💻 computer science

Coordinated motion control of a wire arc additive manufacturing robotic system for multi-directional building parts

This paper proposes a coordinated motion control algorithm for a dual-robot wire arc additive manufacturing (WAAM) system that simultaneously plans the deposition trajectory relative to the workpiece and aligns the build direction with gravity to improve the quality of complex, multi-directional parts.

Original authors: Fernando Coutinho, Nicolas Lizarralde, Fernando Lizarralde

Published 2026-02-24

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Fernando Coutinho, Nicolas Lizarralde, Fernando Lizarralde

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 a master chef trying to build a giant, intricate cake out of molten chocolate. You have a special nozzle that pours the chocolate, and you want to build a cake that isn't just a flat rectangle, but a curved, twisting tower.

Here's the problem: If you try to pour molten chocolate onto a steep slope or an overhang, gravity takes over. The chocolate drips, pools in the wrong places, or creates a messy "staircase" effect instead of a smooth curve. To make a perfect cake, you usually have to pour it flat on a table. But if you only pour flat, you can't build a curved tower without using a lot of extra scaffolding (support structures) that you have to chip away later.

This paper is about a clever robotic solution to this "molten chocolate" problem.

The Setup: A Two-Robot Dance

The researchers set up a "Wire Arc Additive Manufacturing" (WAAM) system. Think of this as a high-tech 3D printer that uses a welding torch instead of plastic.

Robot A (The Artist): Holds the welding torch.
Robot B (The Stage Manager): Holds the metal part being built on a table.

Usually, the "Artist" moves around a stationary "Stage." But for complex shapes, that doesn't work well because the molten metal needs to stay flat relative to gravity, not relative to the part.

The Solution: The "Task Augmentation" Dance

The paper proposes a new way to control these two robots so they move in perfect sync, like a dance partner.

The Analogy: The Painter and the Canvas
Imagine a painter (Robot A) trying to paint a perfect straight line on a canvas (Robot B) that is being tilted and rotated by a second person.

The Goal: The painter needs to keep their brush moving along a specific path on the canvas (the design).
The Constraint: At the same time, the painter must keep their brush pointing straight down toward the floor (gravity) so the paint doesn't drip.

If the canvas tilts, the painter can't just tilt their arm; they have to twist their whole body, and the person holding the canvas has to rotate it to compensate.

How the Paper Solves This:
The authors created a "brain" (an algorithm) that treats the two robots as one single super-robot.

The Main Task: The torch follows the shape of the part (e.g., a curved pipe) on the metal table.
The Extra Task: The torch also constantly checks its angle against the floor (gravity).

The algorithm uses a mathematical trick called "Task Augmentation." Instead of telling the robots "Move here, then move there," it tells them: "Move the torch along this path on the table, AND simultaneously keep the torch pointing at the floor."

If the robots get confused (a mathematical "singularity" where the math breaks down because the table and the floor are aligned in a tricky way), the system uses a "damping" technique. Think of this like a shock absorber in a car. When the road gets bumpy (the math gets hard), the shock absorber smooths out the ride so the car doesn't crash, allowing the robots to keep moving without stopping.

The Results: Building Curved Towers

The team tested this by building three things:

A Slanted Wall: They built a wall leaning at a 45-degree angle. The robots tilted the table just enough so the molten metal always flowed straight down, creating a smooth surface.
A Curved Wall: They built a 90-degree bend. As the wall curved, the robots rotated the table and the torch in perfect harmony to keep the "pour" vertical.
An Intake Funnel: A complex shape that starts as a cylinder and flares out like a trumpet.

Why is this a big deal?

No Scaffolding Needed: Because the metal is always poured flat relative to gravity, it doesn't drip. You don't need to build extra supports that you have to cut off later.
Better Quality: The surface is smooth, not "stair-stepped."
Faster: Less time spent on cleanup and supports means faster production.

The Bottom Line

This paper teaches robots how to juggle two jobs at once: drawing a complex shape on a moving target while keeping their tool perfectly aligned with gravity. It's like teaching a robot to pour a perfect cup of coffee while walking up a spiral staircase, without spilling a drop. This allows us to build stronger, more complex metal parts for things like airplanes, cars, and oil rigs, faster and with less waste.

1. Problem Statement

Wire Arc Additive Manufacturing (WAAM) is a metal 3D printing technology capable of producing large, complex structural parts. However, a significant limitation exists when manufacturing parts with non-planar geometries or variable build directions:

Gravity Constraints: In standard WAAM, the deposition process is typically performed in a flat position to ensure the molten pool remains stable. When building complex shapes (e.g., curved pipes or inclined walls), the build direction often deviates from the gravity vector.
Defects: This misalignment causes unsupported overhangs (where molten metal drips), the staircase effect (poor surface finish due to layer stepping), and reduced volumetric accuracy.
Current Limitations: Traditional solutions involve using support structures (increasing waste and post-processing time) or offline planning that cannot adjust for real-time errors. Furthermore, standard 6-DOF manipulators often lack the redundancy to simultaneously track a complex trajectory on the workpiece and maintain the torch orientation relative to gravity.

