In my work on high-precision motion control for industrial robots, I have repeatedly observed that joint friction remains one of the most stubborn obstacles to achieving consistent trajectory accuracy under real production conditions. The problem becomes especially severe when industrial robots execute small circular interpolation, complex contour tracking, or precise welding tasks at low speeds. In these regimes, the transmission joints inside industrial robots exhibit strongly coupled viscous and Coulomb friction, and the friction force changes abruptly as the joint velocity crosses zero. Conventional servo controllers rely on feedback correction, but their integral action cannot build enough feedforward torque within the few milliseconds available during a reversal. As a result, the end effector hesitates, and the tool center point deviates from the commanded path. I propose a multi-source data fusion approach that extracts friction state information from servo currents, commanded positions, external temperature measurements, and load estimates. The method constructs a dynamic friction correction expression that accounts for both thermal drift and load fluctuations, and it uses an online recursive parameter update algorithm with an outlier cleaning mechanism. The feedforward torque is written into the servo target torque offset object dictionary through the underlying Ethernet bus. I validated the technique on an actual welding line for automotive bodies, and the results show that the method, combined with communication delay look-ahead processing, effectively eliminates reversal chatter and significantly reduces the spatial trajectory root mean square error in the thermal steady state.
1. Introduction
Industrial robots are widely used in automotive welding, assembly, painting, and material handling. In these applications, the robot manipulator must follow a planned trajectory with high geometric fidelity. However, the joint transmission system, which typically includes harmonic drives or RV reducers, introduces nonlinear friction that depends on velocity, temperature, load, and lubrication state. When an industrial robot moves at low speed and reverses direction, the friction torque changes sign almost discontinuously. The servo controller must overcome static friction before motion can begin in the opposite direction. Because the controller bandwidth is finite and the integral term accumulates error slowly, the joint experiences a short dwell at zero velocity. This dwell produces a flat-top distortion or a quadrant protrusion in the end-effector path. For welding, such errors can cause uneven heat input, poor bead formation, and even weld defects. For assembly, they can lead to insertion failures or surface damage.
In my experience with production lines, the common industrial practice is to use offline static calibration parameters that are fixed at the factory. These parameters are often obtained under room-temperature conditions and a nominal payload. After long-term operation, the lubricant temperature rises, and its viscosity decreases nonlinearly. At the same time, the payload may change frequently because the robot picks different fixtures or welding tools. The normal pressure on the contact surfaces of the reducer and bearings fluctuates, which shifts the Coulomb friction baseline. As a result, the static compensation model degrades severely. In some cases, it injects excessive energy at high speed and excites mechanical vibration. If high-precision torque sensors are installed on each joint to measure friction directly, the hardware cost and retrofit effort are too large for mass production lines. Therefore, I focus on extracting friction information from signals that are already available in the servo drive, such as phase current, multi-turn absolute encoder position, and temperature readings from critical structural points. By fusing these multi-source data, I estimate the dynamic friction torque residual that reflects the operating condition drift. I also introduce a robust online parameter update algorithm with a signal cleaning dead zone to suppress abnormal disturbances. A command phase lead preview mechanism compensates for the communication delay in the underlying bus. I implemented this technique on a body-in-white welding line in an automotive plant, and it significantly improved the end-effector accuracy and process stability under variable load and long-duration operation.
2. Problem Analysis: Trajectory Error Induced by Joint Friction
2.1 Low-Speed Reversal Trajectory Distortion
When industrial robots execute small circular arcs or complex contour interpolation, each drive joint must frequently cross the zero-velocity point. At the instant of motion polarity reversal, the contact surfaces of precision gears and bearings first change from relative sliding to transient rest, and then they are forced back into sliding. This transition from static friction to kinetic friction exhibits a very steep nonlinear jump. A conventional proportional-integral-derivative controller requires several discrete sampling periods for its integral term to accumulate the servo error. Therefore, the controller cannot establish a feedforward drive torque that is large enough to overcome the peak static friction resistance within the few milliseconds of the zero-crossing window. This control blind zone directly causes the manipulator end to stall briefly in the reversal quadrant region. On the machining trajectory, this appears as a typical flat-top distortion or quadrant protrusion error. In my tests, I recorded the extreme errors of a main-line industrial robot performing a standard inspection motion. The data came from a real automotive welding production site. Table 1 summarizes the measured extreme errors. As shown in Table 1, under conventional control, the main load-bearing axes all exhibit motion hysteresis deviations that exceed the process tolerance limit in the extremely low-speed crossing interval.
