In the field of robotics and precision engineering, the demand for accurate force measurement has led to the development of multi-axis force sensors, particularly the six-axis force sensor, which can simultaneously measure three-dimensional force and moment components. The six-axis force sensor plays a critical role in applications such as agricultural robotics, where delicate objects require gentle handling, and in industrial automation for tasks like assembly and quality control. However, due to manufacturing imperfections, such as variations in strain gauge placement and material inconsistencies, the actual input-output characteristics of a six-axis force sensor often deviate from theoretical models. To address this, static calibration is essential to determine the sensor’s performance metrics by applying known loads and deriving a calibration matrix that minimizes errors between measured and expected outputs. This paper presents a comprehensive study on the design of a novel static calibration system for six-axis force sensors, leveraging virtual instrumentation to enhance accuracy, efficiency, and user-friendliness. The system integrates hardware and software components to perform bidirectional calibration in a single setup, reducing errors associated with multiple reassemblies and improving overall reliability.
The importance of the six-axis force sensor lies in its ability to provide full spatial force information, which is vital for enhancing the dexterity and precision of robotic systems. For instance, in agricultural robotics, where objects are often soft and irregularly shaped, the six-axis force sensor enables real-time force feedback, allowing robots to adjust their grip and avoid damage. Similarly, in medical devices and automotive testing, the six-axis force sensor ensures accurate force monitoring during complex operations. Despite these advantages, the performance of a six-axis force sensor is highly dependent on its calibration, as even minor deviations can lead to significant errors in force interpretation. Traditional calibration systems suffer from limitations such as inaccurate load application, positional misalignments, and low efficiency due to manual interventions. Our research focuses on overcoming these challenges by designing a system that utilizes virtual instrument technology, specifically LabVIEW, to automate data acquisition, analysis, and calibration processes. This approach not only streamlines the calibration of six-axis force sensors but also provides a robust framework for future advancements in sensor technology.
The calibration principle for a six-axis force sensor is based on a linear model, where the relationship between applied loads and output signals is represented by a calibration matrix. This matrix is derived through a series of experiments where known loads are applied along the six characteristic directions: Fx, Fy, Fz, Mx, My, and Mz. For each direction, a load fi is applied, and the corresponding output voltages from the sensor’s channels are recorded. To minimize random errors, the data is normalized, resulting in a 6×6 calibration matrix. The fundamental equations governing this process are as follows:
$$ F = \begin{bmatrix}
f_1 & 0 & 0 & 0 & 0 & 0 \\
0 & f_2 & 0 & 0 & 0 & 0 \\
0 & 0 & f_3 & 0 & 0 & 0 \\
0 & 0 & 0 & f_4 & 0 & 0 \\
0 & 0 & 0 & 0 & f_5 & 0 \\
0 & 0 & 0 & 0 & 0 & f_6
\end{bmatrix} $$
Here, F represents the calibration load matrix, which contains the applied loads for each direction. The output voltage matrix V is adjusted by subtracting the baseline voltage matrix B to account for any inherent offsets, yielding the normalized voltage matrix W:
$$ W = V – B $$
The calibration matrix C is then obtained by solving the equation:
$$ F = C \times W $$
Rearranging this, we get:
$$ C = F \times W^{-1} $$
However, in practice, W may not be invertible directly, so we use the pseudoinverse or other numerical methods. Let H = W × F^{-1}, then:
$$ C = H^{-1} $$
This formulation highlights that the accuracy of the calibration matrix depends heavily on the precision of the applied loads. Any inaccuracies in load values or misalignments during application can propagate errors into the calibration matrix, underscoring the need for a reliable calibration system. Our design emphasizes precise load application through a calibrated experimental setup, ensuring that the six-axis force sensor is evaluated under controlled conditions. The linear model assumes that the sensor’s response is linear within its operating range, which is generally valid for well-designed six-axis force sensors, but nonlinearities can be addressed through advanced algorithms in future work.
The hardware composition of our static calibration system for six-axis force sensors consists of three main parts: the upper computer (PC), the data acquisition unit, and the calibration test bench. This integrated approach ensures that all components work seamlessly to achieve high-precision calibration. The system block diagram illustrates the flow from load application to data processing: loads are applied to the six-axis force sensor via the test bench, the sensor converts force signals into electrical signals, which are then conditioned through amplification, filtering, and isolation, and finally acquired by a data acquisition card for digital conversion and analysis on the PC. The software, developed in LabVIEW, provides real-time data visualization, analysis, storage, and reporting capabilities, making the system user-friendly and efficient.
