By Edward Y. L. Gu
This ebook offers readers with a high-quality set of assorted and crucial instruments for the theoretical modeling and keep an eye on of complicated robot platforms, in addition to for electronic human modeling and lifelike movement new release. Following a accomplished advent to the basics of robot kinematics, dynamics and keep watch over platforms layout, the writer extends robot modeling systems and movement algorithms to a miles higher-dimensional, higher scale and extra subtle examine zone, particularly electronic human modeling. many of the tools are illustrated by means of MATLAB codes and pattern graphical visualizations, providing a special closed loop among conceptual figuring out and visualization.
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Additional resources for A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming
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. This also implies that a symmetric rotation matrix acts either a 00 rotation or a 1800 rotation, and nothing but these two cases. 3. One of the three eigenvalues for a rotation matrix R ∈ SO(3) must be +1, and the other two are either both real or complex-conjugate such that their product must be +1.
0000 >> which is just the instantaneous partial derivative of R with respect to θ2 . Using the same method, we can also calculate the numerical partial derivatives ∂R ∂R ∂θ1 and ∂θ3 . 2 Dual Vector and Dual Matrix The dual number deﬁnition can be extended to combining two vectors or even two matrices to form either a dual vector or a dual matrix as follows: ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ a1 + b 1 a1 b1 a ˆ = ⎝ a2 + b2 ⎠ = ⎝ a2 ⎠ + ⎝ b2 ⎠ = a + b, a3 + b 3 a3 b3 or Aˆ = A + B for two same dimensional matrices A and B.
While all the achievements after three decades of extensive investigations in digital human modeling for design and engineering applications are quite encouraging [20, 21], there are still many big challenges ahead, and they can be summarized as follows: 10 1 Introduction to Robotics and Digital Human Modeling 1. Although the realism of digital human appearance has made a breakthrough, the high-ﬁdelity of digital human motion may need more improvements, especially in a sequential motion, high-speed motion and motion in complex restricted environments; 2.
A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming by Edward Y. L. Gu