⚡ electrical engineering

Data-Driven Self-Calibration of Force Sensing for Industrial Robots with Unknown Tool Attachments

This paper presents a data-driven self-calibration framework for industrial robots that accurately compensates for force/torque sensor biases caused by unknown tool attachments under both quasi-static and dynamic conditions using regression and machine learning models, thereby enabling reliable force perception without requiring prior tool property knowledge or hardware modifications.

Original authors: Haniyeh Altafi, Soroush Sadeghian, Kourosh Zareinia

Published 2026-08-10

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CC BY 4.0

Original authors: Haniyeh Altafi, Soroush Sadeghian, Kourosh Zareinia

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a robot arm as a super-strong, super-precise painter. To do its job, it needs to know exactly how hard it's pressing against a canvas or a piece of clay. This is where a "force sensor" comes in; it's like the robot's sense of touch, telling it, "Hey, I'm pushing with 5 Newtons of force." But here's the catch: robots often carry tools attached to their hands, like a paintbrush, a screwdriver, or a surgical clamp. These tools have weight, and when the robot moves its arm quickly, that weight creates extra forces—like the feeling of a heavy backpack pulling you down when you run. If the robot doesn't know exactly how heavy its backpack is or where its center of gravity is, it gets confused. It might think the heavy backpack is actually a wall it's bumping into, or it might push too hard because it doesn't realize it's carrying a heavy load. This confusion makes the robot clumsy, unsafe, or unable to perform delicate tasks. Scientists have long tried to fix this by measuring the tools perfectly and writing complex math equations to cancel out the weight, but this is slow and breaks down whenever the robot swaps tools for a new one.

This paper tackles that exact headache with a clever, data-driven trick. Instead of asking the robot to memorize the weight of every possible tool it might ever hold, the researchers taught the robot to "feel" the difference between the weight of its own tools and the actual forces from the outside world. They used a large industrial robot (a KUKA KR 600) equipped with a force sensor and a custom tool holder. First, they let the robot stand still in various positions to learn how gravity pulls on the tool (the "quasi-static" part). Then, they made the robot move wildly in random patterns to see how acceleration and speed mess with the sensor readings (the "dynamic" part). By collecting over 80,000 samples of this motion data, they trained two types of "brain" models: a simple math formula (polynomial regression) and a more complex neural network (MLP). The results were impressive: the models learned to strip away the tool's weight and motion noise with incredible precision. The best model, the neural network, reduced the error to just 0.041 Newtons in tests, which is so small it's practically invisible compared to the sensor's own natural noise. The paper shows that robots can now self-calibrate their sense of touch without needing to know the tool's weight or shape beforehand, making them ready to swap tools instantly and still work with the same steady hand.

Technical Summary: Data-Driven Self-Calibration of Force Sensing for Industrial Robots with Unknown Tool Attachments

1. Problem Statement

Accurate force perception is critical for industrial robots performing contact-rich tasks such as assembly, teleoperation, and surgical assistance. However, force/torque (F/T) sensors mounted on robot end-effectors often produce biased measurements when unknown or interchangeable tools are attached. These biases arise from the tool's mass, center of mass, and inertial properties, which generate gravitational and dynamic offsets during motion.

Traditional calibration methods rely on analytical models requiring precise prior knowledge of tool mass distribution and inertia. These approaches are impractical for systems with frequently changing or custom-designed end-effectors, as they necessitate repeated manual calibration and hardware modifications. Furthermore, existing data-driven methods often focus on static conditions or require embedded sensors (e.g., IMUs) not present in standard commercial setups. There is a need for a software-based, data-driven framework that can self-calibrate force sensors under both quasi-static and dynamic conditions without requiring knowledge of the attached tool's physical properties.

2. Methodology

The study proposes a two-stage, data-driven self-calibration framework implemented on a KUKA KR 600 industrial robot equipped with an ATI Gamma six-axis force/torque sensor. The framework operates without prior knowledge of the tool's mass, center of mass, or inertia.

2.1 Experimental Setup

Data was collected using a custom-made tool holder attached to the robot end-effector, which included surgical forceps and actuation mechanisms. The setup allowed for the collection of raw F/T sensor readings alongside robot kinematic data (joint encoders, end-effector position, orientation, and acceleration).