| Axis | Cold-state extreme error (mm) | Hot-state extreme error (mm) |
|---|---|---|
| Axis 1 | 0.12 | 0.38 |
| Axis 2 | 0.15 | 0.42 |
| Axis 3 | 0.14 | 0.35 |
The data in Table 1 reveal a clear thermal dependence. When the industrial robot is cold, the error is already non-negligible for precision welding. When the robot is hot, the error increases by a factor of two to three. This confirms that a fixed compensation model cannot handle the actual operating state of industrial robots in continuous production.
2.2 Friction Drift Under Continuous Operation and Temperature Rise
Industrial robots often face high-intensity cycle operations. The stator of the servo motor and the rotor of the precision reducer generate a large amount of heat during high-frequency reciprocating motion. The internal lubricating grease temperature continues to rise. Fluid mechanics shows that as the temperature increases, the kinematic viscosity of the lubricating oil decreases nonlinearly. The viscous friction damping coefficient depends on the shear effect of the oil film, and it also decays significantly. At this time, the feedforward compensation value that was tuned in the cold state becomes redundant drive energy input. When it is superimposed on the control loop, it induces weak but continuous high-frequency vibration in the electromechanical system. At the same time, flexible production lines require industrial robots to frequently grasp fixtures of different specifications or carry welding tools of different weights. The dramatic change in end load directly changes the normal pressure between the flex spline and the circular spline inside the reducer, as well as on the raceway surfaces of the support bearings. The fluctuation of the normal pressure on the contact surface causes the Coulomb friction torque baseline to shift irregularly. The two time-varying factors, namely viscous decay caused by temperature rise and Coulomb drift caused by variable load, are intertwined. This makes the static friction compensation model completely ineffective and ultimately reduces the consistency of the entire machining dimension and the stability of welding quality.
3. Multi-Source Data Fusion for Online Friction State Extraction
3.1 Time Synchronization of Underlying Acquisition Signals
In the underlying industrial Ethernet, when motion commands are issued, motor angle feedback is read, and stator current is measured, the signals of each channel have an inherent millisecond-level sampling reference deviation. If the data stream with time misalignment directly participates in the friction torque calculation, the small time offset will be multiplied in the differential solution of angular velocity and angular acceleration. This causes the dynamic observation equation to diverge. To eliminate this problem, I use the distributed clock synchronization function of the field Ethernet master station. At the hardware level, the communication timing of the master station and each servo slave station is forcibly aligned. In this way, the current, position, and speed signals in each computation cycle are anchored to the same microsecond-level timestamp. This fundamentally removes the false high-frequency interference caused by misaligned signal delays. Table 2 lists the main signals I fused and their synchronization requirements.
| Signal | Source | Nominal update rate | Required synchronization error |
|---|---|---|---|
| Phase current | Servo drive | 10 kHz | < 1 microsecond |
| Command position | Motion controller | 1 kHz | < 1 microsecond |
| Encoder position | Multi-turn absolute encoder | 10 kHz | < 1 microsecond |
| Joint temperature | Thermal resistor sensor | 10 Hz | < 1 millisecond |
| Load estimate | Dynamic model observer | 1 kHz | < 1 millisecond |
The synchronization process is not merely a software timestamp. I enforce the alignment at the EtherCAT distributed clock level, and then I resample all signals to a common 1 kHz control grid using a zero-order hold for slow signals and a linear interpolation for fast current signals. This ensures that the friction residual extraction does not suffer from artificial phase lag or lead between current and position.
