Gradient-based Nested Co-Design of Aerodynamic Shape and Control for Winged Robots

TL;DR

This paper presents a general-purpose, gradient-based, nested co-design framework where the motion planner solves an optimal control problem and the aerodynamic forces used in the dynamics model are determined by a neural surrogate model to model complex subsonic flow conditions encountered in aerial robotics.

Abstract

Designing aerial robots for specialized tasks, from perching to payload delivery, requires tailoring their aerodynamic shape to specific mission requirements. For tasks involving wide flight envelopes, the usual sequential process of first determining the shape and then the motion planner is likely to be suboptimal due to the inherent nonlinear interactions between them. This limitation has been motivating co-design research, which involves jointly optimizing the aerodynamic shape and the motion planner. In this paper, we present a general-purpose, gradient-based, nested co-design framework where the motion planner solves an optimal control problem and the aerodynamic forces used in the dynamics model are determined by a neural surrogate model. This enables us to model complex subsonic flow conditions encountered in aerial robotics and to overcome the limited applicability of existing co-design methods. These limitations stem from the simplifying assumptions they require for computational tractability to either the planner or the aerodynamics. We validate our method on two complex dynamic tasks for fixed-wing gliders: perching and a short landing. Our optimized designs improve task performance compared to an evolutionary baseline in a fraction of the computation time.

Figures (6)

• Figure 1: Overview of the proposed co-design pipeline. The airfoil parameterization is mapped to aerodynamic coefficients by a differentiable neural surrogate, from which a local surrogate is built and embedded in the system dynamics. A nonlinear trajectory optimization problem, defined by task objectives and constraints, is then solved and the resulting optimal trajectories evaluated. Gradients are propagated through the solver via implicit differentiation, and through the remaining components via analytical and automatic differentiation, enabling end-to-end optimization.
• Figure 2: Glider schematic. The red dots indicate the centers of mass of the fuselage, wing, and elevator. The notation is described in Tab. \ref{['tab:glider-parameters']}
• Figure 3: Airfoil shape evolution across iterations for the perching (a) and landing (b) tasks. The geometries progressively adapt to the aerodynamic requirements of each task.
• Figure 4: Comparison of the Lagrangian cost between our framework and the evolutionary algorithm Bergonti_2024 for the perching (a) and landing (b) tasks. For the evolutionary algorithm, the best fitness value found across all individuals in the current and all previous generations is plotted. The x-axis shows CPU time in minutes.
• Figure 5: Degenerate airfoil obtained by optimizing lift-to-drag ratio without the NeuralFoil confidence constraint. The geometry collapses to an aphysical shape with near-zero surrogate confidence.