Abstract: Due to factors such as machining errors, assembly errors and clearances, and friction and wear, the actual arm length of a SCARA robot deviates from its theoretical arm length. It is often difficult to ensure that the robot's forearm and arm are perfectly aligned, resulting in zero-point offset. The deviation between the actual zero point and arm length and the theoretical value affects the robot's absolute positioning accuracy. Traditional calibration methods require expensive measuring equipment, are complex, and are not suitable for on-site calibration. This paper proposes a practical, simple, and efficient method for calibrating the zero point and arm length of a SCARA robot. Calibration is completed by aligning the robot's end effector calibration pin with two calibration holes at known distances, with the left and right hand systems aligned accordingly. Simulation and experimental results show that this method is stable and highly accurate, achieving a positioning accuracy of less than 0.09 mm for the robot's left and right hand systems after calibration.
1 Introduction
In 1978, Hiroshi Makino of Yamanashi University in Japan invented SCARA (Selective Compliance Assembly Robot Arm). This robot has four axes and four degrees of freedom (including translation along the X, Y, and Z directions and rotation about the Z-axis), as shown in Figure 1. SCARA robots exhibit compliance in the X and Y directions and good stiffness in the Z-axis direction, making them particularly suitable for assembly work. Their tandem two-bar structure, similar to a human arm, allows them to reach into confined spaces and retract, making them suitable for moving and picking up objects. SCARA robots are compact, flexible, fast, and highly accurate, and are widely used in the electronics, pharmaceutical, and food industries.
Due to factors such as machining errors, assembly errors and clearances, and friction and wear, the actual kinematic parameters of a robot (such as arm length and reduction ratio) deviate from the theoretical design values. The zero-point position of a SCARA robot is where its upper and lower arms are aligned in a straight line; however, it is often difficult to guarantee that the upper and lower arms are strictly aligned, resulting in zero-point offset. The deviation between the actual zero point and arm length and the theoretical values affects the robot's absolute positioning accuracy.
Figure 1 SCARA robot
Fig. 1 SCAR Arobot
Reference [1] proposes two methods for calibrating a planar two-degree-of-freedom robot: single-reference point calibration and three-reference point calibration. However, only the joint error is calibrated, and the arm length is not calibrated. Reference [2] proposes a general serial robot calibration method. Experimental results show that this method greatly improves the absolute positioning accuracy of the robot, but it requires high-precision measuring equipment. Reference [3] proposes a calibration method based on single-point constraints, but some parameters must be obtained by measuring equipment. Reference [4] proposes a single-point two-step calibration method that does not require measuring equipment in field applications, but it requires solving a nonlinear optimization problem, which is more complicated to implement. Reference [5] proposes a four-hole calibration plate calibration method based on SVD decomposition. This method is simple, practical, and has high accuracy, but it requires high precision in the machining of the four holes of the calibration plate.
This paper proposes a simple and practical method for calibrating the zero point and arm length of a SCARA robot. This method requires no specialized measuring equipment, the calibration process is extremely simple, and it can conveniently and accurately calibrate the zero point and arm length of a SCARA robot.
2. Zero point and arm length calibration principle
Since the zero point and arm length calibration of the SCARA robot are not related to three- or four-axis robots, this paper considers the SCARA robot as a planar two-degree-of-freedom robot.
2.1 Correct Kinematics Solution for SCARA Robots
(1)
Figure 2. Schematic diagram of the forward kinematics solution for the SCARA robot.
Fig.2 Schematic diagram of SCARA forward kinematics
2.2 Zero point and arm length calibration steps
Figure 3. Schematic diagram of arm length and zero point calibration
Fig.3 Schematic diagram of arm length and zero position calibration
2.3 Derivation of the Zero Point and Arm Length Calibration Principle
The robot's end-effector calibration pin is aligned with hole M using different hand systems. According to equation (1), the following set of equations can be obtained:
(2)
Using trigonometric identities:
(3)
And perform variable substitution:
(4)
To simplify the symbols, let's call it:
(5)
Equation (2) can be written as:
(6)
The end calibration needle is aligned with hole N using different hand systems, and similarly, the following system of equations can be obtained:
(7)
Combining (6) and (7), we obtain a system of statically indeterminate homogeneous linear equations, which can be solved using the least squares method. For any non-zero real number, the homogeneous linear equations...
Similarly, without loss of generality, constraints can be added. Solving a statically indeterminate homogeneous linear system of equations can be transformed into an optimization problem with equality constraints:
(8)
(9)
(10)
According to equation (4), the zero-point offset value can be obtained:
(11)
The ratio of upper arm to forearm length:
(12)
Since the lengths d of holes M and N are known, the actual value of the arm length can be calculated using equation (1).
