Mem380_06 - Coordinate Transformations 3D rotations Motivation General 3D rotation 0 Ultimately we are interested in the motion of the robot with

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Coordinate Transformations Motivation Ultimately, we are interested in the motion of the robot with respect to a global or inertial navigation frame Motion of robot components ( e.g. wheels, sensor heads, etc.) are measured relative to the robot frame What is required then is a means by which we can easily relate robot motions the positions of targets etc from the © R. Siegwart, I. Nourbakhsh MEM380: Fundamental Robotics I Fal 2009 1 relate robot motions, the positions of targets, etc. from the robot’s reference frame back to the inertial frame This is readily accomplished through coordinate transformations 3D rotations  3 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 SO z z z z z x y x y y y x x z x y x x R General 3D rotation: Special cases Basic rotation matrices MEM380: Fundamental Robotics I Fal 2009 2 cos sin 0 sin cos 0 0 0 1 , x R 1 0 0 0 cos sin 0 sin cos , z R cos 0 sin 0 1 0 sin 0 cos , y R Courtesy of Vijay Kumar Properties of rotation matrices Inverse of a rotation matrix: y y y x x y x x 1 1 0 1 0 1 0 1 0 1 cos ˆ ˆ 2 cos ˆ ˆ 2 cos ˆ ˆ cos ˆ ˆ 1 0 1 0 1 0 1 0 1 1 1 0 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ y y y x x y x x R MEM380: Fundamental Robotics I Fal 2009 3 The determinant of a rotation matrix is always ±1 +1 if we only use right-handed convention T R R 1 0 0 1 cos sin sin cos det 1 cos sin sin cos Courtesy of Vijay Kumar
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/29/2010 for the course MEM MEM380 taught by Professor Zhou during the Spring '09 term at Drexel.

Page1 / 5

Mem380_06 - Coordinate Transformations 3D rotations Motivation General 3D rotation 0 Ultimately we are interested in the motion of the robot with

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online