Robot calibration techniques are an important method to improve the absolute positioning accuracy of a robot end effector. Calibration can be divided into three levels: joint-level calibration, robot kinematic calibration, and robot dynamic calibration.
Kinematic calibration
Robot kinematic calibration is based on a robot kinematic model. By measuring the actual poses of the robot end effector during motion and comparing them with the theoretically calculated end poses, the robot's motion parameters can be identified. Kinematic calibration therefore includes the following three steps.
Step 1: Modeling
As the foundation of kinematic calibration, the robot kinematic model describes the transform from the end effector to the base. Different models have an important effect on calibration accuracy. Generally, the more parameters used to describe robot motion in the model, the higher the model precision, but the calibration difficulty and complexity also increase. End-effector error modeling is a key part of kinematic calibration: it describes the relationship between theoretical and actual end effector pose errors and differential changes in kinematic parameters. Similar to the kinematic model, selecting an error model is a trade-off between accuracy and complexity. The most appropriate modeling approach should be chosen based on the actual application.
In general, the choice of an end-effector error model is closely related to the kinematic model. Many researchers have proposed error models based on different kinematic models.
Step 2: End pose measurement
With the development of computer vision and sensor technologies, many new measurement techniques have been proposed, such as vision-based or sensor-based pose measurement systems.
Step 3: Kinematic parameter identification
The end-effector error model provides the relationship between kinematic parameter errors and end-effector pose errors. The pose measurement system measures the end-effector pose errors, and parameter identification applies mathematical methods to the error model to solve for kinematic parameter errors.
In practical applications, end-effector error models are usually nonlinear, but they are often linearized for processing, which can introduce unnecessary errors. Most kinematic parameter identification methods neglect higher-order error terms and use iterative solving to reduce residual errors, thereby achieving higher identification accuracy.
Dynamic calibration
During motion, as speed increases, centrifugal force, gravity, torques, and Coriolis forces affect robot performance differently. Even when the differential equations of robot motion are known, dynamic parameters cannot usually be obtained directly and must be identified through dynamic parameter calibration techniques. Similar to kinematic calibration, dynamic calibration typically includes three steps: modeling, dynamic accuracy measurement, and dynamic parameter identification.
Offline identification
Offline kinematic parameter identification refers to calibrating kinematic parameters while the robot is offline. Traditional calibration methods largely used offline programming: an operator moves the robot to fixed poses, the control system records the current end pose and joint angles, and a suitable pose measurement system measures the actual end pose. By comparing the theoretical and actual end poses and repeating this process to collect enough data, mathematical methods are used to identify kinematic parameter errors and apply compensation.
Consequently, earlier calibration procedures typically required the robot to be offline and needed substantial manual assistance, making the process complex and inefficient. In dynamic or unstructured environments that are difficult for humans to access (for example, high temperature or high pressure), offline parameter identification is hard to implement. Environmental factors can continuously change the robot geometry, making offline calibration ineffective. Traditional measurement tools used for calibration, such as theodolites, coordinate measuring machines, laser trackers, and telescoping gauges, are often large, expensive, complex to operate, and require trained personnel, which makes online calibration challenging with those tools.
Online identification
Online kinematic parameter identification means the robot performs self-calibration while operating to improve motion accuracy in real time. Compared with offline methods, online identification is simpler, does not require complex equipment installation, and can adapt to various environments. It offers efficiency, high accuracy, and robustness. When a robot operates in environments such as deep-sea high pressure or high-temperature space conditions, its geometry can change, reducing motion accuracy and making offline identification ineffective. Therefore, it is necessary to measure end-effector pose data and identify parameter errors in real time during robot motion to compensate for environmental influences and improve absolute positioning accuracy. Online calibration generally requires little manual intervention, is simple and efficient, and is especially important for improving absolute positioning accuracy in dynamic, unstructured environments.
