Kei Senda

Department of Mechanical Systems Engineering

Kanazawa University

**
Towards Flapping-of-Wings Flight of a Butterfly from Robotic Controls**

This talk is composed of two parts: the flapping-of-wings flight of a
butterfly and the robotic control using a neural oscillator and
modulator. The former is conducted as a preliminary study for
biologically inspired robotics. The latter illustrates how this robotic
engineer realizes a robotic controller using a neural oscillator.

The first part discusses flapping of wings of a butterfly, which is
rhythmic and cyclic motion. The objective of this part is to clarify
the principle of a stable flapping-of-wings flight. First, a dynamics
model of a butterfly is derived for analyses by Lagrange's method, where
the butterfly is considered as a rigid body system. Second, a simple
method and a vortex method are applied to make a simulator where the
methods calculate the aerodynamic force. Next, an experimental system
with a low-speed wind tunnel is constructed for fundamental data of
flapping-of-wings motion, where the system measures the aerodynamic
force and the motion simultaneously by a balance and an optical
measurement system. Validity of the mathematical model is examined by
comparing the measured data with the numerical results. A periodic
orbit of a flapping-of-wings flight is searched so as to fly the
butterfly model. Furthermore, numerical computation examines the
stability of a flapping-of-wings motion generated by a neural network
oscillator.

The latter part presents two methods to generate rhythmic and cyclic motions observed in insects by using oscillators and modulators. The proposed methods enable to specify the approximation accuracy of the generated trajectory to the target one even though typical recurrent neural networks cannot. One of the methods is a Fourier series method based on a nonlinear oscillator generating sinusoidal motion and the Fourier series. The other is a modulation method based on a recurrent neural network oscillator and a layered neural network modulator. The realized dynamics has the desired trajectory as a limit cycle. The modulation method can store some trajectories in a network, which is suitable for feedback control design. This study derives controls containing the proposed methods for a space robot, where the system is under a nonholonomic constraint of the angular momentum conservation. The effectiveness of the proposed methods is examined by numerical simulations of reorientation of the space robot using a cyclic motion of the manipulator and/or a feedback control.

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