An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

Round 1

Reviewer 1 Report

 - The description of the state of the art needs to be given more attention. The reference 15 is a comparative study, and not a study on representation theory. Prof. Clifford introduced Bi-quaternions to add the position information. To my opinion there is not such "quaternion formula for Dual-quaternion"! Could you please elaborate the matter? Reference 12 is based on the geometrical construct of screw theory on the analytical basis of Lie theory. A Lie Algebra should be associated with a Lie group, and expressing kinematics is described using Lie Algebra is not quiet right. Reference 13 introduces the product of exponentials, which dffers from exponential Algebra, if such Algebra exists!

 

 

 - Relation (7) is the result of a nonlinear tranformation on unit quaternions. Hence simple adjoint mapping of a vector does not seem to yield the rotation of the vector, since the length of the vector varies/scales. Could you please provide the relation, including examples, through which a rotation conducted on a vector yields the correct answer? Could you also please mention at which points/sections of references 2, 3, and 12 the cited statements after relation (7) are stated? The continuation of the review requires the answer to these questions.

Author Response

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Reviewer 2 Report

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