Low Speed Flap-Bounding in Ornithopters and Its Inspiration on The Energy Efficient Flight of Quadrotors
Flap-bounding, a form of intermittent flight, is often exhibited by small birds over their entire range of flight speeds. The purpose of flap-bounding is unclear during low to medium speed (2 - 8 m/s) flight from a mechanical-power perspective: aerodynamic models suggest continuous flapping would require less power output and lower cost of transport. This thesis works towards the understanding of the advantages of flap-bounding and tries to employ the underlining principle to design quadrotor maneuver to improve power efficiency. To explore the functional significance of flap-bounding at low speeds, I measured body trajectory and kinematics of wings and tail of zebra finch (Taeniopygia guttata, N=2) during flights in a laboratory between two perches. The flights consist of three phases: initial, descending and ascending. Zebra finch first accelerated using continuous flapping, then descended, featuring intermittent bounds. The flight was completed by ascending using nearly-continuous flapping. When exiting bounds in descending phase, they achieved higher than pre-bound forward velocity by swinging body forward similar to pendulum motion with conserved mechanical energy. Takeoffs of black-capped chickadees (Poecile atricapillus, N=3) in the wild was recorded and I found similar kinematics. Our modeling of power output indicates finch achieves higher velocity (13%) with lower cost of transport (9%) when descending, compared with continuous flapping in previously-studied pigeons. To apply the findings to the design of quadrotor motion, a mimicking maneuver was developed that consisted of five phases: projectile drop, drop transition, pendulum swing, rise transition and projectile rise. The quadrotor outputs small amount (4 N) of thrust during projectile drop phase and ramps up the thrust while increasing body pitch angle during the drop transition phase until the thrust enables the quadrotor to advance in pendulum-like motion in the pendulum swing phase. As the quadrotor reaches the symmetric point with respect to the vertical axis of the pendulum motion, it engages in reducing the thrust and pitch angle during the rise transition phase until the thrust is lowered to the same level as the beginning of the maneuver and the body angle of attack minimized (0.2 deg) in the projectile rise phase. The trajectory of the maneuver was optimized to yield minimum cost of transport. The quadrotor moves forward by tracking the cycle of the optimized trajectory repeatedly. Due to the aggressive nature of the maneuver, we developed new algorithms using onboard sensors to determine the estimated position and attitude. By employing nonlinear controller, we showed that cost of transport of the flap-bounding inspired maneuver is lower (28%) than conventional constant forward flight, which makes it the preferable strategy in high speed flight (≥15 m/s).
Deng, Purdue University.
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