By Edward Y. L. Gu
This booklet offers readers with an exceptional set of varied and crucial instruments for the theoretical modeling and regulate of complicated robot structures, in addition to for electronic human modeling and real looking movement new release. Following a complete creation to the basics of robot kinematics, dynamics and keep watch over platforms layout, the writer extends robot modeling tactics and movement algorithms to a miles higher-dimensional, higher scale and extra subtle examine region, specifically electronic human modeling. lots of the tools are illustrated through MATLAB codes and pattern graphical visualizations, supplying a distinct closed loop among conceptual realizing and visualization.
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Additional info for A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming
A 3 by 3 orthogonal matrix that is a member of the following Special Orthogonal Group can perfectly play such a unique role in performing a rotation as well as in representing the orientation of a coordinate frame: SO(3) = R ∈ R3×3 | RRT = I and det(R) = +1 . Based on the deﬁnition, a 3 by 3 rotation matrix R ∈ SO(3) has the following major properties and applications: 1. R−1 = RT . 2. If a rotation matrix R is also symmetric, then R2 = RRT = I. This means that a vector rotated by such a symmetric R successively twice will return to itself.
Its corresponding skew-symmetric matrix is given by ⎞ ⎛ 0 −k3 k2 S(k) = K = ⎝ k3 0 −k1 ⎠ . −k2 k1 0 It can be shown without diﬃculty that for this 3 by 3 unity skew-symmetric matrix, 1. K is skew-symmetric with tr(K) = 0; 2. K 2 is symmetric with tr(K 2 ) = −2; 3. K 3 = −K. 24 2 Mathematical Preliminaries With the above interesting properties owned by the unity skew-symmetric matrix K, we now develop a realistic rotation process, called the k–φ procedure. First, let φk ∈ R3 be deﬁned as a 3 by 1 vector.
One of the most remarkable achievements in recent digital human modeling history was the research and development of a virtual soldier model: Santos in Center for Computer Aided Design at the University of Iowa, led by Dr. Karim Abdel-Malek during the 2000’s [22, 23, 24]. It is now under continuous development in a spin-oﬀ company SantosHuman, Inc. Not only has the Santos mannequin demonstrated its unique high-ﬁdelity of appearance with deformable muscle and skin in a digital environment, but it has also made a pioneering leap and contribution to the digital human research community in borrowing and applying robotic modeling theories and approaches.
A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming by Edward Y. L. Gu