1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the...
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1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the frame {a} has its ca-axis pointing in the direction (0, 0, 1) and its a-axis pointing in the direction (-1, 0, 0), and frame {b} has its b-axis pointing in the direction (1,0, 0) and its b-axis pointing in the direction (0, 0, -1). The origin of {a} is at (0, 0, 1) in {s} and the origin of {b} is at (0, 2, 0). Draw the {s}, {a}, and {b} frames, similar to examples in the book and videos, for easy reference in this question and later questions. Write the transformation matrix Tsa. All elements of this matrix should be integers. 14. Use the function MatrixExp6 in the given software to calculate the homogeneous transformation matrix TE SE(3) corresponding to the matrix exponential of 2.3562 -2.3562 114 -1.5708 1.5708 [$]0 => All elements of this matrix should be integers. 15. Use the function MatrixLog6 in the given software to calculate the matrix logarithm [S]0 E se(3) of the homogeneous transformation matrix 0 -1 0 3 1 0 00 T = 0 0 1 1 0 0 01 The maximum allowable error for any matrix element is 0.01, so give enough decimal places where necessary. 1. In terms of the s, s, 2s coordinates of a fixed space frame {s}, the frame {a} has its ca-axis pointing in the direction (0, 0, 1) and its a-axis pointing in the direction (-1, 0, 0), and frame {b} has its b-axis pointing in the direction (1,0, 0) and its b-axis pointing in the direction (0, 0, -1). The origin of {a} is at (0, 0, 1) in {s} and the origin of {b} is at (0, 2, 0). Draw the {s}, {a}, and {b} frames, similar to examples in the book and videos, for easy reference in this question and later questions. Write the transformation matrix Tsa. All elements of this matrix should be integers. 14. Use the function MatrixExp6 in the given software to calculate the homogeneous transformation matrix TE SE(3) corresponding to the matrix exponential of 2.3562 -2.3562 114 -1.5708 1.5708 [$]0 => All elements of this matrix should be integers. 15. Use the function MatrixLog6 in the given software to calculate the matrix logarithm [S]0 E se(3) of the homogeneous transformation matrix 0 -1 0 3 1 0 00 T = 0 0 1 1 0 0 01 The maximum allowable error for any matrix element is 0.01, so give enough decimal places where necessary.
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