⚡ electrical engineering

Robust Semi-passive Velocity Field Control with Boundedness Guarantees for Safe Interaction between Mechanical Systems and Physical Environment

This paper proposes a robust semi-passive velocity field control method that relaxes conservative passivity constraints to improve task performance while guaranteeing bounded system states and conditional passivity for safe interaction with unpredictable physical environments.

Original authors: Van Trong Dang, Sumitaka Honji, Takahiro Wada

Published 2026-09-01

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CC BY 4.0

Original authors: Van Trong Dang, Sumitaka Honji, Takahiro Wada

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 robot arm reaching out to touch a human hand, or a mobile robot navigating a crowded room. In these moments of physical contact, safety is not just a feature; it is the absolute priority. For decades, engineers have relied on a principle called energetic passivity to ensure this safety. Think of it as a rule that says a machine can never give back more energy to the world than it has received. If a robot pushes against a wall, it cannot suddenly surge forward with a force it didn't earn. This rule prevents the machine from becoming a dangerous projectile. However, this safety net has a hidden cost. By strictly forbidding the robot from generating its own energy to help a task, the machine can become sluggish, stalling when it needs to move quickly or failing to complete a job if the environment drains its energy. It is a safe but often clumsy partner.

Researchers at the Nara Institute of Science and Technology in Japan have developed a new way to control these mechanical systems that keeps the safety guarantees while allowing the robot to be more agile. They created a control method that acts like a smart energy manager. Instead of being strictly passive all the time, the system monitors its own energy levels. If the energy gets too high, the robot automatically switches to a safe, passive mode to dissipate the excess. But if the energy drops too low, threatening to stop the robot from finishing its task, the system temporarily allows itself to inject energy to keep moving. This approach, tested through detailed computer simulations, proves that a robot can be both safe and effective, even when pushed and pulled by unpredictable forces in its environment.

The core of this work addresses a long-standing dilemma in robotics: how to balance safety with performance. Traditional methods that enforce strict energy rules often result in robots that are too conservative to be useful in dynamic settings. If a robot encounters a heavy object or a sudden push, a purely passive system might simply stop, unable to recover the energy needed to continue its path. The new method, called robust time-varying semi-passive velocity field control, solves this by introducing a flexible boundary. The researchers designed a system where the robot behaves passively only when its internal energy exceeds a specific, pre-set level. This ensures that if the robot starts to accumulate dangerous amounts of energy, it immediately becomes a "sink" that absorbs and dissipates that energy, protecting the environment.

However, when the robot's energy falls below that threshold, the control system relaxes its strictness. It permits the robot to draw from a virtual energy source to compensate for the loss, ensuring the task gets done. This is not a random switch; it is a smooth, continuous adjustment. The researchers proved mathematically that this method keeps the robot's energy and its position within safe, bounded limits, even when external disturbances, such as friction or random pushes, act upon it. In their simulations, they subjected a two-link robot arm to three different types of challenges: rhythmic oscillating forces, constant friction, and pushes that aligned with the robot's movement. In every case, the robot successfully tracked its desired circular path, maintaining its energy within a narrow, safe range of 9 to 11 joules.

The simulations revealed that the robot's ability to recover from energy loss was critical. When the robot faced friction that drained its power, the new controller successfully injected just enough energy to keep it moving without letting the total energy spike dangerously. Conversely, when the environment pushed the robot, adding extra energy, the controller acted as a brake, preventing the system from overheating or becoming unstable. The results showed that the robot's tracking errors remained small and predictable, converging to a stable state within a fraction of a second. This is a significant improvement over older methods that either let the robot stall completely or switch abruptly between modes, which can cause jerky, unsafe movements.

One of the most important findings is that this method also limits the rate at which power flows between the robot and the world. Safety is not just about total energy; it is also about how fast that energy is transferred. A sudden burst of power can be just as dangerous as a large amount of stored energy. The researchers demonstrated that their approach keeps this power flow within a defined limit, ensuring that even if the robot is interacting with a human or a delicate object, the force of the interaction remains controlled. This is achieved by carefully tuning the control parameters, which act like dials that engineers can adjust to prioritize either speed or safety depending on the specific job at hand.

