330 input configurations (Fl,Fr,Δrˉx) . The horizontal axis shows the combined thruster PWM level Levelsum=Levell+Levelr ranging from 0 to 16, serving as a proxy for total thrust. The vertical axis shows the moving-mass offset Δrˉx with 11 setpoints from −5 cm to +5 cm. Each cell reports the average prediction loss for the corresponding input configuration across trials.
Model
Region
ACM
GDM
Transition
Total
ACM-only
0.3946
1.0244
1.1429
0.7812
GDM-only
2.0429
0.4670
1.0183
1.2158
ACM–GDM (hard)
0.3946
0.4670
0.7841
0.4892
ACM–GDM (sigmoid)
0.3946
0.4670
0.5429
0.4494
ACM–GDM (NN)
0.3946
0.4670
0.4495
0.4338
TABLE I : Average prediction RMSE ( ×10−3 ) of each model in the ACM region, the GDM region, the transition region (mentioned in Section IV-C ), and the total across the entire flight envelope.
Fig. 8 : Spiral-climb trajectory for input (Fl,Fr,Δrˉx)=(6.05gf,3.24gf,0cm) in the ACM region. Predicted paths from GDM-only and ACM–GDM (NN) are compared with the measured flight trajectory.
Fig. 9 : Straight downward trajectory on the xz plane for input (Fl,Fr,Δrˉx)=(1.13gf,1.13gf,0cm) in the GDM region. Predicted paths from ACM-only and ACM–GDM (NN) are compared with the measured flight trajectory.
Fig. 10 : Cumulative RMSE comparison of translational and angular velocity predictions during a transition maneuver with control input (Fl,Fr,Δrˉx)=(7.57gf,6.05gf,4cm) , illustrating flight evolution from the GDM region to the ACM region. Results are presented for the ACM–GDM (hard), ACM–GDM (sigmoid) and ACM–GDM (NN) models, with inset boxplots summarizing RMSE distributions.
This paper investigates goal-directed tracking control of underactuated blimps with center-of-mass (CoM) reconfiguration. Unlike conventional overactuated blimp designs that rely on redundant actuation for simplified control, this paper focuses on a compact architecture consisting of two thrusters and a movable internal slider, aiming to improve energy efficiency and payload capacity. This hardware-efficient configuration introduces significant underactuation and strong nonlinear coupling between CoM dynamics and vehicle motion. To address these challenges, this paper proposes a bi-level reinforcement learning framework that explicitly decouples task-level CoM planning from continuous thrust control. The outer policy determines a target-dependent CoM configuration prior to flight, while the inner policy generates thrust commands to track straight-line references. To ensure stable learning, this paper introduces a two-stage learning strategy, supported by a convergence analysis of the resulting bi-level process. Extensive simulations and real-world experiments on a 27-goal evaluation set demonstrate that the proposed method consistently outperforms fixed-CoM baselines and PID-based controllers, achieving higher tracking accuracy, enhanced robustness, and reliable sim-to-real transfer.
Miniature hybrid underwater gliders have attracted increasing attention for long-endurance ocean observation and confined-space inspection. Large-range wing reconfiguration offers a promising yet largely unexplored approach for simultaneously enhancing maneuverability and shape adaptability in constrained underwater environments. However, such morphing introduces substantial challenges in mechanical integration, dynamic modeling, and hydrodynamic characterization. This paper presents FoDeGlider, a miniature hybrid underwater glider equipped with two independently actuated wings capable of large-range folding and deflection. To capture configuration-dependent variations in mass distribution, center-of-geometry location, and hydrodynamic loading, a multibody dynamics model is developed by treating wing configuration as a structural variable. A composite rigid body algorithm (CRBA)-based projection formulates the composite inertia, wrench transformations, and component-level hydrodynamics into a unified Fossen-form dynamic model applicable to arbitrary wing configurations. A sequential parameter-identification framework is further proposed to estimate fuselage and wing hydrodynamic coefficients, resulting in an open benchmark dataset for model identification and validation. Extensive experiments are conducted, the results of which demonstrate accurate dynamic modeling and parameter identification across diverse morphing configurations. Gate traversal experiments further validate FoDeGlider's ability to actively reconfigure its morphology during locomotion, enabling enhanced navigation in confined underwater environments.
Yongjian Zhu, Yusen Tao, Feitian Zhang
Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871, China
In this paper, we present a generalized, comprehensive nonlinear mathematical model and conceptual design for the MetaMorpher, a metamorphic Unmanned Aerial Vehicle (UAV) designed to bridge the gap between vertical takeoff and landing agility and fixed-wing cruising efficiency. Building on the successful design of the spincopter platform, this work introduces a simplified mechanical architecture using lightweight materials and a novel wing-folding strategy. Unlike traditional rigid-body approximations, we derive a nonlinear flight dynamics model that enables arbitrary force distributions across a segmented wing structure. This modularity allows for testing different airfoils, mass distributions, and chord lengths in a single environment. As part of this work, various flight modes were specifically tested and analyzed in the Simulink environment. The results show that the model behaves predictably under different structural configurations, demonstrating its reliability as a tool for rapid design evaluation.
Anja Bosak, Dorian Erić, Ana Milas +1
All authors are with the University of Zagreb, Faculty of Electrical Engineering and Computing, LARICS Laboratory for Robotics and Intelligent Control Systems, Unska 3, 10000 Zagreb, Croatia