29 lines
820 B
Matlab
29 lines
820 B
Matlab
function d = DistanceToSE3(mat)
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% *** CHAPTER 3: RIGID-BODY MOTIONS ***
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% Takes mat: A 4x4 matrix.
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% Returns the Frobenius norm to describe the distance of mat from the SE(3)
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% manifold.
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% Compute the determinant of matR, the top 3x3 submatrix of mat. If
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% det(matR) <= 0, return a large number. If det(matR) > 0, replace the top
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% 3x3 submatrix of mat with matR' * matR, and set the first three entries
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% of the fourth column of mat to zero. Then return norm(mat - I).
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% Example Inputs:
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%
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% clear; clc;
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% mat = [1.0, 0.0, 0.0, 1.2;
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% 0.0, 0.1, -0.95, 1.5;
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% 0.0, 1.0, 0.1, -0.9;
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% 0.0, 0.0, 0.1, 0.98];
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% d = DistanceToSE3(mat)
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%
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% Output:
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% d =
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% 0.1349
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[R, p] = TransToRp(mat);
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if det(R) > 0
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d = norm([R' * R, [0; 0; 0]; mat(4, :)] - eye(4), 'fro');
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else
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d = 1e+9;
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end
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end |