Vibrational control: A hidden stabilization mechanism in insect flight

It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.

On Vibrational Stabilization of a Horizontal Pendulum

This paper describes control design and stability analysis for a horizontal pendulum using translational control of the pivot. The system is a one-link mechanism subject to linear damping and moving in the horizontal plane. The goal is to drive the system to a desired configuration such that the system oscillates in an arbitrarily small neighborhood of that desired configuration. We consider two cases: prescribed displacement inputs and prescribed force inputs. The proposed control law has two parts, a proportional-derivative part for control of actuated coordinates, and a high-frequency, high-amplitude oscillatory forcing to control the motion of unactuated coordinate. The control system is a high-frequency, time-periodic system. Therefore we use averaging techniques to determine the necessary input amplitudes and control gains. We show that using a certain oscillatory input, the amplitudes of that input must follow a constraint equation. We discuss the geometric interpretation of constraint equation and stability conditions of the system. We also discuss the effects of damping and relative phase of the oscillatory inputs on the system and their physical and geometric interpretation.