3.2 Dynamic Friction Residual Extraction
The total electromagnetic torque output by the servo motor is not entirely used to overcome friction resistance. The system also needs to allocate torque for joint inertia acceleration and deceleration, as well as to resist gravity and external loads. Angular acceleration cannot be obtained directly from the encoder signal. In actual engineering, I approximate it by band-limited differentiation of the angular velocity feedback. To suppress the high-frequency spikes generated by the encoder quantization noise after differentiation, I embed a low-pass filter before the differentiation stage. Before extracting the friction signal, I use the motor nameplate torque constant to strip the rigid-body dynamic action from the total output torque according to Equation (1), obtaining a pure friction characteristic residual signal.
$$ \tau_{f,i} = K_{t,i} i_{q,i} – M_i(q) \ddot{q}_i – C_i(q,\dot{q}) \dot{q}_i – g_i(q) \tag{1} $$
In Equation (1), τf,i is the estimated friction torque of axis i (N·m), Kt,i is the motor stator torque constant (N·m/A), iq,i is the effective phase current of the motor (A), Mi(q) is the equivalent joint rotational inertia scalar (kg·m2), ¨qi is the angular acceleration of joint i (rad/s2), Ci(q,·q) is the centrifugal and Coriolis force coefficient, ·qi is the real-time feedback angular velocity of joint i (rad/s), gi(q) is the gravity torque (N·m), q is the joint space position vector (rad), and ·q is the full joint space velocity vector (rad/s).
I compute Equation (1) for each joint independently. The rigid-body dynamic terms are evaluated using the robot’s kinematic and inertial model, which I identify through a separate offline experiment. The friction residual is then filtered with a second-order Butterworth low-pass filter with a cutoff frequency of 50 Hz. This cutoff preserves the essential friction dynamics while removing the quantization noise that would otherwise corrupt the recursive parameter estimation.
3.3 Corrected Formula Combining Temperature Rise and Load Variation
The basic nonlinear model describes the friction evolution of the joint from low speed to medium-high speed under normal temperature and rated load. It covers the low-speed smooth transition characteristics and the medium-high-speed viscous damping behavior. Equation (2) constructs the physical process with pure velocity as the independent variable.
$$ \tau_{base} = \left[ F_c + (F_s – F_c) e^{-\left| \frac{\dot{q}}{v_s} \right|^{\delta}} \right] \operatorname{sgn}(\dot{q}) + \sigma_v \dot{q} \tag{2} $$
In Equation (2), τbase is the basic nonlinear friction torque (N·m), Fc is the basic Coulomb friction torque (N·m), Fs is the maximum static friction resistance (N·m), vs is the smooth switching critical angular velocity (rad/s), δ is the dimensionless geometric curvature exponent, σv is the viscous damping friction coefficient (N·m·s/rad), and ·q is the real-time feedback angular velocity of the joint (rad/s).
For a time-varying production environment, a single velocity variable cannot reflect the full physical resistance. Therefore, I introduce temperature fluctuation and load variation into the calculation chain. Equation (3) constructs a multivariable coupled compensation formula through dimensionless factors. Based on this formula, the system can dynamically scale the baseline value of the basic friction torque according to the current lubricant temperature rise and the end-effector force condition. This makes the compensation torque fit the actual loss state of the mechanical structure.
$$ \tau_{comp} = \left[ 1 + \alpha_T (T – T_{ref}) \right] \left[ 1 + \beta_L |\tau_L| \right] \tau_{base} \tag{3} $$
In Equation (3), τcomp is the target compensation torque issued after environmental correction (N·m), αT is the thermal temperature compensation proportional coefficient (1/°C), T is the real-time temperature obtained by the external sensor (°C), Tref is the offline initial calibration reference normal temperature (°C), βL is the external load coupling proportional coefficient (1/(N·m)), and τL is the observed external physical load from the force model (N·m).
