• Journal of Advanced Marine Engineering and Technology
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• v.39 no.10
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• pp.1023-1030
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• 2015

The purpose of this paper is to present the basic mathematical modeling of a hexacopter, which could be used to develop proper methods for stabilization and trajectory control. A hexacopter consists of six rotors with three pairs of counter-rotating fixed-pitch blades. This mechanism is an under-actuated, dynamically unstable, six-degrees-of-freedom system. The whole motion of this object consists of translational and rotational motion in three dimensions, where the translational motion is created by changing the direction and magnitude of the upward propeller thrust. The hexacopter is controlled by adjusting the angular velocities of the rotors, which are spun by electric motors. It is assumed to be a rigid body; thus, the differential equation of the hexacopter dynamics can be derived from the Newton-Euler equation. The Euler-angle parametrization of the three-dimensional rotations contains singular points in the coordinate space that can cause failure of both the dynamical model and control. In order to avoid singularities, the rotations of the hexacopter are parametrized in terms of quaternions. This choice has been made considering the linearity of the quaternion formulation and their stability and efficiency. Further, control simulation of a hexacopter applying cascaded-PID control is also presented in this paper.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.36-42
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• 2007

This paper presents mechanical design, fabrication and test of a biomimetic fish robot actuated by a unimorph piezoceramic actuator, LIPCA(Lightweight Piezo-Composite curved Actuator.) We have designed a linkage mechanism that can convert bending motion of the LIPCA into the caudal fin movement. This linkage system consists of a rack-pinion system and four-bar linkage. Four types of artificial caudal fins that resemble caudal fin shapes of ostraciiform subcarangiform, carangiform, and thunniform fish, respectively, are attached to the posterior part of the robotic fish. The swimming test under 300 $V_{pp}$ input with 0.6 Hz to 1.2 Hz frequency was conducted to investigate effect of tail beat frequency and shape of caudal fin on the swimming speed of the robotic fish. At the frequency of 0.9 Hz, the maximum swimming speeds of 1.632 cm/s, 1.776 cm/s, 1.612 cm/s and 1.51 cm/s were reached for fish robots with ostraciiform, subcarangiform carangiform and thunniform caudal fins, respectively. The Strouhal number, which means the ratio between unsteady force and inertia force, or a measure of thrust efficiency, was calculated in order to examine thrust performance of the present biomimetic fish robot. The calculated Strouhal numbers show that the present robotic fish does not fall into the performance range of a fast swimming robot.