Analysis and control of flapping flight: from biological to robotic insects

This dissertation explores flapping flight as an effective form of locomotion for unmanned micro aerial vehicles (MAVs). Flapping flight is analyzed from three different perspectives: biological, technological and control-theoretic. To the author's knowledge, this dissertation is one of the first attempts to study flapping flight from a control theory perspective. From a biological perspective, the extraordinary maneuverability of many flying insects is the result of two main factors: (1) their ability to generate and control the production of large aerodynamic forces and torques from unsteady state aerodynamic mechanisms unique to flapping flight, and (2) a hierarchical architecture for their sensory and neuromotor systems. Inspired by real insects, this dissertation proposes a similar hierarchical architecture for the design of a control unit for micromechanical flying insects (MFIs). By combining averaging theory and biomimetic principles, it is shown that flapping flight allows the independent control of five degrees of freedom out of a total of six, as suggested but never experimentally confirmed by many biologists. From a technological perspective, it is shown that a simple proportional feedback is sufficient to stabilize a wide range of flight modes such as hovering, cruising and steering. This is done under the assumption of the linearity of the wing-thorax dynamics and that the feedback's gain is a periodic function with the same period as the wingbeat. This is vital to the successful implementation of flight controllers given the limited computational resources available on MFIs. Moreover, the controller design methodology developed here is not limited to the mathematical models of aerodynamics considered in this thesis, but can be easily adapted to experimental data as it becomes available. Finally, from a control-theoretical perspective, flapping flight is proposed as a compelling example of high-frequency control of an underactuated system present in nature. Averaging theory and separation of timescales is applied rigorously to ground the controller design approach and to highlight trade-offs between mechanical efficiency and overall responsiveness of the body dynamics.

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