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Embedding ISO 10218 Safety Compliance in Robots via Control Barrier Functions for Human-Robot Collaboration

This paper proposes a Control Barrier Function (CBF) integrated into a Sequential Quadratic Programming (SQP) framework that leverages human acceleration data to analytically predict minimum separation distances, thereby enabling a UR10e robot to comply with ISO 10218 safety standards while significantly reducing trajectory errors and avoiding unnecessary operational halts compared to standard Speed and Separation Monitoring methods.

Original authors: Federico Parma, Cesare Tonola, Nicola Pedrocchi, Manuel Beschi

Published 2026-06-12

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CC BY 4.0

Original authors: Federico Parma, Cesare Tonola, Nicola Pedrocchi, Manuel Beschi

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 a factory floor where a human worker and a robot arm are working side-by-side, like two dancers in a tight routine. The goal is for them to collaborate efficiently without bumping into each other. However, there's a strict safety rulebook (called ISO 10218) that says: "If the human gets too close, the robot must slow down or stop immediately to avoid a crash."

The Problem: The "Paranoid" Robot

The current way robots handle this is like a paranoid driver who sees a pedestrian 50 meters away and slams on the brakes immediately, assuming the pedestrian will walk straight toward them at a steady pace.

In the paper, the authors call this the Standard SSM (Speed and Separation Monitoring). It's very safe, but it's also very clumsy. Because it assumes the human moves at a constant speed and doesn't predict acceleration, the robot often stops unnecessarily. It's like the driver stopping at a red light that hasn't even turned red yet. This kills productivity because the robot spends more time waiting than working.

The Solution: The "Crystal Ball" Robot

The authors propose a new system using something called a Control Barrier Function (CBF). Think of this as giving the robot a crystal ball or a predictive GPS.

Instead of just looking at where the human is right now, this new system looks at:

Where the human is.
How fast they are moving.
Crucially, how fast they are speeding up or slowing down (acceleration).

By knowing the human's acceleration, the robot can calculate the worst-case scenario: "If the human suddenly sprints toward me, exactly how close will we get before I can stop?"

This allows the robot to make smarter decisions. If the human is walking slowly, the robot keeps working. If the human starts sprinting, the robot slows down just enough to stay safe, rather than coming to a complete, jarring halt.

The Two Methods Tested

The researchers tested two different ways to use this "crystal ball" on a real robot (a UR10e arm):

Method I (The "Reactive" Dancer): This method uses the safety prediction to adjust the robot's speed, but it's a bit like a dancer who panics when the music changes. It avoids collisions, but it gets so scared of hitting the human that it swerves wildly off its path. It works fast, but it misses its target spots (the "waypoints") and makes messy movements.
Method II (The "Graceful" Dancer): This is the winner. It uses the same crystal ball but adds a "spatial tube" constraint. Imagine the robot is running inside a transparent, flexible tube. It can speed up, slow down, or wiggle slightly to avoid the human, but it must stay inside the tube.
- If the human gets close, the robot slows down smoothly.
- If the human moves away, the robot speeds back up.
- It never swerves wildly outside the tube.

The Results

The team ran thousands of tests in simulation and with real humans. Here is what happened:

The Old Way (Baseline): The robot stopped constantly. It was safe, but it only completed 41 tasks in a long test. It was too slow to be useful.
Method I: The robot kept moving fast and completed 994 tasks. However, it was so erratic that it missed its target spots 37% of the time and swerved into the human's workspace.
Method II (The New Approach): This was the sweet spot. It completed 789 tasks (much faster than the old way) and hit its target spots 93% of the time.

The Bottom Line:
By using a mathematical trick that predicts how fast a human is accelerating, the robot can stay safe without being a "paranoid stopper." It moves like a skilled partner rather than a frightened machine. The new system reduced the robot's errors by 63% compared to the first method, proving that you can have both high safety and high productivity in a factory.

