Trajectory Optimization of Morphing Aerial Vehicles Based on Mid-Fidelity Aeroservoelastic Models

Technical Summary: Trajectory Optimization of Morphing Aerial Vehicles Based on Mid-Fidelity Aeroservoelastic Models

Problem Statement
Morphing aerial vehicles offer potential advantages in maneuverability and fuel efficiency compared to fixed-wing configurations. However, the trade-off between performance gains and the control costs required for dynamic, unsteady maneuvers remains under-explored. Existing literature often relies on quasi-steady aerodynamic analyses or low-fidelity models that neglect the complex, coupled interactions between unsteady aerodynamics, structural flexibility, and control actuation. Furthermore, previous trajectory optimization studies frequently omit the physics-based cost of actuation or fail to integrate full six-degree-of-freedom (6-DOF) flight dynamics with high-fidelity aeroservoelastic models. Consequently, there is a lack of rigorous frameworks capable of quantifying the true maneuverability benefits of morphing while accounting for the energy required to overcome instantaneous aerodynamic hinge moments.

Methodology
This study addresses these gaps by integrating a trajectory optimization framework with a mid-fidelity aeroservoelastic model. The methodology comprises three primary components:

1. Aeroservoelastic Modeling: The authors utilize the open-source SHARPy package, which couples a non-linear multi-body structural dynamics solver (based on Geometrically Exact Beam Theory, GEBT) with an Unsteady Vortex Lattice Method (UVLM) for aerodynamics. The model represents an aircraft with flexible, high-aspect-ratio wings and morphing winglets that rotate around articulated joints. The system is formulated as a set of Differential-Algebraic Equations (DAEs) that capture the interaction between structural deformation, unsteady wake effects, and 6-DOF flight dynamics.
2. Hybrid Trim Procedure: To establish valid initial conditions for dynamic maneuvers, a hybrid static-dynamic trimming procedure is employed. This approach combines a static algebraic solution with a dynamic optimization over a short horizon to ensure the aircraft reaches a stable, fully coupled equilibrium, avoiding the convergence issues common in purely static approaches for flexible, multi-body systems.
3. Trajectory Optimization with Physics-Based Cost: The trajectory optimization problem seeks to minimize a cost function subject to system dynamics and operational constraints. A key innovation is the inclusion of a physics-based control cost model. Unlike traditional quadratic cost functions, this model calculates actuation effort using the principle of virtual work, directly computing the power required to overcome aerodynamic hinge moments. This captures the non-linear, state-dependent nature of morphing actuation, including the potential for aerodynamic coupling to reduce resistance.

Key Contributions

• Integrated Framework: The paper presents a novel framework that couples high-fidelity, unsteady aeroservoelastic dynamics with trajectory optimization, explicitly accounting for 6-DOF flight dynamics and articulated joint constraints.
• Physics-Based Control Cost: The study introduces a control cost model that moves beyond simple quadratic penalties, utilizing aerodynamic loading data to quantify the actual energy required for morphing and conventional control surface deflections.
• Decoupling of Lift and Pitch: The research demonstrates how morphing winglets can be used to decouple lift generation from pitch control, fundamentally altering the aircraft's trim capabilities.

Results
The framework was applied to an aircraft with morphing winglets across four scenarios:

• Trim Analysis: The morphing configuration successfully achieved steady-state trim across a broad velocity range (27.5 to 40 m/s), whereas rigid and elastic fixed-wing configurations were limited to single trim speeds. By modulating spanwise lift distribution, the morphing winglets decoupled lift requirements from the elevator, expanding the operational flight envelope.
• Pull-Up Maneuver: In a maximum altitude gain maneuver, the morphing configuration achieved a 28.95% increase in altitude gain compared to the non-morphing flexible baseline. However, this performance gain came at a significant cost, with the morphing configuration requiring approximately 40 times more control energy (22.27 J vs. 0.55 J).
• Banked Turn Maneuver: In a lateral displacement maneuver, the morphing configuration improved performance by 8.62% (increasing lateral displacement) while simultaneously reducing total control cost by 13.40%. This efficiency was attributed to the strategic coordination of ailerons and winglets in opposing directions, which canceled aerodynamic resistance and reduced hinge moments.
• Reachability and Obstacle Avoidance: Reachability analysis showed that morphing enabled the aircraft to reach target altitudes (0.9 m) that were infeasible for the non-morphing baseline. In an obstacle avoidance scenario, the morphing configuration reduced total control cost by 65.65% (1.18 J vs. 3.43 J). This was achieved by exploiting aero-mechanical coupling to offload aerodynamic loads from the ailerons, allowing the morphing surfaces to maneuver with minimal power consumption.

Significance and Claims
The authors claim that this work underscores the potential of wing morphing to achieve extreme maneuvers with superior energy efficiency, provided that control strategies are optimized to exploit aero-mechanical coupling. The study highlights that the control cost penalty associated with morphing is not absolute; through intelligent control allocation, morphing can be both operationally superior and energetically efficient.

The paper emphasizes that the combination of trajectory optimization and high-fidelity aeroservoelastic modeling is essential for accurately quantifying the dynamic maneuver capabilities of morphing aircraft. The authors note that while the current framework is computationally intensive, it provides a necessary foundation for future multi-disciplinary design optimization, potentially aided by reduced-order modeling techniques to improve computational tractability. The findings suggest that morphing can significantly expand the flight envelope and enhance maneuverability, but these benefits are highly dependent on the specific maneuver and the ability to coordinate control surfaces to mitigate actuation costs.