How to Properly Use Industrial Robot Coordinate Systems: Step-by-Step Guide

Robot Coordinate System
Base Coordinate System
Robots have a coordinate system that does not change, called the base coordinate system or the world coordinate system (each family calls it something different, the principle is the same).
Where does the base coordinate system come from?
Take a 6-axis robot for example:
The axis of rotation of the first axis
Generally define the first axis of the robot’s axis of rotation for the base coordinate system Z axis, the center of rotation that is the origin of the coordinate system, the X and Y direction is the zero point of the motor to determine, so as long as you do not replace the zero point of the motor and the mechanical structure of a single robot in the base coordinate system is never changed!
Robot external axes
There is a situation will be reset to a new (base) coordinate system, the new coordinate system for the world coordinate system (each different call, you can think of it as a base coordinate system), that is, the robot plus the external axis of travel, or external rotary axes, with the walking axis, for example, in this case, the base coordinate will be located in the walking axis of the zero position, if there are more than one axis of travel, then set the base coordinate to the bottom of the axis of the zero point, so the robot configuration of external axes is the principle of measurement. The principle of the robot configuration of the external axis is to measure some mechanical parameters, the robot 1 axis of the base coordinate system to the external axis of travel, this transformation is also called the DH transformation, the following tool coordinate system when the detailed description.
User coordinate system
After the above content determines a (base) coordinate system, the tool coordinate system and the user coordinate system can be deduced by the chi-square transformation!
User coordinate system
First, the user coordinate system, the essence of the user coordinate system is to rotate the (base) coordinate system offset to the workpiece, in order to facilitate programming, so that the robot’s direction of movement and the direction of the surface of the workpiece is the same! For example, there is a workpiece surface inclined at 45 degrees, if you use the base coordinate system, the robot is walking along the direction of the base system, horizontally and vertically, it is difficult to walk along the 45-degree surface, difficult to operate for programming. So just rotate the (base) coordinate system by a chi-square transformation offset to get a new user coordinate system!
Subsequent Transformation Rotation Algorithm
Chiral transform translation plus rotation algorithm
The new user coordinate system is obtained after the chi-square transformation.
Tool Coordinate System
The tool coordinate system, also called TCP, has a lot to do with the accuracy of the robot. It is on the robot’s end-effector, which is the gripper or torch. This coordinate system is not moving relative to the 6-axis, but in reality the robot is constantly moving in the 6-axis, so the coordinate system follows the 6-axis and changes in real time!
Tool coordinate system
What is the position of the robot and what is the coordinate data? In reality, it’s the value of X, Y, Z, A, B, C of the origin of the tool coordinate system (TCP) in the base coordinate system or the user coordinate system. X, Y, Z are the three axes of the coordinate system, and A, B, C are the angular data of the rotation around the coordinate system X, Y, Z with the origin of the tool coordinate system (TCP) as the rotating center (some robots, such as the KUKA rotating A, B, C corresponds to the rotation around Z, Y, X; the standard robot rotates around Z, Y, and X; the standard robot rotates around Z, Y, and X; and the standard robot rotates around Z, Y, and X. The robot rotates around Z, Y, and X. (Some robots, such as KUKA, rotate A, B, and C around Z, Y, and X; the standard Euler angles are also rotated around ZYX). Here note that the center of rotation, robots use Euler angles, the center of rotation is the TCP, not around the base coordinates or user coordinates of the axis of rotation, said here around the X rotation, in fact, the coordinate system is translated to the TCP position, and then around the coordinate system X rotation! If you know vectors, it’s easy to understand why this is so, because the transformation calculations are all in the form of unit vector matrices!
How do you get the TCP? In fact, it also has a lot to do with the base coordinates that will not change, determine the base coordinates, the base coordinates of the Z axis can be imagined as a one-axis motor rotation axis, one-axis motor zero can determine the X and Y direction, so that the one-axis joint coordinate data converted into the form of Cartesian XYZ coordinate system! For the same reason, the two-axis motor relative to the first axis mechanical position and zero point is also fixed, through the mechanical parameters can be converted to the joints of the second axis is also the form of the coordinate system, the three-axis relative to the second axis, four-axis relative to the third axis, five-axis relative to the four-axis, six-axis relative to the five-axis, there is a relative position and the zero point of the fixed and unchanged, this is the 6-axis tandem robots, so that one-axis one-axis converted to the six-axis, the six-axis And then converted to the tool (torch or gripper), the resulting coordinate system is fixed relative to the six-axis tool coordinate system is also known as TCP, the following figure.
TCP calculation diagram
Joint Coordinate System
Joint Coordinate System
This coordinate system is very simple, it is the angle of rotation of the six motors! In joint coordinates, we change the data of the six motors to move each joint individually! In reality, its most useful feature is the inverse operation, that is, when we use the user coordinate system or the base coordinate system plus TCP to move the robot, the robot internally has to invert the data from the coordinate system into the data of the six joint motors, which is very complicated, and the solution is not unique (I talked about the robot’s attitude parameters in the previous post), so I won’t go into detail here, but I will do so in the future.