2.2 Quasi-Static Calibration

To address gravity-induced offsets, a quasi-static calibration strategy was developed:

Data Collection: The robot was positioned at various orientations and held stationary to eliminate acceleration effects.
Feature Selection: Two input models were compared: one based on joint angles and another based on end-effector orientation (roll, pitch, yaw). The orientation-based model yielded superior results.
Model: A third-degree polynomial regression model was trained using the orientation vector as input to estimate the static gravitational offset ( $\hat{w}_{qs}$ ).
Process: The estimated static offset is subtracted from the raw sensor reading to isolate the residual dynamic component.

2.3 Dynamic Calibration

To compensate for motion-induced inertial forces, a dynamic calibration framework was developed:

Data Collection: Over 80,000 motion samples were collected during random robot movements involving varying positions, orientations, and velocities.
Feature Selection: A nine-dimensional input vector ( $x_d$ ) was constructed, comprising end-effector position ( $x, y, z$ ), orientation ( $\phi, \theta, \psi$ ), and Cartesian linear acceleration ( $a_x, a_y, a_z$ ). Joint-space variables (angular velocity/acceleration) were tested but showed weaker correlation with force data compared to Cartesian features.
Modeling Approaches:
1. Polynomial Regression: A second-degree polynomial model was selected as the optimal trade-off between accuracy and complexity. Higher degrees (3 and 4) exhibited overfitting.
2. Multilayer Perceptron (MLP): A feedforward neural network with three hidden layers (64, 128, 64 neurons), ReLU activation, batch normalization, and dropout (0.2) was trained to capture complex nonlinearities.
Process: The dynamic model estimates the residual dynamic offset ( $\hat{w}_{dyn}$ ) from the quasi-static corrected data. The final compensated wrench ( $w_{comp}$ ) is calculated by subtracting both static and dynamic estimates from the raw reading.

3. Key Contributions

Tool-Agnostic Quasi-Static Calibration: A data-driven strategy that compensates for gravity-induced offsets using only end-effector orientation, eliminating the need for tool mass or center-of-mass parameters.
Dynamic Compensation Framework: A comprehensive approach for modeling motion-induced force disturbances using both interpretable polynomial regression and deep learning (MLP) under realistic operating conditions.
Physical Validation: The method is demonstrated on a physical industrial robot (KUKA KR 600) with a standard commercial F/T sensor, showing scalability to applications with interchangeable tools and minimal manual intervention.

4. Results

The performance of the models was evaluated using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) on test and independent benchmark datasets.

4.1 Quasi-Static Performance

Model: Third-degree polynomial regression.
Metrics: Achieved a test-set MSE of 0.005 and a benchmark RMSE of 0.036 N.
Accuracy: Maximum absolute errors were 0.13 N (X), 0.06 N (Y), and 0.11 N (Z), corresponding to less than 0.03% of Full Scale Output (FSO).

4.2 Dynamic Performance

Polynomial Regression (2nd Degree):
- Benchmark RMSE: 0.0458 N.
- Maximum total force magnitude error: 0.54 N (0.108% FSO).
MLP Model:
- Test-set RMSE: 0.041 N; Benchmark RMSE: 0.049 N.
- Maximum total force magnitude error: 0.53 N (0.106% FSO).
Comparison: The MLP model demonstrated superior capability in capturing highly dynamic, nonlinear behaviors compared to the polynomial model, though both performed within the practical accuracy limits of the ATI Gamma sensor.

4.3 Correlation Analysis

Correlation analysis revealed that simple pairwise linear relationships between individual acceleration components and force readings were weak. This confirmed that dynamic force offsets are multivariable and nonlinear, justifying the use of full nine-dimensional input vectors and complex models (MLP) rather than simple linear regressions.

5. Significance and Claims

The paper claims that the proposed framework significantly improves force perception reliability for robots operating with unknown or changing tool attachments. Key significance points include:

Elimination of Manual Modeling: The method enables accurate force compensation without requiring prior knowledge of tool properties (mass, inertia) or hardware modifications (e.g., adding IMUs).
Robustness in Dynamic Conditions: By separating tool-induced disturbances from true interaction forces, the system supports more reliable contact detection and control in dynamic environments.
Practical Applicability: The results indicate that the proposed method operates close to the sensor's noise floor, making it suitable for integration into autonomous, haptic, and teleoperated robotic systems where accurate force feedback is essential for safety and task execution.
Scalability: The data-driven nature of the approach allows it to scale to various tool configurations and motion profiles without the need for re-deriving analytical models.

The authors note that while the calibration performance is strong, the study evaluated the method at the sensing level. Future work is suggested to integrate these calibrated estimates into closed-loop control experiments to assess their direct impact on contact-rich manipulation tasks.