In the field of aerospace and robotics, the six-axis force sensor plays a critical role in enabling precise force and torque measurements for applications such as space manipulators. These sensors are subjected to extreme environmental conditions, including wide temperature variations, which can significantly impact their accuracy. To address this, I have developed a novel static calibration system specifically designed for six-axis force sensors used in space manipulators. This system ensures high-precision calibration under varying temperature conditions, thereby enhancing the reliability of the six-axis force sensor in real-world operations. The importance of the six-axis force sensor cannot be overstated, as it directly influences the performance of robotic systems in critical missions.
The static calibration system I designed comprises three main components: a calibration platform, a data acquisition device, and a split-type temperature control device. The calibration platform features 18 independent force channels, allowing for the application of calibration forces and moments in 12 directions through a single setup. This design minimizes repositioning errors and improves efficiency. The data acquisition system utilizes an Advantech UNO-3083G industrial computer paired with a PCI-1742U data acquisition card, enabling high-speed sampling of the six-axis force sensor output signals. The temperature control device includes a temperature control box, an insulation box, and insulated air supply pipes, facilitating calibration experiments across a temperature range of -50°C to +150°C. This comprehensive approach ensures that the six-axis force sensor can be accurately calibrated under conditions mimicking its operational environment.
The calibration platform is constructed with a robust frame made of 16#b channel steel, with outer dimensions of 2000 mm × 2000 mm × 2000 mm. It includes a calibration center table where the six-axis force sensor equivalent and loading disk are mounted. The platform incorporates force application components such as screw rods, nuts, keys, wire ropes, pulleys, standard sensors, and loading disks. Each of the 18 force channels is independently controlled, enabling precise application of forces and moments in the ±Fx, ±Fy, ±Fz, ±Mx, ±My, and ±Mz directions. The use of wire ropes and pulleys ensures that the applied forces are directed accurately, while standard sensors monitor the calibration values in real-time. This setup allows for a comprehensive evaluation of the six-axis force sensor’s performance without the need for multiple reassemblies, thereby reducing potential errors introduced by handling.
The data acquisition device is designed to handle the output signals from the six-axis force sensor efficiently. It includes a power conversion module that transforms 220 V AC to ±12 V DC, supplying the necessary power to the six-axis force sensor. The Advantech PCI-1742U data acquisition card, with 16 analog input channels and a maximum sampling rate of 1 MS/s, captures the sensor outputs with high resolution. The industrial computer processes this data, facilitating real-time analysis and storage. The accuracy of the data acquisition is crucial for the calibration process, as any discrepancies can lead to significant errors in the six-axis force sensor’s performance evaluation. The system’s ability to handle high-speed data acquisition ensures that even dynamic effects can be accounted for in static calibration scenarios.
The split-type temperature control device is a key innovation in this system, addressing the challenges posed by extreme temperatures. The temperature control box, with dimensions of 1200 mm × 1000 mm × 1950 mm, houses heating and cooling systems. The heating system uses nickel-chromium heating wires with solid-state relays for precise control, providing a heating power of 6 kW. The cooling system employs two French Tecumseh fully enclosed compressors in a cascade configuration, with a cooling power of 8.95 kW. The insulation box, with an internal space of 0.8 m × 0.8 m × 0.8 m, is constructed with composite insulation layers including 100 mm thick rigid polyurethane foam and 50 mm thick ultra-fine centrifugal glass wool. The temperature is regulated using a UMC1200 temperature and humidity program controller, which supports preset programs and real-time monitoring. This setup ensures that the six-axis force sensor can be calibrated under stable temperature conditions, critical for space applications where temperature fluctuations are common.
In the error analysis of the calibration system, I have identified two primary types of errors: Type I errors, which represent the deviation between the actual and rated force/moment values, and Type II errors, which account for crosstalk between different force channels. The mathematical expressions for these errors are given by:
$$ \delta_I = \frac{F_{IB} – F_I}{F_{IB}} $$
and
$$ \delta_{II} = \frac{F_{II}}{F_{IB}} $$
where \( F_I \) is the actual force/moment value in a specific direction, \( F_{IB} \) is the rated force/moment value, and \( F_{II} \) is the interference force/moment induced in other directions. These errors are critical in assessing the overall accuracy of the six-axis force sensor calibration.
