Chapter 2 robotSpatial descriptionsand transformations

Main point. DESCRIPTION: Transformation POSITIONS,

ORIENTATIONS, FRAMES

Con…• MAPPINGS: CHANGING DESCRIPTIONS FROM

FRAME TO FRAM• OPERATORS: TRANSLATIONS, ROTATIONS, AND

TRANSFORMATIONS• TRANSFORMATION ARITHMETIC• TRANSFORM EQUATIONS.• coordinate systems• Translational mapping

Con…• 1. positions: it represent like{A};{B};{C}……• A point A P is represented as a vector andcan equivalently be thought of as a position in space, or simply as an

ordered set of three numbers. Individual elements of a vector are given the subscripts x, y, and z:

A P=[PX,PY,PZ]……………………….1.2. orientation: {A} Az Ap

Ax Ay• figure 2.1: Vector relative to frame (example).

Con…• NB.1.position of apposition of a point is

represented with a vector, and orientation of a body is represented with a matrix.

The dot product of two unit vectors yields the cosine of the angle between them. this is called direction cosine.

In order to describe the orientation of a body, we will attach a coordinate system to the body and then give a description of this coordinate system relative to the reference system.

Con…• 3.frame:• EXAMPLE 2.1Figure 2.6 shows a frame {B} that

is rotated relative to frame {A} about Z by 30 degrees. Here, Z is pointing out of the page.

• YB YA• XB• ZB(0,0,1) ZA XA