Find out the torque control performance of the robot joint based on the principle of harmonic reducer under the pure current loop

（Reproduced）

In recent years, there has been a significant advancement in force-controlled manipulators, specifically the KUKA iiwa model. This manipulator is based on a servo joint integrated with a torque sensor, providing outstanding force control performance. However, the introduction of the torque sensor also leads to an increase in the Bill of Materials (BOM) cost, as well as increased complexity and potential unreliability in structure integration, signal processing, and motion control.

This article aims to briefly explore an alternative approach to force control performance in robot joints. Specifically, we will examine the potential of a pure current loop based on the principle of the harmonic reducer.

Experiment analysis

To begin, the hardware configuration required for the implementation of the joint control based on the principle of the harmonic reducer is as follows:

It is important to highlight the hardware configuration of the harmonic reducer due to its superior performance advantages, such as hollow wiring, high deceleration/mass ratio, and zero backlash. These features make it an essential component for robot arms/mandrels. However, compared to semi-direct drive joints (QDD) based on planetary gear reducers with low reduction ratios, the harmonic reducer has relatively low anti-drive transparency, making it challenging to control using torque-free reducers based on current loops.

In this article, we describe the extent to which force control can be achieved using the harmonic reducer under this hardware configuration. The article does not solve the issue of accurately identifying the starting torque of the harmonic reducer. Instead, it focuses on describing the force control performance achieved using this hardware configuration.

In our experiments, we found that the minimum threshold for external force observation in collision detection is approximately 0.5Nm. In a collision experiment specific to tofu, the external force applied to the tofu was measured to be around 1.5Nm. This is sufficient for some collision detection scenarios. In terms of quality, in zero-torque dragging, a certain small force needs to be applied to overcome the static friction force at the start time. However, after start-up, the friction force identification achieves better results, and the overall dragging appears very light and supple. This performance is comparable to servo joints with integrated torque sensors.

Figure 1 shows the estimated value of the external torque of the joint under uniform rotation conditions (without the influence of acceleration noise), accurately compensating the joint friction torque and gravity torque (without external force). It can be seen that there is a 0.2Nm external torque. In actual collision detection, the external force estimation threshold will be increased to about 0.5Nm to avoid false touches caused by signal noise.

Model identification

In this section, we will provide a brief introduction to the model parameter identification work required for force control experiments on the harmonic reducer joint based on the current loop. This work is primarily divided into two parts: friction force identification and correction of the current torque coefficient of the frameless torque motor in the joint.

Friction identification

In order to identify the friction force of the joint at a horizontal uniform speed, the joint is placed horizontally to eliminate the influence of the gravity moment. The joint is also run at a constant speed to eliminate the influence of acceleration and deceleration. To improve the accuracy of identification, two working conditions of low-speed start-up and high-speed start-up deceleration are used in the experiment, considering that the efficiency of the harmonic reducer in the joint will increase with the increase of temperature.

To take into account the influence of joint forward and reverse rotation, high and low speed, temperature, etc. on friction, four experiments were carried out to test the corresponding relationship between the speed and torque of the joint at different speeds, as shown in Figure 2:

From the experimental curve presented in Figure 2, several observations can be made. Firstly, in the initial low-speed section of the joint, there is a small decreasing trend in the torque value as the speed increases (I). Secondly, in the subsequent acceleration section of the joint, the torque value exhibits a decreasing trend (II). Lastly, in the final high-speed section of the joint, the torque value shows a saturation phenomenon (III). This behavior can be roughly explained by the Coulomb's viscosity + Stribeck friction model.

That is:

After corresponding fitting by Matlab, we get:

To improve the stability of the low-speed section in practical applications, it is necessary to add a certain transition zone under the current friction model when the estimated friction force jumps positively and negatively due to speed jump and the current friction model is close to zero. This will prevent the friction compensation from increasing the instability of the system.

Current Torque Coefficient Correction

Based on our experience, the current torque coefficient provided by most frameless torque motor manufacturers is not very accurate. Therefore, before implementing force control based on the current loop, it is necessary to correct the current torque coefficient. This is done by experimental calibration, which involves hanging different mass blocks on the rod. The basic principle is based on the dynamic equation of the joint, which can be expressed as:

Question Discussion

In qualitative terms, the force control effect based on the current loop without a torque sensor is better with a smaller reduction ratio of the harmonic reducer. This is because a high reduction ratio can reduce the transparency of the reverse drive force, making it difficult to accurately identify the starting torque value, and ultimately affecting the feel of zero-torque dragging, especially at the start. Additionally, achieving accurate current sampling function is crucial for force control based on the current loop without a torque sensor. The driver used for this joint is an Elmo driver, with the performance of the driver current sampling level being fully utilized. However, using a cost-controllable drive in actual mass production may lead to a discount in the force control performance to some extent.

• Compared to the servo joint with an integrated torque sensor at the output end, the pure current loop solution is easier to realize overall force control. However, as an additional sensor, the torque sensor must consider its own signal processing, particularly its noise floor processing, and its ability to resist bending and anti-rotation torque fluctuations (due to the joint's poor coaxiality). If not handled well, the drag feel after overcoming the starting torque may not be much better than that based on the current loop, or even worse. Nevertheless, it will still be superior to the current loop in observing the starting torque ring.
• In general, the small-load manipulator based on pure current loop force control provides acceptable force control performance while considering hardware cost. However, for scenarios with high requirements for force control accuracy, the mechanical arm integrated with a torque sensor still has an absolute performance advantage, especially in the dragging feel at the moment the mechanical arm is started. Whether customers are willing to pay for this enhanced experience is unclear and may require specific discussions, as seen in the sales results of various collaborative robotic arm models currently on the market.