⚡ electrical engineering

Integrated Identification of Collaborative Robots for Robot Assisted 3D Printing Processes

This paper proposes and validates a model-based, five-step integrated identification methodology that ensures physical consistency to generate a reliable dynamic model for collaborative robots, thereby enhancing precision, control, and error prediction in robot-assisted 3D printing processes.

Original authors: Alessandro Dimauro, Davide Tebaldi, Fabio Pini, Luigi Biagiotti, Francesco Leali

Published 2026-04-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alessandro Dimauro, Davide Tebaldi, Fabio Pini, Luigi Biagiotti, Francesco Leali

Original paper licensed under CC BY 4.0 (http://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 you are trying to build a complex sculpture out of melted plastic, but instead of using a stationary machine, you are using a giant, flexible robotic arm (like a human arm with a 3D printer attached to its hand). This is Robot-Assisted 3D Printing.

The problem? These robotic arms are incredibly complex. They wiggle, they vibrate, and they have "muscles" (motors) and "joints" (gears) that don't always move exactly how the computer tells them to. If the robot thinks it's moving in a straight line but actually wobbles a tiny bit, your plastic sculpture ends up looking like a melted mess instead of a perfect cube.

This paper is about teaching the robot to know itself so perfectly that it can predict its own mistakes before they happen.

Here is the breakdown of their solution, explained simply:

1. The Problem: The "Black Box" Robot

Usually, when you buy a robot, you get a manual that says, "Here is how it moves." But in reality, every robot is slightly different. The gears wear down, the motors heat up, and the plastic arm bends a little under its own weight.

The Analogy: Imagine trying to drive a car where the steering wheel feels different every time you turn it, and the brakes are sometimes sticky. You'd crash. The researchers wanted to stop guessing and start knowing exactly how their specific robot behaves.

2. The Solution: A Five-Step "Self-Check"

The authors created a special five-step recipe to figure out exactly how their robot works. They call this an "Integrated Identification Procedure." Think of it like a doctor giving a robot a full physical exam, but in reverse order.

Step 1: The Blueprint Check (Geometric & Inertial)
- What they did: They started with the robot's digital blueprints (CAD files).
- The Analogy: This is like looking at a car's factory manual to see how heavy the engine is and where the wheels are. They used the computer to guess the weight and balance of every part of the robot.
Step 2: The "Hold Still" Test (Refining Weight)
- What they did: They made the robot hold specific poses and measured how hard the motors had to work to keep it there.
- The Analogy: Imagine holding a heavy box. If you hold it with your arm straight out, your muscles work harder than if you hold it close to your chest. By measuring the "effort" (torque) the robot needed to hold still, they corrected their weight guesses from Step 1.
Step 3: The "Rubbing" Test (Friction)
- What they did: They made the robot move back and forth at a steady speed.
- The Analogy: Think of sliding a heavy box across a carpet. It's hard to start (static friction), but once it's moving, it's easier (kinetic friction), though it still drags. The robot's joints have "rubbing" inside them too. By moving it back and forth, they could calculate exactly how much "drag" exists in each joint.
Step 4: The "Brain" Test (Controller)
- What they did: They gently pushed the robot while it was trying to stay still to see how its "brain" (the controller) reacted.
- The Analogy: If you push a shopping cart, the cart doesn't just move; it wobbles before settling. The robot's computer tries to correct this wobble. Since collaborative robots (cobots) are designed to be safe and can't move super fast, the researchers had to be clever. They gave the robot tiny nicks to see how quickly and strongly its "brain" tried to fix the error.
Step 5: The "Gut Feeling" Check (Remaining Parts)
- What they did: For the tiny electrical details they couldn't measure easily (like the exact resistance in a wire), they used educated guesses based on what is typical for similar robots.
- The Analogy: If you are fixing a watch and you don't have a microscope to see a tiny spring, you assume it's the standard size for that brand of watch.

3. The Result: A "Digital Twin"

Once they finished these five steps, they built a Digital Twin.

The Analogy: Imagine creating a perfect video game version of your real robot. This digital version knows exactly how heavy every part is, how much friction is in every joint, and how the brain reacts to a push.
The Test: They then told the real robot and the digital robot to do the exact same 3D printing tasks.
The Outcome: The real robot and the digital robot moved almost identically. The errors were tiny (less than a millimeter).

Why Does This Matter?

In the past, if a robot made a mistake while 3D printing, you had to wait until the part was finished, see it was wrong, and throw it away.

With this new method:

Prediction: The computer can now say, "Hey, if I move that fast, I'm going to wobble and ruin the print."
Correction: The robot can adjust its movements in real-time to compensate for its own wobbles.
Efficiency: You can print faster and with better quality because the robot isn't guessing; it knows its own limits.

In a nutshell: The authors taught a robot to understand its own body, muscles, and brain so well that it can now print complex shapes with the precision of a surgeon, even though it's a heavy, flexible machine. This is a huge step forward for making high-quality parts (like for cars) using 3D printing.

1. Problem Statement

The integration of Additive Manufacturing (AM) with industrial robotics offers significant advantages for producing complex, large-scale components (e.g., in the automotive sector) by overcoming the workspace and kinematic limitations of traditional Cartesian systems. However, this integration introduces critical challenges:

Dynamic Complexity: Collaborative robots (cobots) have articulated arms with lower stiffness and strongly coupled joint dynamics compared to Cartesian systems.
Precision Limitations: These dynamic characteristics significantly affect positional accuracy, especially during high-speed trajectories required for efficient 3D printing.
Modeling Gaps: Existing identification methods often fail to account for the full system dynamics (including actuators and controllers) or struggle to ensure the physical consistency of identified parameters (e.g., ensuring mass and inertia values remain realistic).
Sensory Constraints: Collaborative robots often lack high-fidelity external sensors and have safety limitations that prevent the execution of abrupt movements needed for traditional frequency-domain identification.

