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The body frame of an hexacopter  

The body frame of an hexacopter  

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The purpose of this paper is to present the basic mathematical modeling of microcopters, which could be used to develop proper methods for stabilization and trajectory control. The microcopter taken into account consists of six rotors, with three pairs of counter-rotating fixedpitch blades. The microcopter is controlled by adjusting the angular vel...

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Citations

... Attitude of a UAV is usually described by means of Euler angles defined as pitch (θ), roll (ϕ), and yaw (ψ) [42][43][44]. In this study, we utilized an extended Kalman filter to integrate data from multiple sensors of the MEMS (Micro-Electro-Mechanical System) gyroscope, accelerometer, and magnetometer for attitude estimation. ...
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... BIRD conceptual framework equations[15] since the air vehicle is a hexacopter drone,(2) and(3)present the kinematics equations of the model. BIRD design methodology ...
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... Translational kinetic energy of hexarotor is = 1/2(̇̇) where = × , with 3×3 is the identity matrix and is the mass of hexarotor. The potential energy is = − where is the gravitational acceleration and = 1/2( ) is the rotational kinetic energy where = � , , � ∈ ℝ 3×3 is the inertia matrix [1,4,5,12]. ...
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... The rotational dynamics investigation is achieved by Euler-Lagrange and Newton-Euler methods. The Newton-Euler method sums all the forces that impact the quadrotor body [12,22]. The main Newton-Euler equation is given as: (17) where is generated torques by rotors, is the angular acceleration generated by the inertia of the quadrotor, x are centripetal forces, Γ is gyroscopic forces. ...
... The resultant equation of angular acceleration in the body frame can be transformed from the body frame to the inertial frame by finding the inverse of the above equations as follows: (22) The linear and angular acceleration vector of the system will be as follows: ...
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... From the literature survey [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], it was found that the octocopter-based frame has been used for high-stability-based/high-payload-based applications; thus, it was implemented in this work. The application addressed in this work was very challenging; therefore, instead of a complicated design, a simple configuration was imposed, as follows: ...
... Length of the connecting arm Thickness of the connecting arm (6) Generally, an FR ratio of 8-to-10 is more suitable for long arms, so the FR ratio was assumed to be 10, as follows: ...
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... which shows thatV is non-positiveV ≤ 0 and in particular, V = 0 for e 2 = 0 regardless the values of e 1 . Note that e 2 = 0 impliesė 2 = 0 and substituting (21) into (18), one may notice that e 2 = 0 is only achieved by setting e 1 = 0. This means thaṫ V = 0 is only attained at the origin. ...
... In this section, the hexacopter is regarded as a point of mass but without size [12], the translational motion of the hexacopter in the inertial coordinate system N-E-D is derived in this subsection. ...
... where v is the control variable, the error dynamic can be obtained by substituting the formula (13) into (12). ...
... The Unmanned Aerial Vehicles (UAVs) known as drone, have been used in many fields such as agriculture, transportation, navigation, and military fields. UAVs have many types, including fixed-wing [1], quad-rotor [2], hexacopter [3], and helicopter [4]. Among them, the quadrotor UAV is many interested from researchers due to simple structure, and potential to hover, takeoff, and land in small areas. ...