Technical Summary: Embedding ISO 10218 Safety Compliance in Robots via Control Barrier Functions for Human-Robot Collaboration

Problem Statement
Human-Robot Collaboration (HRC) requires strict adherence to safety standards, specifically ISO 10218, to prevent harmful interactions. A primary mechanism for ensuring safety in shared workspaces is Speed and Separation Monitoring (SSM). However, standard industrial SSM filters rely on conservative assumptions, such as constant human velocity and the requirement that the robot must come to a complete stop before the human reaches a certain distance. These assumptions often lead to inaccurate predictions of minimum separation distances, resulting in unnecessary operational halts and reduced productivity. Furthermore, existing control strategies often fail to constrain the robot's spatial deviation during evasive maneuvers, potentially causing collisions with static infrastructure or confusing human operators.

Methodology
The paper proposes a Control Barrier Function (CBF) framework that explicitly incorporates real-time human acceleration data to analytically forward-predict the minimum human-robot separation distance during a worst-case robotic stopping trajectory. This predictive approach is integrated as an inequality constraint within a Sequential Quadratic Programming (SQP) control framework. The system state includes the Cartesian position, velocity, and acceleration of both the robot and the human.

Two specific control methods are proposed and evaluated:

Method I (CBF-Constrained PD Controller): A minimally invasive safety filter that tracks a nominal PD Cartesian acceleration reference while satisfying the CBF safety constraints. This method prioritizes throughput but lacks explicit constraints on spatial deviation from the nominal path.
Method II (Task-Scaling SQP Controller): A more advanced controller that introduces a task-scaling parameter to modulate the progression along the nominal trajectory. Crucially, this method enforces a "spatial tube constraint" to prevent evasive maneuvers from deviating chaotically from the intended path. It also includes a recovery strategy for infeasible states, where the controller switches to maximum braking while dynamically relaxing spatial bounds to ensure fail-safe behavior.

The CBF is derived from ISO 10218 kinematic limits, calculating the minimum distance ( $d_{min}$ ) by analyzing relative velocities and identifying critical time instants (e.g., reaction time end, full stop) where the distance might be minimized.

Key Contributions

Predictive CBF Derivation: The authors derive a CBF that accounts for real-time human acceleration, overcoming the over-reactivity of standard SSM filters that assume constant human velocity.
Spatially Constrained Task-Scaling: The proposal of a task-scaling SQP controller that integrates a spatial tube constraint. This allows the robot to modulate speed and safely deflect from its path without chaotic maneuvers, addressing a gap in previous CBF applications that often ignored spatial fidelity.
Experimental Validation: The algorithms are validated in both simulation and real-world scenarios using a UR10e robot, a ZED 2 camera for human skeletonization, and an Inxpect X-300 radar-camera sensor.

Results
The proposed methods were compared against a standard industrial SSM module baseline and against each other over long-duration tests (15,000 seconds):

Efficiency vs. Safety: The baseline SSM module ensured safety but resulted in severe inefficiency, completing only 41 laps with a mean scaling factor of 0.15 due to frequent stops. Method I achieved the highest throughput (994 laps) but suffered from severe spatial deviations (62.91% waypoint accuracy) and excessive evasive footprints.
Optimal Balance (Method II): Method II achieved an optimal balance, completing 789 laps with a mean scaling factor of 0.81. It successfully reached 92.91% of designated waypoints.
Trajectory Accuracy: Method II demonstrated a 63% reduction in mean trajectory error compared to Method I (0.0142 m vs. 0.0384 m in simulation; 0.0113 m vs. 0.0232 m in real-world trials).
Real-Time Feasibility: The SQP solver maintained real-time performance, failing to find a solution within the 2ms control period in only 0.0004% of cycles, with a fallback strategy in place for such instances.

Significance and Claims
The paper claims that coupling predictive human kinematics with a task-scaling CBF framework mathematically guarantees safety while maximizing spatial fidelity and task productivity. By moving beyond instantaneous distance metrics to forward-predict worst-case stopping distances, the framework avoids the severe conservatism of traditional reactive filters. The authors assert that Method II successfully demonstrates that high-throughput, contactless collaboration is achievable without sacrificing the strict safety requirements of ISO 10218 or the geometric precision of the robot's path.

The authors note limitations for future work, specifically the reliance on a constant human acceleration assumption (which requires a conservative safety buffer) and the use of static SQP cost-function weights. They suggest that integrating probabilistic human motion models and adaptive weighting strategies could further optimize throughput and responsiveness.

The Problem: The "Paranoid" Robot

The Solution: The "Crystal Ball" Robot

The Two Methods Tested

The Results

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