2. Methodology

The authors propose a five-step integrated parameter identification procedure that combines model-based approaches with experimental data. The workflow decouples the complex identification problem into manageable sub-problems to ensure physical consistency without relying on heavy constraint optimization (like Semidefinite Programming).

A. Dynamic Modeling Framework

The system is modeled as a multibody chain of $n$ rigid bodies connected by ideal revolute joints, actuated by electric motors with spring-damper transmissions. The model includes:

Manipulator Dynamics: Euler-Lagrange equations including Coriolis, centrifugal, and gravitational terms.
Friction Model: A Stribeck plus viscous friction formulation.
Actuator Dynamics: Electrical dynamics (inductance, resistance, back-EMF) and mechanical rotor dynamics.
Transmission: Elastic torsional stiffness and damping.
Controller: A linear SISO PI controller with a tracking error feedback loop.

B. The Five-Step Identification Procedure

Geometric and Inertial Analysis (CAD-based):
- Leverages existing CAD files to extract link volumes and calculate initial mass/inertia estimates based on average density.
- Identifies 39 geometric parameters (joint axes, link vectors) and 60 inertial parameters (center of mass, inertia tensors) for a 6-DoF robot.
Inertial Parameter Refinement (Static Measurements):
- Uses static poses to measure joint torques.
- Applies correction coefficients ( $\lambda_k$ ) to CAD-derived masses and inertias to minimize the error between estimated and measured static torques, eliminating the need for iterative optimization.
Friction Parameter Identification (Low-Speed Dynamic):
- Utilizes symmetric periodic trajectories with constant velocity segments in both positive and negative directions.
- By subtracting the equations of motion for opposite velocities, inertial, Coriolis, and gravitational terms cancel out, isolating the friction torque.
- Identifies Coulomb, static, viscous, and Stribeck friction parameters.
Controller Parameter Identification (Disturbance Response):
- Addresses the limitation of cobots (inability to perform fast, abrupt movements).
- Applies artificial external torque disturbances while the robot is at rest (static set point).
- Uses MATLAB's System Identification Toolbox to iteratively identify PI controller gains ( $K_p, T_z$ ) based on the position error response.
Remaining Parameters Estimation:
- Estimates difficult-to-measure parameters (transmission ratios, motor constants, electrical time constants, transmission stiffness/damping) based on typical literature values and scaling laws, as these are less critical for the specific dynamic behavior of interest but necessary for model completeness.

3. Key Contributions

Integrated System Modeling: Unlike traditional approaches that focus solely on manipulator dynamics, this work models the entire chain: robot kinematics, friction, electric actuators, transmission elasticity, and the controller.
Physical Consistency without Constraints: The methodology ensures physical consistency by starting with CAD data and refining it through specific physical tests, rather than imposing mathematical constraints on the final optimization.
Overcoming Cobots Limitations: The proposed disturbance-based method for controller identification allows for accurate modeling of collaborative robots without violating safety protocols or requiring high-speed excitation signals.
Validation in Real-World AM: The approach is validated on a thermoplastic extrusion process, a domain where dynamic errors directly translate to print quality defects.

4. Experimental Results

The methodology was validated using an ABB GoFa CRB15000 collaborative robot equipped with an extrusion head.

Experimental Setup: A Design of Experiments (DoE) was conducted with 19 test points varying:
- Slow printing velocity ( $v_{slow}$ ): 10–40 mm/s.
- Fast transition velocity ( $v_{fast}$ ): 10–100 mm/s.
- Acceleration ( $a$ ): 10%–100% of max.
- Distance from base ( $d$ ): "Close" vs. "Far" configurations.
Model Accuracy:
- Trajectory Tracking: The identified model showed strong agreement with experimental joint trajectories.
- Error Metrics: Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) for the Tool Center Point (TCP) were low. For example, in the best-case scenario, RMSE-X was ~0.08 mm and RMSE-Y was ~0.08 mm.
- Print Quality: The study correlated model predictions with actual printed cube deviations. It found that printing speed ( $v_{slow}$ ) was the dominant factor affecting print quality, with higher speeds leading to increased deviations.
Key Findings:
- The model accurately predicted the degradation of performance at higher velocities and extended configurations.
- The "Far" configuration (extended arm) consistently showed higher errors in experiments than the model predicted, suggesting unmodeled stiffness effects in extreme poses, though the overall trend was captured correctly.

5. Significance and Impact

Enhanced Precision: By providing a reliable dynamic model that includes controller and actuator dynamics, the approach enables better error prediction and compensation strategies for robot-assisted 3D printing.
Process Optimization: The ability to simulate and predict the impact of velocity and acceleration on print quality allows for the optimization of printing parameters before physical execution, reducing material waste and trial-and-error time.
Scalability: The methodology is particularly valuable for the automotive and luxury sectors where complex, large-scale 3D printing is emerging, as it bridges the gap between the flexibility of robotics and the precision required for industrial manufacturing.
Digital Twin Potential: The validated model serves as a robust foundation for creating Digital Twins of robotic AM systems, facilitating advanced control and real-time quality monitoring.