I identify the coefficients αT and βL through a series of controlled heating and loading experiments. In these experiments, I run the industrial robot through a standard trajectory while gradually increasing the joint temperature and applying known payloads. I record the friction residual and fit the coefficients using least squares. The temperature coefficient is typically negative because the lubricant viscosity decreases with temperature, which reduces the viscous friction component. The load coefficient is positive because a higher normal force increases the Coulomb friction baseline. Table 3 shows typical identified values for a heavy-load industrial robot joint.
| Parameter | Value | Unit |
|---|---|---|
| Fc | 18.6 | N·m |
| Fs | 24.3 | N·m |
| vs | 0.008 | rad/s |
| δ | 1.75 | – |
| σv | 3.42 | N·m·s/rad |
| αT | -0.0062 | 1/°C |
| βL | 0.021 | 1/(N·m) |
| Tref | 25 | °C |
These parameters are not fixed for the lifetime of the industrial robot. They serve as initial values for the online update algorithm. The online update then adjusts them gradually as the actual operating conditions change. This hybrid approach combines the physical interpretability of the offline model with the adaptability of online estimation.
4. Online Parameter Update with Data Cleaning
4.1 Robust Recursive Estimation
In stamping or welding workshops, a running industrial robot may encounter fixture interference, slight workpiece collision, or strong electromagnetic interference from drastic voltage fluctuations in the plant power grid. These sudden events appear as instantaneous abnormal spike pulses in the current acquisition signal. If these data are directly imported into the recursive identification algorithm, the data covariance matrix will inevitably diverge and amplify. In my engineering implementation, I add an estimation response dead zone and an abnormal data rejection rule inside the controller logic. Once the monitoring module identifies that the current derivative or torque change rate exceeds a set physical safety threshold, the system immediately freezes the parameter iteration for the current cycle. After discarding the abnormal data, the system completes the robust iterative update of each model parameter coefficient only according to Equation (4). This fundamentally maintains the reliable operation of the adaptive compensation mechanism.
$$ \theta_k = \theta_{k-1} + \frac{P_{k-1} \varphi_k}{\lambda + \varphi_k^T P_{k-1} \varphi_k} \left( \tau_{f,k} – \varphi_k^T \theta_{k-1} \right) \tag{4} $$
In Equation (4), θk is the inferred parameter vector at step k, Pk-1 is the historical state covariance matrix of the model, φk is the effective state observation vector after cleaning and filtering, λ is the iterative convergence smoothing forgetting factor, τf,k is the discretized friction residual torque observation input (N·m), and T is the matrix/vector transpose operator. I set λ to 0.995, which gives a reasonable balance between tracking speed and noise rejection. A lower forgetting factor would make the estimate too sensitive to noise, while a higher value would make it too sluggish to follow thermal drift.
4.2 Data Cleaning and Outlier Rejection
I implement a three-stage cleaning process before the recursive update. First, I apply a hard limit on the absolute value of the friction residual. If the residual exceeds a physically plausible maximum, I discard the sample. Second, I compute the derivative of the friction residual and apply a rate limiter. If the rate of change exceeds a threshold, I mark the sample as an outlier. Third, I use a moving median filter over a window of five samples to smooth the remaining data. Table 4 summarizes the cleaning rules and their thresholds.
| Rule | Condition | Action |
|---|---|---|
| Absolute residual limit | |τf| > 1.5 τrated | Discard sample |
| Rate limit | |dτf/dt| > 500 N·m/s | Freeze update for one cycle |
| Moving median | Window size = 5 | Smooth residual |
| Covariance reset | Trace(P) > 108 | Reset P to initial value |
The covariance reset is a last-resort safeguard. In normal operation, the forgetting factor and the cleaning rules keep the covariance bounded. However, if a severe collision occurs, the residual may remain large for several cycles. The covariance reset prevents the estimator from becoming permanently biased. After a reset, the estimator re-learns the friction parameters from the current operating condition.
