USE OF MATRIX IN ROBOTICS

Transformation matrices can be used to describe that at what angle the  servos need to be to reach the desired position in space or may be an  underwater autonomous vehicle needs to reach or align itself with several  different obstacles inside the water.

1. USE OF MATRIX IN ROBOTICS Presented by: Roll No:33-Talha Momin Roll No:34- Sugam Pandey Roll No:35- Atharva Parab Roll No:36- Simran Pardeshi

2. MATRIX IN ROBOTICS AND AUTOMATIONS FOR CHECKING ROBOT MOVEMENTS CONTROLLING THE ROBOT

3. HOMOGENIOUS TRANFORMATION MATRICES TRANSFORMATION MATRICES ARE THE 4*4 MATRICES THAT DESCRIBES   THE ROTATION AND TRANSLATION WITH RESPECT TO SOMETHING   ELSE. IT IS USED IN ROBOTICS AS IT HELPS IN THE MOVEMENT AND   AUTOMATION OF THE PARTS OF THE ROBOTS. IT IS VERY USEFUL FOR   EXAMINING RIGID BODY POSITION AND ORIENTATION OF A SEQUENCE   OF ROBOTIC LINKS AND JOINT FRAMES.

4. HOW TRANSFORMATION WORKS   IN ROBOTICS Transformation matrices can be used to describe that at what angle the   servos need to be to reach the desired position in space or may be an   underwater autonomous vehicle needs to reach or align itself with several   different obstacles inside the water. In other words, transformations helps  us to determine the movement of   the parts of the objects or the robots with respect to one another.

5. STRUCTURE OF HOMOGENOUS TRANSFORMATION Here A represents, translation, Rotation, Stretching or Shrinking and Perspective transformation.

6. ORIENTATION AND POSITION   REPRESENTATION THE COLUMNS OF THE ROTATION MATRIX FORM AN SUB-ORIENTATION   MATRIX WHILE VECTOR IS THE FRAME’S ORIGIN OFFSET. NOW HERE COLUMN 1 IS A VECTOR THAT ORIENTS THE FRAME’S AXIS   RELATIVE TO THE BASE X,Y,Z AXES RESPECTIEVELY. SIMILAR   INTERPRETATIONS ARE MADE FOR THE FRAME’S Y AND Z AXES   REPRESENTED BY COLUMN 2 AND 3. ALSO , ORIGIN VECTOR WITH THREE COMPONENTS REPRESENT THE   FRAME’S ORIGIN RELATIVE TO THE REFERENCE AXIS.

7. FRAME INTERPRETATION OF    TRANSFORMATION HERE WE HAVE BEEN GIVEN WITH THE   VECTOR u AND IT'S TRANSFORMATION IS REPRESENTED BY v=Hu NOW THIS VECTOR HAS COMPONENTS AS Ux, Uy,   Uz IN A COLUMN AND IT HAS TO BE EXPANDED TO   4*1.

8. INTERPRETATION OF HT NOW  IN THIS THE 1 IS ADDED TO FRAME ORIGIN THE   ROTATION VECTOR (3*3) RESOLVES THE VECTOR U IN THE   BASE FRAME.

9. GRAPHICAL     RE P R E SEN T ATI ON HOMOGENEOUS TRANSFORMATION IS GRAPHICALLY REPRESENTED AS:

10. THEORITICAL EXPLANATION THE HOMOGENOUS TRANSFORMATION EFFECTIVELY MERGES A FRAME ORIENTATION MATRIX, AND FRAME TRANSLATION VECTOR INTO ONE MATRIX. THE ORDER OF THE OPERATION SHOULD BE   VIEWED AS ROTATION FIRST, THEN TRANSLATION. IT CAN B E VIEWED AS POSITION OR ORIENTATION RELATIONSHIP OF   ONE FRAME RELATIVE TO ANOTHER FRAME CALLED THE REFERENCE   FRAME. IT CAN BE INTERPRETED AS FRAME A DESCRIBED RELATIVE TO THE   FIRST OR BASE FRAME WHILE FRAME B IS DESCRIBED RELATIVE TO   FRAME A.   WE CAN ALSO INTERPRET B IN THE BASE FRAME   TRANSFORMED BY A IN THE BASE FRAME. BOTH THE INTERPRETATIONS   GIVE THE SAME RESULT.

11. References : WWW.RESEACHGATE.NEt WWW.PLANNING.CS.UIUC.EDU https://ieeexplore.ieee.org WWW.SLIDESHARE.NET