Wing Trajectory Optimization and Modelling for Flapping Flight
Open Access
- Author:
- Bayiz, Yagiz
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 28, 2021
- Committee Members:
- Mark Maughmer, Outside Unit & Field Member
Hosam Fathy, Special Member
Bo Cheng, Chair & Dissertation Advisor
Xiang Yang, Major Field Member
Asok Ray, Major Field Member
Daniel Haworth, Professor in Charge/Director of Graduate Studies - Keywords:
- Bioinspired Robotics
Aerial Robotics
Locomotion
Flapping Flight
Optimization
Machine Learning - Abstract:
- Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. As a result, optimal flapping wing trajectories are often difficult to identify. Moreover, the vast wing trajectory space available to flapping fliers renders this optimization problem even more arduous. This dissertation aimed to develop the necessary tools to pursue flapping wing trajectory optimization through modeling, optimization, machine learning, and robotics. To achieve this goal, first, a dimensionless and multi-objective wing trajectory optimization framework based on a quasi-steady aerodynamic model was developed. With this framework, the family of optimal wing trajectories maximizing lift generation and minimizing power consumption was identified together with the corresponding Pareto fronts. This optimization was repeated at various Reynolds numbers (Re, from 100 to 8000) and aspect ratios (from 2 to 8) to reveal the sensitivity of the optimal wing trajectories and Pareto fronts to these control variables. These results were later compared with the performance of rotary wings. This study showed that the rotary flight is more power-efficient when the lift requirement is low, whereas the flapping flight is more capable and efficient in generating a high lift. Furthermore, it was also observed that as Reynolds number drops, the flapping wings become more and more preferable compared to the rotary wings. Next, a policy gradient algorithm was implemented on a dynamically scaled robotic wing to train the robot to (locally) optimal wing trajectories for flapping wings at the low Re. This model-less learning scheme avoided the issues observed in model-based trajectory optimization, and it was applied to two distinct scenarios. The first scenario was designed as an efficiency maximization problem for wing trajectories with simple parameterization and two degrees of freedom. In order to investigate the effects of stroke amplitude on the maximal efficiency, the wing was trained repeatedly with various prescribed stroke amplitudes while Re was kept constant. It was observed that as stroke amplitudes increased, the optimum efficiency increased. In the second application, a lift maximization problem at Re =1200 hovering flight was solved. In comparison to the first problem, this application included all three degrees of freedom of the wing kinematics in the learning problem and allowed the significant amount of trajectory space available to flapping fliers. Additionally, the locomotion control was performed by a central pattern generator (CPG) network. The CPG provided a biologically inspired means to generate rhythmic wing trajectories, enabling the application of the algorithms to even more complex problems and reducing the time span of the learning experiments by improving the sample generation speed. The results implied that the deviation from the stroke plane, which was often overlooked in the literature on wing kinematics optimization, might play an important role in lift generation. These studies were among the first to demonstrate that robotic systems can be trained in real-time to find high-performing locomotion strategies in complex fluid environments. As the final contribution of this dissertation, a computationally efficient and data-driven model of flapping wing aerodynamics was developed using Gaussian Process State-Space Models. The developed model dynamically mapped the local wing kinematics to aerodynamic forces/moments, and it was trained and validated using a large dataset of flapping-wing motions collected from a dynamically scaled robotic wing. This dynamic model surpassed the accuracy and generality of the existing data-driven quasi-steady models and captured the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. Furthermore, the existence of this model implied that the unsteadiness of the flapping aerodynamics might pose a lesser problem to fliers’ control systems than originally postulated. In addition, using this model, a comprehensive assessment of the control authority of key wing kinematic variables was provided through a cross-correlation analysis. This analysis revealed that the instantaneous aerodynamic forces/moments are largely predictable by the wing motion history within a half-stroke cycle. Moreover, the angle of attack, normal acceleration, and pitching motion had the strongest effects on the aerodynamic force/moment generation. Combined with the previous contribution, it was concluded that the flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial robots.