By Edward Y. L. Gu
This ebook presents readers with a great set of diverse and crucial instruments for the theoretical modeling and keep watch over of advanced robot structures, in addition to for electronic human modeling and lifelike movement iteration. Following a complete creation to the basics of robot kinematics, dynamics and keep an eye on structures layout, the writer extends robot modeling strategies and movement algorithms to a far higher-dimensional, better scale and extra refined learn zone, specifically electronic human modeling. lots of the equipment are illustrated by means of MATLAB codes and pattern graphical visualizations, supplying a distinct closed loop among conceptual figuring out and visualization.
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Extra info for A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming
K1 Let a unit vector k = ⎝ k2 ⎠ be referred and projected onto a given k3 frame to be performed for a rotation. Clearly, k 2 = k12 + k22 + k32 = 1. 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.
0 Then, a ˆ × cˆ = S(ˆ a)ˆ c = S(a)c + (S(b)c + S(a)d) = a × c + (b × c + a × d). Likewise, the product between two dual matrices Aˆ = A + B and Cˆ = C + D for four n by n square matrices A, B, C and D is similar to the dual vector products: AˆCˆ = AC + (BC + AD), and also ˆa = Aa + (Ab + Ba) Aˆ without exception. Furthermore, to determine the inverse of a dual square matrix Aˆ = A+ B, we have to ﬁrst assume that the real part A must be nonsingular. Then, the inverse of Aˆ can be determined by Aˆ−1 = (A + B)−1 = A−1 − A−1 BA−1 , which may easily be veriﬁed by testing Aˆ−1 Aˆ = (A−1 − A−1 BA−1 )(A + B) = I + O = I, where I and O are the n by n real identity and zero matrix, respectively, and so is its commutation AˆAˆ−1 = I.
One of the earliest eﬀorts of computerized human performance models in history, according to Chaﬃn’s review, was done by K. Kilpatrick in 1970. He made a 3D human graphic model to demonstrate how the model reaches and moves in a seated posture. After the 1970’s, a number of sophisticated digital human models emerged. 2 Digital Human Modeling: History, Achievements and New Challenges 9 Interaction Evaluation) was developed in the United Kingdom at that time and is now one of the leading packages in the world to run digital human simulations.