CDS Lecture Series

Tuesday, August 5, 2003, 2:00 p.m.

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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