AeroVantage ~ Control (Flight & Power) - Equation
Overview:
Note
The following material is from;
A Generic Simulator for Quad-Rotor Unmanned Aerial Vehicles. There is a copy on the removable stick.Equations of Motion:
Figure A1 defines the symbols used in the equations of motion for the dynamic model of a quadrotor flyer in Figure A2. Refer to the original papers for their derivations.
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Symbol: |
Description: |
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x, y, z |
Position relative to the world origin |
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φ |
Roll angle |
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θ |
Pitch angle |
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ω |
Yaw angle |
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Ω i |
Rotor i angular velocity |
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I x, I y, I z |
Moments of inertia for the body |
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J r |
Moment of inertia for a rotor |
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b |
Thrust factor |
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d |
Drag factor |
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l |
Distance from center of gravity to motors |
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U1, U2, U3, U4 |
Intermediate formulations for input to the equations of motion |
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W |
Disturbance due to unbalanced rotor speeds |
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K1, K2, K3 |
The drag coefficients |
Figure A1 – Definition of the symbols used in the equations of motion.
Inputs to the Equations of Motion:
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Total Thrust: |
U1 = b(Ω12 + Ω22 + Ω32 + Ω42) |
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Rolling Force: |
U2 = b(Ω42 - Ω22) |
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Pitching Force: |
U3 = b(Ω32 + Ω12) |
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Yawing Force: |
U4 = d(Ω22 + Ω42 - Ω12 - Ω32) |
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Disturbance: |
Δ = Ω 12 + Ω22 + Ω32 + Ω42 |
The Equations of Motion:
These are the equations from [Boua04], with linear drag added from [Chen03].
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Linear accelerations: |
Angular accelerations: |
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Not yet added. |
Not yet added. |
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Not yet added. |
Not yet added. |
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Not yet added. |
Not yet added. |
Working Papers:
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Last Revised: March 28, 2008