There are six common coordinate systems for industrial robots: base coordinate, DH, Joints, World, Workbench, Tools
Industrial robots can be utilized in various applications in automated operations, such as welding, spraying, polishing, loading and unloading, and sorting. As long as a suitable solution is available, various applications can come to fruition. These all rely on the flexible use of coordinate systems by robots. The importance of industrial robot coordinate systems lies in providing precise position and attitude control for robots, simplifying programming and debugging, adapting to complex application scenarios, ensuring consistency and accuracy, and many other aspects.
The coordinate system is like a compass for robot operations, used to confirm the robot's position and posture or to establish benchmarks on other workpieces. There are several types of coordinate systems used in robotics, including the base coordinate system, DH coordinate system, joint coordinate system, world coordinate system, workbench coordinate system, and tool coordinate system.
1. Base coordinate system
The base coordinate system is the reference coordinate system for the robot mounting base, usually with the intersection point of the robot mounting surface and the first axis of rotation as the origin. It is the foundation of other coordinate systems used to describe the overall position and posture of the robot. The base coordinate system is a fixed coordinate system that does not change with the robot's posture. The origin of the base coordinate system is generally located at the intersection of the robot's mounting surface and the first axis of rotation, with the X-axis moving forward, the Y-axis moving left, and the Z-axis moving upward, following the right-hand rule.
The main function of the base coordinate system is to provide a stable reference point for the robot, enabling accurate motion control. Even in the case of joint rotation and torsion angle changes, the base coordinate system can ensure the accuracy and consistency of robot motion In complex industrial applications, it is necessary to establish multiple different coordinate systems to meet different production needs. The base coordinate system serves as the benchmark for these coordinate systems, allowing robots to flexibly switch between different coordinate systems, thereby improving production efficiency and machining accuracy.
2. DH coordinate system
The full name is Denavit Hartenberg coordinate system, which is a mathematical model used to describe the geometric relationships between robot linkages. It is widely used in fields such as robot kinematic modeling, trajectory planning, and motion control.
The DH coordinate system describes the spatial relationship between adjacent links of a robot through four parameters: link length aa, link offset angle alpha alpha, angle of rotation theta, and link angle beta. These parameters define the transformation relationship from one coordinate system to another, typically including rotation and translation operations. This method establishes a coordinate system on each connecting rod and achieves coordinate transformation on two connecting rods through homogeneous coordinate transformation. In a multi link series system, multiple uses of homogeneous coordinate transformation can establish the relationship between the head and end coordinate systems, and each axis always rotates around the Z-axis of that axis coordinate system when moving.
The D-H parameter method establishes a coordinate system on each connecting rod and uses a homogeneous transformation matrix (4x4 matrix) to describe the transformation relationship between adjacent coordinate systems. In a multi-link system, by applying these transformation matrices multiple times, the relationship between the head and end coordinate systems can be established to describe the kinematic model of the entire system.
The D-H parameter method is:
Label each connecting rod (establish a coordinate system).
Describe the relationship between adjacent linkages using four parameters.
Calculate the final position and direction from the first connecting rod to the last connecting rod.
3. Joint coordinate system
The joint coordinate system is a reference coordinate system based on the axes of each joint of a robot, used to describe the motion state of each joint of the robot. Each joint has a corresponding coordinate system used to record the rotation and direction of the joint. The origin of the joint coordinate system is usually set at the center point of the joint, reflecting the absolute angle of each joint relative to its origin position.
By controlling the angles in the joint coordinate system, independent motion of each axis of the robot can be achieved. For example, we can control one axis of the robot to move from point a to point b, and two axes to move from point c to point d. Each axis can be independently recorded, and complex action combinations can be completed.
Just to add, the origin of the joint coordinate system is related to the value of the motor encoder. The system will record the encoder value of a state as the origin, and in this state, the joint coordinate values are all 0. The robot uses an absolute value encoder motor, which is powered by a battery when the power is off. After restarting, the system will read the absolute encoder value of the motor from memory to ensure that the origin is not lost.
4. World coordinate system
The direction of the world coordinate system is consistent with the direction of the robot base coordinate system, which means that the X, Y, and Z axis directions of the world coordinate system and the robot base coordinate system are the same. The data of coordinate system XYZ is obtained by adding the linkage parameters of each axis, which is used to represent which point in space the robot is located at and determine its position in space.
X-axis: X1eec + L34b + L56Y
Axis: Y1eec Z-axis: Z+L23+L34a UVW. The three data items are represented by Euler angles, and the rotation direction is Rx Ry,Rz.
Rx： The rotation angle around the X-axis.
Ry： The rotation angle around the Y-axis.
Rz： The rotation angle around the Z-axis.
5. Workbench coordinate system
A manually set world coordinate system for a certain work platform. When the working plane of the robot is not parallel to the base coordinate system, to facilitate debugging, the workbench coordinate system is established with the two edges of the workbench as the reference axes.
Why do we need a workbench coordinate system?
① Convenient debugging: When the working plane of the robot is not parallel to the base coordinate system, directly using the base coordinate system will complicate the debugging process.
② Simplified operation: The workbench coordinate system moves the robot's reference point from the base coordinate system to the origin of the workbench coordinate system, making the operation more intuitive.
After establishment, the robot's reference point moves from the base coordinate system to the origin of the workbench coordinate system, and the direction of the coordinate system is consistent with the base coordinate. Setting method: Select a corner of the workbench, record Po, Px, and Py points in sequence, and confirm the modifications. The direction of the workbench coordinate system refers to the base coordinate, ensuring that the Z-axis direction is consistent. After the robot moves to Po, it switches to the workbench coordinate system with XYZ values of 0.
Po： The origin of the workbench coordinate system.
Px: Point in the X-axis direction.
Py: Point in the Y-axis direction.
Confirm modification: Click OK to modify and establish the workbench coordinate system.
6. Tool coordinate system
The tool coordinate system of industrial robots is a coordinate system that describes the position and orientation of the robot's end effectors, such as suction cups, grippers, welding guns, etc. Its core function is to define the position and direction of the tool center point (TCP), which is used as the origin to describe the posture of the tool through the direction and angle of the X, Y, and Z axes. Suitable for scenarios that require frequent adjustment of tool posture.
TCP is usually located at the tip or end flange center of the tool, and the two can be switched through calibration.
Normally, the attitude transformation reference of the end TCP is at the center point of the robot's flange, with the U axis rotating around the X axis, the V axis rotating around the Y axis, and the W axis rotating around the Z axis.
When the fixture is installed at the end, the reference point of the tool needs to be transformed from the flange coordinate system to the end effector. Generally, the 6-point method is used for calibration calculation. When switching to the calibrated tool coordinate system, the reference point for robot posture calculation is no longer the flange coordinate system, but the calibrated position.
6-point calibration method
Step: Select a fixed reference point. Record 6 sets of data by contacting the reference point at different positions through the end of the fixture. Calculate the position and direction of the reference point at the end of the fixture relative to the flange coordinate system based on the recorded data.
Result: After calibration, the reference point of the tool coordinate system is no longer the flange coordinate system, but the position of the end of the fixture.
The application of coordinate systems for robots is crucial in determining their posture and position. These coordinate systems play an important role in different application scenarios, helping to achieve precise motion control and task execution. What coordinate system do you most commonly use?