Neuroinspired control strategies with applications to flapping flight

This dissertation is centered on a theoretical, simulation, and experimental study of control strategies which are inspired by biological systems. Biological systems, along with sufficiently complicated engineered systems, often have many interacting degrees of freedom and need to excite large-displacement oscillations in order to locomote. Combining these factors can make high-level control design difficult. This thesis revolves around three different levels of abstraction, providing tools for analysis and design. First, we consider central pattern generators (CPGs) to control flapping-flight dynamics. The key idea here is dimensional reduction we want to convert complicated interactions of many degrees of freedom into a handful of parameters which have intuitive connections to the overall system behavior, leaving the control designer unconcerned with the details of particular motions. A rigorous mathematical and control theoretic framework to design complex three-dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show that flapping-flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of central pattern generator parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using a Hopf bifurcation, we show that tailless aircraft (inspired by bats) alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the central pattern generator network. Results of numerical simulation with a full six-degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach. ii Further, we present experimental micro aerial vehicle (MAV) research with lowfrequency flapping and articulated wing gliding. The importance of phase difference control via an abstract mathematical model of central pattern generators is confirmed with a robotic bat on a 3-DOF pendulum platform. An aerodynamic model for the robotic bat based on the complex wing kinematics is presented. Closed loop experiments show that control dimension reduction is achievable unstable longitudinal modes are stabilized and controlled using only two control parameters. A transition of flight modes, from flapping to gliding and vice-versa, is demonstrated within the CPG control scheme. The second major thrust is inspired by this idea that mode switching is useful. Many bats and birds adopt a mixed strategy of flapping and gliding to provide agility when necessary and to increase overall efficiency. This work explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of nonlinear switching limit cycles from our work on flapping flight. This level of abstraction has been found to be useful in many ways, but it also produces its own challenges. For example, we discuss death of oscillation which can occur for many limit-cycle controllers and the difficulty in incorporating fast, highdisplacement reflex feedback. This leads us to our third major thrust considering biologically realistic neuron circuits instead of a limit cycle abstraction. Biological neuron circuits are incredibly diverse in practice, giving us a convincing rationale that they can aid us in our quest for flexibility. Nevertheless, that flexibility provides its own challenges. It is not currently known how most biological neuron circuits work, and little work exists that connects the principles of a neuron circuit to the principles