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# Inertial and body-fixed frame of quadrotor.

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The paper focuses on mathematical modelling of a quadrotor and identification of parameters used in presented models. There are several models of the quadrotor that can be used to design a controller. The nonlinear model is presented with respect to the body-fixed frame and also to the inertial frame. The next model is defined in terms of quaternio...

## Contexts in source publication

Context 1
... direction of the rotation. Propellers with the angular speed ω1 and ω3 spin counter-clockwise and the other two spin clockwise. The alteration of the position and the orientation is reached by varying the thrust of a specific rotor. Angular velocities corresponding to the inertial frame EI ( ζ ) and the body- fixed frame EB (ƞ) are presented in Fig. ...
Context 2
... that the quadrotor is a rigid body, the dynamics of the quadrotor can be described using Newton-Euler equations. Several forms of mathematical models can be derived. In [1] a piecewise affine model was used to design a switching model predictive attitude controller. A linearized model of the quadrotor was used in [12] to design a linear quadratic (LQ) controller. This article focuses on the nonlinear model with respect to the inertial frame and also to the body-fixed frame, the model described by quaternions and the model of the quadrotor near the hover position. Each propeller rotates at the angular velocity ω i producing the corresponding force F i directed upwards and the counteracting torque directed opposite to the direction of the rotation. Propellers with the angular speed ω 1 and ω 3 spin counter-clockwise and the other two spin clockwise. The alteration of the position and the orientation is reached by varying the thrust of a specific rotor. Angular velocities corresponding to the inertial frame E I ( ζ ) and the body- fixed frame E B ( ƞ ) are presented in Fig. 1. The rotation matrix from E B to E I is an orthogonal matrix given by equation (1), where C angle and S angle designate cos(angle) and sin(angle) respectively [13, ...

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... The first kind uses a system model to capture the physical system's dynamics [13,24,46]. For example, a set of differential equations [14] or a machine learning model can be used to describe the motion of a quadcopter. The second kind of physical invariant refers to sensor correlation, where multiple (heterogeneous) sensors correlatively respond to the same physical aspect at the same time [2,28,54]. ...
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