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Perch like a bird: bio-inspired optimal maneuvers and nonlinear control for Flapping-Wing Unmanned Aerial Vehicles

C. Ruiz, J. Á. Acosta

TL;DR

The paper tackles the challenge of securely perching a bio-inspired flapping-wing UAV by deriving an analytical optimal approach that minimizes terminal velocity under dynamic and kinematic limits, and by designing a nonlinear adaptive control framework comprising velocity, attitude, and guidance subsystems. The velocity and attitude controllers use Lyapunov-based and averaging techniques to provide stability and convergence across post-stall regimes, while the guidance law ties the optimized trajectory to the inertial frame for accurate path tracking. Key contributions include the first analytic solution to the optimal perching maneuver, a robust nonlinear adaptive control architecture with stability guarantees, and validation against real bird data showing close agreement with natural perching trajectories. The work lays a rigorous foundation for practical onboard perching controllers in FW-UAVs and informs design choices for future bio-inspired perching prototypes.

Abstract

This research endeavors to design the perching maneuver and control in ornithopter robots. By analyzing the dynamic interplay between the robot's flight dynamics, feedback loops, and the environmental constraints, we aim to advance our understanding of the perching maneuver, drawing parallels to biological systems. Inspired by the elegant control strategies observed in avian flight, we develop an optimal maneuver and a corresponding controller to achieve stable perching. The maneuver consists of a deceleration and a rapid pitch-up (vertical turn), which arises from analytically solving the optimization problem of minimal velocity at perch, subject to kinematic and dynamic constraints. The controller for the flapping frequency and tail symmetric deflection is nonlinear and adaptive, ensuring robustly stable perching. Indeed, such adaptive behavior in a sense incorporates homeostatic principles of cybernetics into the control system, enhancing the robot's ability to adapt to unexpected disturbances and maintain a stable posture during the perching maneuver. The resulting autonomous perching maneuvers -- closed-loop descent and turn -- , have been verified and validated, demonstrating excellent agreement with real bird perching trajectories reported in the literature. These findings lay the theoretical groundwork for the development of future prototypes that better imitate the skillful perching maneuvers of birds.

Perch like a bird: bio-inspired optimal maneuvers and nonlinear control for Flapping-Wing Unmanned Aerial Vehicles

TL;DR

The paper tackles the challenge of securely perching a bio-inspired flapping-wing UAV by deriving an analytical optimal approach that minimizes terminal velocity under dynamic and kinematic limits, and by designing a nonlinear adaptive control framework comprising velocity, attitude, and guidance subsystems. The velocity and attitude controllers use Lyapunov-based and averaging techniques to provide stability and convergence across post-stall regimes, while the guidance law ties the optimized trajectory to the inertial frame for accurate path tracking. Key contributions include the first analytic solution to the optimal perching maneuver, a robust nonlinear adaptive control architecture with stability guarantees, and validation against real bird data showing close agreement with natural perching trajectories. The work lays a rigorous foundation for practical onboard perching controllers in FW-UAVs and informs design choices for future bio-inspired perching prototypes.

Abstract

This research endeavors to design the perching maneuver and control in ornithopter robots. By analyzing the dynamic interplay between the robot's flight dynamics, feedback loops, and the environmental constraints, we aim to advance our understanding of the perching maneuver, drawing parallels to biological systems. Inspired by the elegant control strategies observed in avian flight, we develop an optimal maneuver and a corresponding controller to achieve stable perching. The maneuver consists of a deceleration and a rapid pitch-up (vertical turn), which arises from analytically solving the optimization problem of minimal velocity at perch, subject to kinematic and dynamic constraints. The controller for the flapping frequency and tail symmetric deflection is nonlinear and adaptive, ensuring robustly stable perching. Indeed, such adaptive behavior in a sense incorporates homeostatic principles of cybernetics into the control system, enhancing the robot's ability to adapt to unexpected disturbances and maintain a stable posture during the perching maneuver. The resulting autonomous perching maneuvers -- closed-loop descent and turn -- , have been verified and validated, demonstrating excellent agreement with real bird perching trajectories reported in the literature. These findings lay the theoretical groundwork for the development of future prototypes that better imitate the skillful perching maneuvers of birds.

Paper Structure

This paper contains 11 sections, 3 theorems, 38 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Ornithopter dynamics
  3. Optimal perching maneuver
  4. Nonlinear Control
  5. Velocity control: $\Sigma_{V}$
  6. Attitude control: $\Sigma_{\gamma}$
  7. Guidance law: $\Sigma_{p}$
  8. Results
  9. Conclusions and future work
  10. Aerodynamic Model Parameters
  11. Optimal trajectory solution

Key Result

Proposition 1

Consider the velocity error dynamics eV and $V_{R}(t), \dot V_{R}(t), \ddot V_{R}(t)\in \cal{L}_\infty$. For any control gain $k_0$ and $\Gamma_V$ positive, the adaptive state feedback control_ct--control_ct_ad guarantees the boundedness of $e$ and ${\hat{\Theta}}_{{D}_w}^\alpha$ and the convergence

Figures (7)

  • Figure 1: Sketch of the proposed methodology for the autonomous approach for the perching maneuver.
  • Figure 2: Trajectory model for approach maneuver. Three principal points (Initial, Intermediate and Perching) and two phases (Deceleration and Turning).
  • Figure 3: Selection of the minimum deceleration rate (left) and maximum turn rate (right). $V_d$ is the minimum velocity for deceleration, where $\dot{V}_D=0$ at point A. Point B is the magnitude at minimum velocity.
  • Figure 5: Optimal trajectories for $\gamma_0=-0.65 \ rad.$ and $V_0=6 \ m/s$. The sample point highlighted as $\circ$ corresponds to: $x_0=-20$$m$, $z_0=6$$m$, $\dot{V}_D^*=-1.15$$m/s^2$, $\dot{\gamma}_T^*=0.37$$rad/s$, ${V}_P^*=3.5$$m/s$ and $\gamma_P^*=0.69$.
  • Figure 6: Function $\eta^1=\eta(\alpha_R^1)$ for $\alpha_R^1=10 \space deg$ and $k_R=1.2$ and $\eta^2$ for $\alpha_R^2=20 \space deg$ Note that $\eta (\alpha-\alpha_R) \geq 0$ for $\alpha_R<\alpha_s$ even if $\alpha$ is greater than the stall ($\alpha_s$) as $\alpha_R<\alpha_s$.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Remark 1
  • Proposition 1
  • proof
  • Proposition 2
  • Remark 2
  • Remark 3
  • Proposition 3
  • proof
  • Remark 4