The calibration test bench is a critical component designed to address common issues in traditional systems, such as friction effects, directional inaccuracies, and unidirectional loading limitations. It comprises a worktable, a rotary table, a crossbeam, support columns, and a set of pulleys. The six-axis force sensor is mounted at the center of the rotary table, with a loading disk attached to its upper end. During calibration, standard weights are connected via fine strings to a standard sensor, which is attached to a loading rod that runs over pulleys to apply known loads to the sensor’s specific directions. The use of a standard sensor allows for direct measurement of the applied load, compensating for frictional losses in the pulleys, rather than relying solely on the weight of the masses. The rotary table enables bidirectional calibration by rotating the sensor to different orientations, ensuring that all six directions are covered in a single setup. To achieve accurate load direction and position, calibration procedures include using a level to adjust the crossbeam horizontally and a plumb bob to align the pulley’s vertex with the sensor’s reference origin. For example, in the Fz direction, the load is applied vertically, and alignment checks ensure that the force vector passes through the sensor’s center, minimizing moment couplings.
The data acquisition system is engineered to handle the low-level signals from the six-axis force sensor, which are typically in the microvolt range. The electrical schematic includes a high-gain amplification circuit that boosts the differential signals to a range of -10 V to 10 V, followed by an active low-pass filter to remove noise, and an isolation stage to prevent interference. The conditioned signals are then digitized by a NI USB-6210 multifunction data acquisition card, which offers 16 analog input channels, a sampling rate of 250 kS/s per channel, and selectable voltage ranges from ±0.2 V to ±10 V. This card is compatible with LabVIEW, allowing for efficient driver integration and rapid software development. The choice of USB connectivity ensures easy setup and portability, while the embedded microprocessor handles initial signal processing, ensuring that data transmitted to the PC is clean and reliable. This hardware setup is crucial for maintaining the integrity of the six-axis force sensor’s output, as any signal degradation could lead to calibration inaccuracies.
In terms of software design, the LabVIEW-based data acquisition and analysis software is divided into configuration and display modules. The configuration module allows users to set hardware parameters such as channel selection, sampling frequency, and voltage input range; data processing parameters including filter type, calibration matrix for the six-axis force sensor, and standard sensor coefficients; and curve parameters like sample points and amplitude. Once configured, the software initiates data acquisition, displaying real-time dynamic curves for all six channels of the six-axis force sensor and two channels from the standard sensor. This real-time feedback enables operators to monitor the calibration process and capture stable data points efficiently. The software automatically saves data in append mode for each channel, storing it in specified locations for post-processing and performance analysis. This approach eliminates the need for manual data entry and reduces human error, enhancing the overall accuracy of the calibration for the six-axis force sensor. The front panel of the software provides an intuitive interface with graphs, controls, and indicators, making it accessible even to users with limited technical expertise.
To validate the effectiveness of our static calibration system for six-axis force sensors, we conducted multiple experiments in a controlled, static environment free from vibrations, shocks, and external accelerations. A six-axis force sensor, previously calibrated using a traditional system, was used for comparison. The sensor’s full scale was divided into 10 equal parts, and standard weights were applied sequentially to each of the six directions (Fx, Fy, Fz, Mx, My, Mz). The actual load values were monitored and recorded using the standard sensor to account for any discrepancies. The output signals from both the six-axis force sensor and the standard sensor were captured and stored by the software during stable loading periods. After data collection, the calibration matrix was computed through decoupling calculations, resulting in the following matrix for the six-axis force sensor:
$$ C = \begin{bmatrix}
-0.0749 & -0.0001 & 0.0001 & -0.0006 & -0.0974 & -0.0005 \\
0.0008 & -0.0759 & -0.0001 & 0.1024 & 0.0012 & -0.0020 \\
-0.0004 & -0.0011 & -0.0580 & -0.0011 & 0.0029 & -0.0012 \\
0.0012 & -0.0578 & 0.0007 & 0.1876 & 0.0042 & -0.0016 \\
0.0567 & 0.0008 & -0.0029 & -0.0011 & 0.0042 & -0.0011 \\
0.0004 & 0.0001 & -0.0001 & 0.0018 & -0.0008 & -0.492
\end{bmatrix} \times 10^2 $$
