学习笔记 | A Mathematical Introduction to Robotic Manipulation

Textbook:

  • A Mathematical Introduction to Robotic Manipulation, Richard M. Murray, Zexiang Li, S. Shankar Sastry
    • In short as RM in the following description.

Note:

***** Chapter 2 Rigid Body Motion *****

***** Chapter 3 Manipulator Kinematics *****

  • Denavit-Hartenberg Parameters
    • While it is possible to carry out all the analysis using an arbitrary frame, a commonly used frame of reference in robotic applications is the Denavit-Hartenberg or D-H convention.
    • Wikipedia: The Denavit–Hartenberg parameters (also called DH parameters) are the four parameters associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain, or robot manipulator.
    • DH1: The axis x1 is perpendicular to the axis z0.
    • DH2: The axis x1 intersects with the axis z0.

    • The following four transformation parameters are known as D–H parameters:.[4]

      • d\,: offset along previous z to the common normal
      • heta \,: angle about previous z, from old x to new x
      • r\,: length of the common normal (aka a, but if using this notation, do not confuse with alpha ). Assuming a revolute joint, this is the radius about previous z.
      • alpha \,: angle about common normal, from old z axis to new z axis

    • In summary, the reference frames are laid out as follows:

      1. the z-axis is in the direction of the joint axis
      2. the x-axis is parallel to the common normal: {displaystyle x_{n}=z_{n} imes z_{n-1}}
        If there is no unique common normal (parallel z axes), then d (below) is a free parameter. The direction of x_{n} is from z_{{n-1}} to z_{n}, as shown in the video below.
      3. the y-axis follows from the x- and z-axis by choosing it to be a right-handed coordinate system.

Reference:

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原文地址：https://www.cnblogs.com/casperwin/p/7599799.html