The main sources of error in the calibration system include the standard sensor measurement accuracy error, data acquisition card resolution error, pulley positioning error, and deformation-induced position error. The standard sensor used is a high-precision S-type tension sensor with an accuracy class of 0.02, certified by metrological institutes. Its error, based on a uniform distribution, is calculated as:
$$ \delta_s = \frac{\lambda}{k} $$
where \( \lambda = 0.05\% \) is the indication error and \( k = \sqrt{3} \) is the uniform distribution coefficient. This results in \( \delta_s = 0.029\% \). For the six-axis force sensor with design ranges as shown in Table 1, the errors in force and moment directions are derived accordingly.
| Parameter | Value |
|---|---|
| Fx, Fy, Fz | 1500 N |
| Mx, My, Mz | 2000 N·m |
The data acquisition card resolution error is determined by the input range and conversion precision. For the Advantech PCI-1742U card, with an input range of ±UR and n-bit conversion, the resolution S is:
$$ S = \frac{U_R}{2^{n-1}} $$
Given that the six-axis force sensor output voltage is related to the applied forces and moments through a first-order static influence coefficient matrix G, the error due to resolution can be expressed as:
$$ \delta_c = S \cdot \eta_i $$
where \( \eta_i = \sum_{j=1}^{6} a_{ij} \) represents the influence coefficients for the i-th force/moment direction. With a 16-bit conversion and ±5 V range, S = 1.5 mV, leading to specific errors in each direction as summarized in later analysis.
Pulley positioning error arises from misalignment during installation, causing the applied forces to deviate from the intended directions. For instance, in the Fx direction, if the force F is applied at an angle a1 in the XOZ plane, the actual force component is \( F \cos a1 \), and the error is \( F(1 – \cos a1) \). Additionally, forces from other directions contribute to crosstalk errors. Assuming pulley misalignment is within ±0.1°, and considering the symmetric layout of force channels, the errors in each direction are computed. The deformation-induced position error results from thermal and mechanical loads during calibration. Using finite element analysis in ABAQUS, I modeled the loading disk, six-axis force sensor, and calibration center table under temperature loads of 70°C and full-scale force/moment applications. The average displacements and rotations were used to calculate additional errors, with Type II errors dominating this category.
The total error for the calibration system is the sum of individual errors, assuming they are independent. The results are presented in Table 2, which shows the overall error and full-scale accuracy for each direction. The analysis reveals that pulley positioning and deformation errors are the primary contributors, accounting for 92.3% to 97.1% of the total error, while standard sensor and data acquisition errors are negligible in comparison.
| Direction | Total Error | Full-Scale Accuracy |
|---|---|---|
| Fx | 31.550 N | 2.10% |
| Fy | 27.549 N | 1.84% |
| Fz | 25.261 N | 1.68% |
| Mx | 16.998 N·m | 0.85% |
| My | 16.843 N·m | 0.84% |
| Mz | 21.109 N·m | 1.06% |
In conclusion, the developed static calibration system for the six-axis force sensor effectively addresses the challenges posed by extreme temperature environments in space manipulator applications. By integrating a multi-channel calibration platform, high-speed data acquisition, and precise temperature control, the system enables accurate calibration across a wide temperature range. The error analysis highlights that Type II errors, particularly from pulley positioning and structural deformation, are the main factors affecting accuracy, but the overall system error remains below 2.10%, meeting the stringent requirements for space missions. This research underscores the importance of comprehensive calibration in enhancing the performance of six-axis force sensors, and future work could focus on optimizing the system for higher temperature ranges or miniaturized sensors.
The six-axis force sensor is pivotal in ensuring the reliability of robotic systems in space, where environmental factors can lead to significant measurement drifts. Through this calibration system, I have demonstrated that it is possible to maintain high precision under varying conditions, thereby supporting the advancement of aerospace robotics. The use of advanced materials and control strategies in the temperature device further ensures that the six-axis force sensor can be validated for operational readiness. As technology evolves, continuous improvements in calibration methodologies will be essential for next-generation six-axis force sensors.
Moreover, the mathematical models and error formulations provided here serve as a foundation for further research. For example, the influence coefficient matrix G for the six-axis force sensor can be expanded to include non-linear effects, and the error analysis can be extended to dynamic calibration scenarios. The integration of machine learning algorithms for real-time error compensation could also be explored to enhance the six-axis force sensor’s accuracy in unpredictable environments. Ultimately, this work contributes to the broader goal of achieving autonomous and reliable robotic operations in space, where the six-axis force sensor plays a central role in force feedback and control.
In summary, the static calibration system I designed not only meets the current needs for six-axis force sensor calibration but also provides a scalable framework for future adaptations. The emphasis on temperature resilience and error minimization ensures that the six-axis force sensor can perform optimally in the harsh conditions of space, thereby supporting long-duration missions and complex manipulative tasks. The continued focus on refining calibration techniques will be crucial as the demands on six-axis force sensors grow with advancing robotic applications.