Quadrotor Equations of Motion

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1、QuadrotorEquationsofMotion1F3M3b3F2F4M2M4bF12a3CMa12ra41bF=F1+F2+F3+F4mga31M=r1⇥F1+r2⇥F2+r3⇥F3+r4⇥F4+M1+M2+M3+M42BNewton-EulerEquationsAωB=pb+qb+rb123Rotationofthrust23vectorfromB2toA300m¨r=405+R405ComponentsintheinertialmgF+F+F+Fframealonga,a,anda1234123u123232323p˙L(F2F4)ppI4q˙5=4L(F3F1)5

2、4q5⇥I4q5r˙M1M2+M3M4rrComponentsinthebodyframealongb,b,u12andb,theprincipalaxes233Howdoweestimatealltheparametersinthismodel?232300m¨r=405+R405mgF1+F2+F3+F423232323p˙L(F2F4)ppI4q˙5=4L(F3F1)54q5⇥I4q5r˙M1M2+M3M4rr4232323pc✓0cs✓˙Roll4q5=401s54✓˙5Pitchrs✓0cc✓˙Yawb3Angularvelocitycompon

3、entsinBa3b2re2Roll,pitchψb1a2aψe115PlanarQuadrotorModela3u=thrustforce1ucosϕ1u=moment2usinϕ1a26StateSpaceforQuadrotorsStateVector•qdescribestheconfiguration⎡x⎤PlanarQuadrotor(position)ofthesystem⎢⎥y•xdescribesthestate⎢⎥⎡y⎤ofthesystem⎢z⎥⎡q⎤⎢⎥⎡q⎤q=⎢⎥,x=⎢⎥q=⎢z⎥,x=⎢⎥⎢φ⎥⎣q!⎦⎢⎥⎣q!⎦⎣ϕ⎦⎢θ⎥⎢⎥⎢⎣ψ⎥⎦⎡x0⎤Eq

4、uilibriumatHover⎢y⎥⎢0⎥•qedescribesthe⎡y⎤0equilibrium⎢z0⎥⎡qe⎤⎢⎥⎡qe⎤configurationoftheq=⎢⎥,x=q=z,x=system00e⎢0⎥e⎢0⎥e⎢0⎥•xdescribesthe⎢⎥⎣⎦⎢0⎥⎣⎦e⎢⎥⎣⎦equilibriumstateof0thesystem⎢⎥⎢⎣ψ0⎥⎦7