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~1tí

it*

where qK = (qK\,qx^Ky9k*)T> K-E, T, or 0\ and qE is the error quaternion. If the observed and target quaternions are equal, then the error quaternion is qE = (0,0,0,1)T and B(qE) is the 3x3 identity matrix.

One goal of the control laws is to minimize the projections of the observed X and Y body axes on the target Z axis; thus, we require that

XoZrs0

Because these projections are the 1,3 and 2,3 components of B = B(qE), Eq.

(18-44) can be written as

y0Z7

Let ip, and £, denote the infinitesimal rotations about the body X, Y, and Z axes required to achieve the target attitude. Then B(qE) transforms vectors from the body to the target frame and is given by

0 0

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