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Decoding the Nature of Flapping Flight by port-Hamiltonian System Theory

Periodic Reporting for period 3 - PORTWINGS (Decoding the Nature of Flapping Flight by port-Hamiltonian System Theory)

Reporting period: 2021-10-01 to 2023-03-31

What are the secrets of bird flights? After 500 years from the first studies of Leonardo da Vinci, we understand much better the principles, but we are far from having decoded the various details of the interaction between the wings motion and the fluid around it which allows birds to fly. In PortWings we have the ambition to change this by using novel modeling methods based on Port Hamiltonian System theory to deeply understand the multi-physics described by coupled Partial Differential Equations (PDEs) involved and then build new mechatronic prototypes which use the developed theory together with innovative engineering techniques in design and materials to built a new robotic bird prototype. If we will manage to do that, the knowledge gained in the process will have a multitude of applications in energy, biology and all those filelds where multi-physics and control of complex dynamics plays a role.
Our work performed is divided into four pillars: P1) Modeling and Simulation, P2) Validation, P3) Realization, and P4) Optimization:

P1) Modeling and Simulation:

In this first period, we have gone back to the first principles of physics to reconsider how we can model multi-physical systems related to fluid dynamics in a way which would shift the paradigm to a real composable methodology: a real “LEGO of physics”: a LEGO-piece for the kinetic energy of the fluid, another one for the potential energy of the fluid, another piece to represent viscosity effects in the fluid, another LEGO-piece for the rigid/flexible structure placed in the fluid and so forth.
We performed a careful physical modeling procedure to build a coordinate-free, port-Hamiltonian model of fluid-solid interconnection. The work was done in an incremental way, first describing ideal fluid dynamics (no viscosity) in the desired setting, then extending the theory to viscous fluids. Subsequently we developed a way to treat fluid-solid interconnection system in the proposed language by relaxing the assumption of fixed spatial domains for the fluid, and defining a way to dynamically impose constraints in the interface of the two systems.

The mathematical models developed in the first two years of the project so far cannot be readily implemented using turnkey numerical tools. The current challenge for the next part of the project is the developement of a discretization strategy that retains the main properties of the continous systems and is computationally efficient. We are currently exploring the possibility of developing novel exterior-calculus based algorithms that avoid the necessity of using two different, topologically dual meshes.

P2) Validation:

Based on previously performed planar PIV measurements in the wake of a flapping robotic-bird wing, we developed a potential flow wake model to serve a design tool for the development of a new robotic bird. We investigated if it would be feasible to validate this model by efficiently automating our 2D PIV setup using robotic manipulators. However, we discovered that a more promising alternative track is to use a volumetric measurement method that uses the recently perfected helium filled soap bubbles as tracer particles. The system components required for this new wind-tunnel setup, such as high-speed cameras, bubble generators and illumination sources, are currently being ordered and we expect to be operational within the next 3 months.

We have also finished the conceptual design (+proof-of-concept , see Fig.) of a new 2D flapping-mechanism that allows for better isolation of 3D effects and should help making understanding thrust and lift generation for a theoretically infinite-span wing. Such 2D setup, which is now in production phase, will be interfaced with the new particle tracking wind-tunnel setup to validate the theory and simulation results of the first pillar.
In addition, the conceptual design of a complementary 3D flapping-mechanism (see Fig.) used for replicating a wide range of full-wing motion profiles is finished and now a proof-of-concept is being finalized.

P3) Realization:

Embedded sensing and actuation are essential for realizing new robotic bird prototypes. To realize this, 3D-printing of electrical conductors has been studied by means of models and new experimental methods for characterization (see Fig.). The gained insights are already applied in embedded 3D-printed sensors for measuring beam deformations and for measuring air flow (See Fig.). In combination with a variable stiffness mechanism by means of an axial load, this already allowed for studying new energy-based control laws that are interesting for flapping wings. Such control method was validated on a proof-of-concept mechatronic prototype (see Fig.).

We have also finished designing a fixed-wing aerial robotic platform that will be incrementally transformed into a morphing-wing robot and then a flapping-wing robot.

P4) Optimization:
We are investigating control strategies based on novel machine-learning tools, which can use the data generated by simulations of the fluid-solid interconneection system of interest, to optimise high level performance metrics (e.g. lift generated along a flapping cycle) for some low level control actions (e.g. torque input at joint level).
Our main achievements in the theoretical side that are beyond the state of the art include the mathematical modeling of fluid-dynamic systems using the geometric port-Hamiltonian theory relying on exterior calculus which is in contrast to the widely used vector calculus formulation. Such exterior calculus formulation has provided great understanding of the underlying physical principles of the system without being contaminated by certain coordinate representations.
Thanks to the multi-physical nature of the port-Hamiltonian theory, such knowledge displayed in the geometric formulation can be easily transfered to other physical domains including electromagnetism and quantum mechanics, which is currently being investigated by the project's PI and some collaborators within another project.

We expect by the end of the project the fluid-dynamical port-Hamiltonian models we developed so far to be coupled with rigid and flexible and simulated with a new structure-preserving discretization tool that we are currently developing.
Such simulated models will be representative of a full robotic-bird with flexible wings performing maneuvers.

By the end of the project, we intend to use the newly-designed wind-tunnel helim-soap bubble setup combined with the mechanical 2D and 3D flapping setups to generate a large amount of data.
Such measurement data will allow us to estimate the pressure distribution over the wing, and from that the aerodynamic loads which will be validated against a custom-designed force/torque measurement system made for us by the NLR.
We also intend at the end of the project to share this data with the public and we are investigating the possibility of using a software- platform that facilitiates this data-sharing process.

Finally, we expect to integrate the knowledge we gain from the separate wind-tunnel experiments to have at least one fully-functional robotic bird that is capable of outdoor flapping-flight and with integrated flow/strain gauge sensors that is superior to its predecessor Robird (see Fig.)
Proof of Concept of 2D flapping setup to be used in wind tunnel
3D printed flow sensors for embedded sensing
The Clear-Flight-Solutions Robird
3D printed electric conductors
Proof of concept of variable stiffness beam with embedded 3D printed strain gauges
Conceptual design of 3D flapping setup