Rigid vs. flapping: The effects of kinematic formulations in force determination of a free flying Flapping Wing Micro Air Vehicle

Several studies have focused on deriving kinematic formulations of simulated flapping wing micro air vehicles (FWMAV). However, very few used real-life flight data and none have compared the predicted aerodynamic forces and moments across different kinematic formulation principles. Hence, the present study compares and assesses the quality of simple equations of motion against complex multi-body formulations using real flight data. In particular, the position and attitude of an autonomous flying FWMAV was logged by an external high resolution visual tracking system. States were reconstructed using flight path reconstruction techniques and were used as inputs for the determination of the aerodynamic forces and moments that acted on the FWMAV. Two kinematic models of a 4 wing FWMAV were derived and used to compute the aerodynamic forces and moments: 1) simple Newton-Euler formulation of rigid aircraft equations of motion; 2) complex 5 body kinematic model using D´Alembert´s principle. The results are presented for trimmed flight, as well as for system identification maneuvers characterized by doublet inputs on the rudder and elevator. These results show the difference between both formulations and indicate that rigid body kinematic forms can be used for FWMAV aerodynamic system identification, with the advantageous use in control design of iterative versions of ornithopters, showing an average correlation of 0.98 (out of 1) with more complex formulations. Multi-body kinematics, on the other hand, despite more time-expensive to derive, capture more contributions of the different FWMAV structures as well as the internal forces and moments (like driving motor torque), thus being more suitable for simulation and robust control of complex ornithopters.