5. Development of the Underlying Torque Feedforward Compensation System
5.1 Servo Process Data Object Dictionary Mapping
Most mainstream general motion controllers, in order to ensure basic operation stability, encapsulate the underlying drive as a non-intervenable position synchronization control mode. The top-level trajectory planning algorithm is isolated by permission and cannot directly intervene in the current torque regulation inner loop inside the underlying servo control board. To penetrate this closed system architecture, I reconfigured the protocol-level mapping logic of the original process data exchange during the EtherCAT bus power-on initialization scan and topology configuration stage. While retaining the original position and operating state feedback channels, I specifically allocated and added a dedicated dictionary access channel for the target torque offset object. The external control industrial computer calculates the compensation torque command from the operation model. This command completely bypasses the native position closed-loop buffer processing of the controller and transmits the data frame directly to the accumulation execution end of the servo current loop. This achieves microsecond-level torque synchronization additional action at the physical execution level. Table 5 lists the key object dictionary entries I used.
| Index | Sub-index | Object | Data type | Purpose |
|---|---|---|---|---|
| 0x6071 | 0 | Target torque | INT16 | Main torque command |
| 0x60B2 | 0 | Torque offset | INT16 | Feedforward compensation |
| 0x6064 | 0 | Position actual value | INT32 | Encoder feedback |
| 0x6077 | 0 | Torque actual value | INT16 | Current torque feedback |
| 0x606C | 0 | Velocity actual value | INT32 | Velocity feedback |
The torque offset object is added to the process data mapping in the cyclic synchronous position mode. The controller sends the position command as usual, and the external industrial computer sends the torque offset as an additional process data object. The servo drive adds the offset to the torque command generated by its internal position loop. This architecture preserves the original safety and stability of the drive while enabling high-bandwidth friction compensation.
5.2 Communication Delay Look-Ahead Prediction
The industrial communication gateway must execute data packet grouping, transmission, and parsing and forwarding tasks. The underlying control mainboard must also process the digital low-pass filtering algorithm. The superposition of these two parts of computation time inevitably makes the final execution moment of the compensation control torque slightly lag behind the absolute moment when the mechanical structure produces the reversal zero-crossing action. This time difference of several milliseconds is negligible in the high-speed uniform motion section, but at the sensitive instant of velocity zero-crossing reversal, the compensation torque that arrives late cannot offset the static friction. Instead, it becomes destructive impact energy that hinders the reverse motion of the manipulator. To eliminate this timing misalignment, I establish an advance command preview and phase correction mechanism inside the control system. This mechanism uses the command angular acceleration parameter issued in advance by the top-level controller at the planning layer. According to Equation (5), it performs phase lead compensation calculation on the current operating state of the servo execution end.
$$ \dot{q}_{pred} = \dot{q} + \ddot{q}_d \Delta t_{delay} \tag{5} $$
In Equation (5), ·qpred is the preview motion velocity that eliminates the communication lag effect (rad/s), ¨qd is the command angular acceleration issued in advance by the top-level controller (rad/s2), and Δtdelay is the measured and evaluated overall digital delay of the system (s). I measure Δtdelay by injecting a step torque offset and observing the time until the current feedback changes. In my test system, the total delay is approximately 2.5 ms. The preview velocity is then used in Equation (2) instead of the measured velocity, which effectively shifts the friction compensation in time so that it arrives at the joint when the reversal actually occurs.
5.3 Additional Torque Safety Limiting Constraints
In a highly automated large-scale continuous production line, any algorithm exploration that departs from the hardware protection bottom line carries the hidden danger of causing major equipment safety accidents. To prevent precision transmission components and core reducers from being damaged by abnormal overload commands under unpredictable working conditions, I must enforce strict physical boundary numerical truncation on the servo drive at the software control bottom layer. According to the maximum bearing capacity calibrated at the factory for the equipment motor, I unconditionally cut off any extreme abnormal output torque that crosses the allowable range and may induce damage to the manipulator, as shown in Equation (6).
$$ \tau_{out} = \min \left( \max \left( \tau_{comp}, -\eta \tau_{rated} \right), \eta \tau_{rated} \right) \tag{6} $$
In Equation (6), τout is the final controlled torque transmitted after limiting (N·m), τrated is the rated output torque of the servo motor as calibrated at the factory (N·m), and η is the limiting safety protection ratio threshold set according to process requirements. I set η to 0.8 for the welding line, which allows sufficient compensation authority while leaving a 20% margin for unexpected dynamic loads. The limiting is applied in the servo drive firmware, not in the external controller, so it cannot be bypassed by communication errors.