This matrix represents the sensitivity and coupling characteristics of the six-axis force sensor. To evaluate key performance metrics, we focused on parameters such as linearity, sensitivity, repeatability, and inter-axis interference for each direction. For instance, in the Fx direction, we applied loads ranging from -200 N to 200 N and recorded the output voltages. Using least squares fitting, we derived a linear relationship, as shown in the fitted line for Fx channel data. The linearity, which indicates the deviation from ideal linear behavior, was calculated as 0.06%, demonstrating high accuracy. Sensitivity, defined as the slope of the fitted line, was found to be 22.978 mV/N, indicating how much the output voltage changes per unit force. Repeatability, measured by performing multiple loading cycles, was 0.04%, reflecting the sensor’s consistency. Inter-axis interference, which quantifies the cross-talk between different directions, was 0.37% for Fx, suggesting minimal coupling effects. The table below summarizes these static performance indicators for the Fx direction of the six-axis force sensor:
| Parameter | Value for Fx |
|---|---|
| Linearity | 0.06% |
| Sensitivity | 22.978 mV/N |
| Repeatability | 0.04% |
| Inter-Axis Interference | 0.37% |
The experimental results confirm that our system provides more efficient and accurate calibration compared to traditional methods. The integration of bidirectional loading, standard sensor feedback, and comprehensive test bench calibration significantly reduces errors in load application. Moreover, the software’s dynamic data visualization and automated data capture facilitate quick identification and storage of valid data points, avoiding the tedious process of manually filtering out outliers. This enhances the precision of data processing for the six-axis force sensor. The decoupling accuracy in static linear algorithms is influenced by both experimental precision and data handling; our system addresses these factors through hardware innovations and software capabilities, resulting in a reliable calibration matrix for the six-axis force sensor.
Further analysis involved assessing the overall system performance by comparing the calibrated six-axis force sensor outputs with theoretical expectations. The error metrics were computed using the following formula for relative error:
$$ \text{Relative Error} = \frac{|\text{Measured Value} – \text{Theoretical Value}|}{|\text{Theoretical Value}|} \times 100\% $$
For the six-axis force sensor, the average relative error across all directions was below 0.1%, indicating high calibration accuracy. Additionally, we evaluated the system’s efficiency by measuring the time required for full calibration; our system completed the process in approximately 30 minutes, whereas traditional methods often take over an hour due to multiple reassemblies and manual adjustments. This efficiency gain is attributed to the virtual instrument platform, which automates data acquisition and analysis for the six-axis force sensor. The use of LabVIEW also allows for easy customization and scalability, enabling future integrations with advanced algorithms, such as neural networks or nonlinear models, to handle complex sensor behaviors.
In conclusion, the integration of virtual instrumentation into the static calibration system for six-axis force sensors represents a significant advancement in sensor technology. Our design addresses the shortcomings of existing systems by enabling bidirectional calibration in a single setup, providing an intuitive user interface, and enhancing data accuracy through automated processes. The experimental validation demonstrates that the system achieves high linearity, sensitivity, and repeatability for the six-axis force sensor, with minimal inter-axis interference. The hardware components, including the calibrated test bench and precise data acquisition system, ensure reliable load application and signal integrity, while the LabVIEW-based software streamlines data handling and analysis. This approach not only meets the current demands for six-axis force sensor calibration but also paves the way for future innovations in multi-axis force measurement. As robotics and automation continue to evolve, the need for accurate and efficient calibration of six-axis force sensors will grow, and our system provides a robust foundation for addressing these challenges. By leveraging virtual instrument technology, we have created a scalable and user-friendly solution that can be adapted to various sensor types and applications, ultimately contributing to improved performance and reliability in force-sensitive systems.
The potential applications of this six-axis force sensor calibration system extend beyond robotics to fields such as aerospace, biomedical engineering, and automotive testing, where precise force monitoring is crucial. For example, in prosthetic devices, the six-axis force sensor can provide feedback for natural movement, and accurate calibration ensures safe and effective operation. In industrial quality control, the system can be used to calibrate sensors in production lines, enhancing consistency and reducing waste. Future work may focus on incorporating environmental factors, such as temperature and humidity, into the calibration process to further improve the accuracy of the six-axis force sensor. Additionally, machine learning techniques could be integrated into the software to automatically optimize the calibration matrix based on historical data, making the system even more adaptive and intelligent. Overall, our research underscores the importance of innovative calibration methodologies in unlocking the full potential of six-axis force sensors, driving progress in technology and engineering.