(13)
Similarly, the lengths of the forearm and upper arm can be obtained as follows:
(14)
3. Algorithm Stability Analysis
The forward kinematics of the SCARA robot show that the factors affecting absolute positioning accuracy are: upper arm length, forearm length, and zero-point offset.
The angles of joint 1 and joint 2 are given. Since the angles of joint 1 and 2 are determined by the encoder reading and the reduction ratio, and the encoder and reducer are usually highly accurate, the joint angles are assumed to be accurate here. Therefore, for the calibration algorithm proposed in this paper, there are two aspects affecting the accuracy of the robot's zero point and arm length calibration: the accuracy of the end-effector calibration target point and the hole spacing of the calibration plate.
Let the theoretical values of the SCARA arm length and zero point be: , . The actual values of the arm length and zero point are: . Taking the calibration plate hole distance, the calibration point error is defined as an error circle centered at the accurate point with an error radius of . Using MATLAB to randomly simulate the calibration process 10,000 times, the calibration results under different calibration plate hole distances and point accuracy can be obtained, and then the standard deviations of the arm length and zero point offset can be calculated. The simulation results are shown in Figures 4-6.
Figure 4 shows the relationship between the calculated standard deviation and the hole spacing and the radius of the error circle.
Fig.4 The relation between standard deviation of calculated and hole distance and error radius
Figure 5 shows the relationship between the calculated standard deviation and the hole spacing and the radius of the error circle.
Fig.5 The relation between standard deviation of calculated and hole distance and error radius
Figure 6 shows the relationship between the calculated standard deviation and the hole spacing and the radius of the error circle.
Fig.6 The relation between standard deviation of calculated and hole distance and error radius
Figures 4-6 show that the proposed SCARA robot zero-point and arm length calibration algorithms are stable. A larger hole spacing enhances the stability of the calculated arm length and its resistance to alignment errors. The calculated zero-point offset values exhibit excellent stability, with different hole spacings having minimal impact on the stability of the offset values.
4. Calibration Experiment
This paper uses the AR4215SCARA robot independently developed by Shenzhen Zowell Technology Co., Ltd. (hereinafter referred to as "Zowell") for experiments. Figure 7 shows the AR4215 robot with a calibration pin at the end effector. The design values for the robot's upper arm and lower arm, and the hole spacing of the calibration plate are shown. The calibration plate is placed randomly in the robot's workspace plane. The experiment is conducted according to the calibration steps, and the robot's easy dragging function makes the experiment very convenient. The measurement data and calibration results are shown in Table 1. The actual upper arm length is calculated by taking the average of five calibration results.
Forearm length, zero offset value.
Figure 7 AR4215 SCARA robot
Fig. 7 AR4215 SCARA robot
Table 1. Calibration Experiment Data and Calculation Results
Tab.1 Calibration experimental data and calculation results
5. Calibration and Verification
This paper uses Zowell's independently developed AVS vision system and Daheng CCD industrial camera with a resolution of 1628*1236. The experimental platform for calibration and verification is shown in Figure 8.
Figure 8 Calibration and verification experimental platform
Fig.8 Experiment platform for calibration verification
5.1 Calculate the average pixel equivalent
5.2 Verification of Positioning Accuracy of Left and Right Hand Systems
Using the inner circle of the lead screw at the end effector of a SCARA robot as a template, four verification points were randomly selected within the camera's field of view. The robot moved to these points using its left and right hands respectively, and the pixel coordinates of the center of the inner circle of the lead screw were obtained using the AVS vision system. The measurement and calculation results are shown in Table 2.
Table 2. Calibration Experiment Data and Calculation Results
Tab.2 Calibration experimental data and calculation results
6. Conclusion
This paper proposes a practical, simple, and efficient method for zero-point and arm-length calibration of SCARA robots. Calibration is completed simply by dragging the robot's end-effector calibration pin and aligning the left and right hand systems with two calibration holes at known distances, recording the current angles of joint 1 and joint 2. The operation is extremely simple. The calibration holes only need to meet distance accuracy requirements, greatly reducing the machining difficulty of the calibration plate. Compared to traditional calibration methods that require expensive measuring equipment and involve complex calibration processes, this method is more suitable for on-site calibration of SCARA robots. Simulation results show that the calibration method is stable, and the larger the hole spacing, the more stable the arm-length calibration result; the zero-point calibration result is less affected by the hole spacing. Experimental results show that the calibration method has high accuracy; after calibration, the positioning accuracy of the left and right hand systems at the same point on the robot is within 0.09 mm.
