Modeling and Validation of a Flapping-Wing Robot With Compliant Joint-Based Passively Foldable Wings

Birds can generate sufficient lift and save energy by folding their wings. Inspired by this, we design a flapping-wing robot featuring passively foldable wings with compliant joints. The joints comprise a flexible beam and blocks, enabling asymmetric wing folding motions. The wings are modeled as three segments using Euler-Bernoulli beam theory. We first establish the kinematics and aerodynamics of the wings. Then, we characterize the wing aerodynamics using a rotating test platform to determine relationships between aerodynamic forces, wing bending, and flight parameters. These measurements are subsequently integrated into our dynamic model to simulate inertial and aerodynamic forces. The simulation results demonstrate high fidelity, with force trend similarities exceeding 0.98 and mean squared errors below 0.15 N². Finally, we compare two robot prototypes with foldable and non-foldable wings using the rotating test platform and free flight tests. Results indicate that foldable wings demonstrate superior aerodynamic performance at higher flapping frequencies, exhibiting greater lift and efficiency. These findings highlight the potential of foldable wing designs for applications demanding endurance, biomimetic function, and adaptability.