2. Methodology

The authors propose a closed-loop coordinated motion control algorithm for a dual-robot system consisting of a 6-DOF manipulator (holding the torch) and a 2-DOF positioning table (holding the workpiece).

A. System Modeling

The two robots are treated as a single redundant kinematic chain (8-DOF total). The system defines two distinct frames:

Deposition Frame ( $F_d$ ): Attached to the workpiece.
Inertial Frame ( $F_{ab}$ ): Fixed to the robot base (aligned with gravity).

The control objective is twofold:

Main Task: The Tool Center Point (TCP) must follow a desired trajectory defined relative to the workpiece ( $F_d$ ).
Constraint Task: The torch orientation (specifically the Z-axis) must remain aligned with a desired direction in the inertial frame (e.g., gravity), regardless of the workpiece's orientation.

B. Control Strategy: Task Augmentation

Instead of using a task-priority method (which can fail at singularities), the authors utilize Task Space Augmentation combined with the Augmented Jacobian approach.

Augmented Jacobian ( $J_A$ ): The main task (trajectory tracking) and the constraint task (orientation alignment) are stacked into a single differential kinematic relation:
$\begin{bmatrix} v \\ \omega_s \end{bmatrix} = J_A(\theta) \dot{\theta}$
Where $v$ is the TCP velocity and $\omega_s$ represents the orientation error dynamics.
Control Law: The joint velocities ( $\dot{\theta}$ ) are computed using the pseudo-inverse of the augmented Jacobian. To handle the internal dynamics of the industrial robots (which are not fully accessible), the control assumes the robots have fast internal loops that track velocity commands.
Stability: The authors prove asymptotic stability of the closed-loop system using Lyapunov theory, accounting for unmodeled dynamics ( $\eta$ ) inherent in the robot controllers.

C. Singularity Handling

A common algorithmic singularity occurs when the deposition frame's Z-axis aligns with the inertial frame's Z-axis (e.g., when the part is flat), causing the augmented Jacobian to lose rank.

Solution: The authors implement a Damped Least Squares (DLS) method with numerical filtering. This strategy progressively reduces the velocity associated with the conflicting task (orientation alignment) near singularities without disrupting the primary deposition path tracking.

3. Key Contributions

Dual-Robot Coordinated Control: A novel algorithm that decouples the workpiece motion from the torch orientation, allowing for multi-directional building without support structures.
Task Augmentation Framework: Demonstrates that the constrained Jacobian method is mathematically equivalent to the augmented Jacobian method in this context, providing a robust theoretical foundation for handling redundant systems.
Robust Singularity Management: A specific implementation of DLS with filtering that maintains deposition quality even when the algorithmic singularity is approached.
Experimental Validation: Successful production of complex geometries (inclined walls, curved walls, and intake funnels) using a real-world KUKA robotic cell.

4. Experimental Results

The proposed method was validated using a KUKA KR90 manipulator and a KUKA KP2 positioning table with a CMT-WAAM process. Three distinct parts were manufactured:

Inclined Thin Wall ( $45^\circ$ ):
- Successfully deposited 20 layers at a $45^\circ$ angle.
- The torch maintained alignment with gravity while the table tilted the workpiece.
- Result: Position and orientation errors converged to near zero; the part showed high symmetry and no dripping.
Curved Thin Wall ( $90^\circ$ Arc):
- Manufactured a curved section by continuously adjusting the torch orientation relative to the workpiece while keeping it vertical relative to gravity.
- Result: The system handled the continuous change in build direction. The RMS error for the inclination angle converged rapidly to zero. The system also demonstrated adaptability by adjusting the torch angle to avoid collisions with substrate screws.
Intake Funnel (Cylinder + Bell-mouth):
- A complex part requiring a transition from a straight cylinder to a flared bell-mouth section.
- Result: The system successfully managed the changing curvature and radius. Despite minor calibration issues (requiring dry-run adjustments), the final part exhibited good symmetry and surface quality, verified by 3D scanning.

Performance Metrics:

Tracking errors for position and orientation were consistently small (RMS errors converged to zero).
The DLS filtering successfully prevented instability during singular configurations.
Surface quality was significantly improved compared to traditional fixed-angle deposition, eliminating the need for support structures.

5. Significance and Impact

This work addresses a critical bottleneck in metal additive manufacturing: the ability to produce complex, non-planar geometries with high surface quality and structural integrity.

Elimination of Supports: By aligning the build direction with gravity dynamically, the need for sacrificial support structures is removed, reducing material waste and post-processing time.
Operational Efficiency: The closed-loop nature of the control allows for real-time corrections, making the process more robust than offline planning methods.
Scalability: The approach is generalizable to other redundant robotic systems and can be extended to hybrid manufacturing or obstacle avoidance scenarios in future work.

In summary, the paper presents a mathematically rigorous and experimentally validated solution for multi-robot coordination in WAAM, enabling the fabrication of complex industrial parts that were previously difficult or impossible to produce with high quality.