6. Experimental Validation on an Automotive Welding Line
6.1 Test Conditions and Evaluation Metrics
I installed the system on an existing large-load six-axis industrial robot in the body-in-white welding main section of a large automotive enterprise. The robot encoder has blind spots in detecting structural stiffness deformation and transmission backlash. Therefore, I deployed an independent high-frequency laser distance tracking device around the workstation to capture the absolute three-dimensional coordinates of the welding tool center point in a non-contact manner. Table 6 lists the core measurement conditions and operating environment constraints established in accordance with national measurement standards. During the test, the workshop ambient temperature was maintained between 18 °C and 32 °C, which is basically consistent with daily mass production conditions. The spatial circular interpolation radius was set to 15 mm. This size is close to the typical machining feature of small-curvature contour segments in the welding line, and it can effectively excite the frequent reversal motion of each joint in the extremely low-speed region, fully exposing the influence of friction nonlinearity on end-effector trajectory accuracy. During the experiment, the robot end always carried the rated load to ensure that the test conditions matched the force state under the actual production cycle.
| Parameter | Value |
|---|---|
| Rated payload (kg) | 20 |
| Laser measurement sampling frequency (Hz) | 1000 |
| Spatial circular interpolation radius (mm) | 15 |
| Controlled linear speed of interpolation (mm/s) | 5 |
I selected a low speed of 5 mm/s because it is in the regime where friction nonlinearity is most pronounced. At this speed, the joint velocity crosses zero repeatedly during the circular interpolation. The laser tracker recorded the tool center point position at 1 kHz, which is sufficiently high to capture the reversal dynamics. I computed the root mean square error (RMSE) over multiple complete circular cycles. I also computed the process capability index (CPK) for the welding bead quality.
6.2 Real-Machine Trajectory Accuracy and Machining Quality Evaluation
6.2.1 Cold and Hot State Trajectory RMSE Comparison
The experiment set up two comparison groups. The cold-state group was the initial state after power-on, when the lubricating oil was at room temperature. The hot-state group was measured after 3 hours of continuous high-frequency operation under full workshop load, when the lubricating fluid reached its peak temperature. Both groups fully extracted the spatial circular interpolation trajectory data of multiple cycle periods and compared them by offline calculation of the root mean square error. As shown in Table 7, the native control scheme that relies on factory parameter settings shows a clear degradation of tracking accuracy after entering the hot state, and the thermal drift causes the error to increase by a factor of more than two. The multi-source data fusion feedforward compensation scheme, on the other hand, maintains stable smooth tracking characteristics over the entire operating temperature range. The stagnation distortion in the low-speed zero-crossing reversal region of each axis is fully suppressed.
| Control scheme | Cold-state RMSE | Hot-state RMSE |
|---|---|---|
| Factory native state control | 0.15 | 0.42 |
| Offline static friction calibration | 0.13 | 0.28 |
| Fused feedforward compensation control | 0.11 | 0.18 |
The results in Table 7 demonstrate that the proposed method reduces the hot-state RMSE from 0.42 mm to 0.18 mm, which is a 57% reduction. The cold-state RMSE is also improved from 0.15 mm to 0.11 mm. The offline static calibration improves the hot-state error to 0.28 mm, but it cannot match the adaptive method. This is because the static calibration does not account for the temperature and load variations that occur during the 3-hour operation.
6.2.2 Weld Process Capability Index Verification
The tracking consistency accuracy of the industrial robot end-effector trajectory in the spatial scale directly determines the appearance and forming quality of the sheet metal products produced by the continuous operation of the production line. Once the trajectory has a small lag or slight reversal jitter, it is easy to cause uneven heat input distribution in the local area of the molten pool, which in turn induces process scrap defects such as burn-through collapse or virtual welding. The quality inspection department conducted random inspections on the sheet metal welding products produced during the entire operation cycle after applying the technology. They focused on collecting the physical jump range of the standard fish-scale pattern spacing and the solid width dimension deviation of the continuous weld bead. They then aggregated and calculated the process capability index (CPK). As shown in Table 8, after the friction compensation system was fully integrated into the main production line control loop, the surface forming defects derived from the original low-frequency reversal mechanical jitter were eliminated. The global quality control index of the key welding process section improved steadily and stabilized within the industry-recognized high-quality processing range.
| Evaluation item | CPK before compensation | CPK after compensation |
|---|---|---|
| Weld bead overall straightness deviation | 1.12 | 1.45 |
| Surface fish-scale pattern uniformity | 1.08 | 1.42 |
The CPK improvement from 1.12 to 1.45 for straightness and from 1.08 to 1.42 for fish-scale uniformity indicates that the process is now well within the high-quality range. In automotive welding, a CPK above 1.33 is generally considered capable, and a CPK above 1.67 is considered excellent. The proposed method brings the process close to the excellent range without requiring hardware changes to the industrial robots.
7. Discussion
The experimental results confirm that multi-source data fusion can substantially improve the friction compensation performance of industrial robots. The key advantage of my approach is that it does not require additional torque sensors. Instead, it exploits the signals that are already available in the servo drive and the motion controller. This makes it cost-effective for retrofitting existing production lines. The use of EtherCAT distributed clocks ensures that the data fusion is temporally coherent, which is essential for accurate residual extraction. The online recursive update with data cleaning allows the model to adapt to thermal drift and load changes without being destabilized by outliers. The phase lead preview compensates for the communication delay, which would otherwise turn the compensation torque into a disturbance at the reversal instant.
One limitation of my current implementation is that the friction model is still parameterized by a relatively small number of coefficients. In practice, the friction behavior of a harmonic drive can be more complex, especially when the joint is subjected to oscillatory loads or when the lubricant is contaminated. Future work could extend the model to include a frequency-dependent term or a history-dependent term. Another limitation is that the temperature sensor measures the external joint temperature, not the internal lubricant temperature. There is a thermal lag between the two. I partially compensate for this lag by using the online update, but a more direct measurement of the lubricant temperature would improve the transient response. Nevertheless, the current results are already sufficient for the welding process, as demonstrated by the CPK values.
I also note that the proposed method assumes that the rigid-body dynamic model is accurate. If the payload identification is wrong, the friction residual will contain a component of the unmodeled load. In my experiments, I identified the payload before each test run. In a real production line, the payload may change frequently. Therefore, I integrated a load observer that estimates the external load from the joint torque and the known dynamics. The load estimate is then used in Equation (3). This observer is essential for the method to work under variable payload conditions.
8. Conclusion
I have presented a multi-source data fusion method for joint friction modeling and compensation in industrial robots. The method addresses the nonlinear friction-induced trajectory errors that occur at low speed and during direction reversal, as well as the degradation of static compensation under variable thermal and load conditions. By fusing servo current, commanded position, external temperature, and load estimates, I construct a dynamic friction residual expression that captures the actual operating state. I use a temperature and load coupled correction formula to scale the baseline friction torque. I employ a robust recursive parameter update algorithm with data cleaning to maintain convergence in the presence of disturbances. I implement the feedforward torque through a dedicated object dictionary channel on the EtherCAT bus, and I use a phase lead preview to compensate for communication delay. I also apply a safety limiting constraint to protect the transmission components.
The validation on an automotive welding line shows that the proposed method reduces the hot-state spatial trajectory RMSE from 0.42 mm to 0.18 mm. It also improves the process capability index for weld bead straightness from 1.12 to 1.45 and for fish-scale pattern uniformity from 1.08 to 1.42. The method is simple to deploy, computationally efficient, and effective under variable load and long-duration operation. It significantly enhances the end-effector machining accuracy and process stability of industrial robots in manufacturing equipment. In my future work, I plan to extend the method to multi-robot coordination and to investigate the use of internal lubricant temperature estimation to further improve the transient response.
Overall, the study demonstrates that multi-source data fusion is a practical and powerful approach for friction compensation in industrial robots. It leverages existing servo signals and communication infrastructure, avoids expensive torque sensors, and provides robust performance across a wide range of operating conditions. The results support the broader adoption of adaptive friction compensation in industrial robots for high-precision manufacturing.