The study also compared this new approach against two existing methods. One older method, which strictly enforces passivity, failed when the robot's energy was drained by friction, causing the robot to stop moving entirely. Another method that switches between different control modes worked better but introduced sudden jumps in behavior that could be jarring and less safe. The new semi-passive method outperformed both by maintaining smooth, continuous motion while keeping the energy and power flow strictly bounded. The researchers noted that while the simulations were successful, the next step is to test the system on real hardware, where physical limits like motor saturation will need to be considered.

Ultimately, this work offers a path forward for robots that need to work alongside humans in unstructured environments. By relaxing the rigid rules of traditional safety controls in a controlled, mathematically proven way, the researchers have shown that machines can be both safe and capable. They have created a system that knows when to hold back and when to push forward, ensuring that the robot remains a reliable partner in tasks ranging from manufacturing to human assistance. The findings suggest that the future of safe robotics lies not in stricter constraints, but in smarter, more adaptive energy management.

Technical Summary: Robust Semi-passive Velocity Field Control with Boundedness Guarantees for Safe Interaction between Mechanical Systems and Physical Environment

Problem Statement
Ensuring stability and safety during physical interactions between nonlinear mechanical systems (e.g., robot manipulators) and unstructured environments is a critical challenge. While energetic passivity-based control (PBC) provides a principled theory for safe interaction by ensuring the closed-loop system does not generate net energy, strictly adhering to passivity constraints often introduces inherent conservatism. This conservatism can restrict control performance, leading to sluggish behaviors or task failure, particularly when the system's energy is depleted by external disturbances. Conversely, purely aggressive control strategies may compromise safety by allowing excessive energy accumulation or high instantaneous power flow. Furthermore, existing methods that attempt to relax passivity, such as switching-based approaches, may induce discontinuities and oscillatory behaviors. The core problem addressed is the need for a control framework that balances task performance with safety, specifically by relaxing conservative passivity constraints in a controlled manner while guaranteeing bounded energy states and power flow under unpredictable external disturbances.

Methodology
The paper proposes a Robust Time-varying Semi-passive Velocity Field Control (SPVFC) for multi-input multi-output (MIMO) nonlinear mechanical systems. The methodology integrates several key components:

Augmented System with Fictitious Flywheel: The system dynamics are augmented with a fictitious flywheel state to serve as an energy storage component. This allows for the formulation of a time-varying velocity field that encodes the desired trajectory and manages kinetic energy redistribution.
Semi-passive Control Law: The control input is designed to guarantee passivity with respect to the force–velocity input–output pair only when the system's kinetic energy exceeds a predefined threshold. When the energy level falls below a lower bound, the controller permits non-passive behavior (energy injection) to prevent task failure.
Smooth Saturation and Energy Compensation: To avoid the discontinuities associated with switching-based methods, the controller employs a smooth saturation function. This function modulates energy compensation terms (including integer and fractional-order elements) based on the energy error.
- When energy is excessive, the system actively dissipates energy.
- When energy is depleted, the system injects energy.
- Within a designed "dead-zone," the system operates passively without active compensation.
Theoretical Analysis: The stability and boundedness of the system are rigorously analyzed using Lyapunov methods. The authors prove that:
- The kinetic energy level converges to a bounded region within a finite time, even in the presence of external disturbances.
- The tracking errors (position and velocity) are Uniformly Ultimately Bounded (UUB) with an exponential convergence rate.
- The instantaneous power flow between the system and the environment is bounded, enhancing interaction safety.

Key Contributions

Relaxed Conservatism with Guarantees: Unlike classical PBC which enforces strict passivity at all times, the proposed SPVFC allows for controlled non-passive behaviors to maintain task performance during energy-depleted conditions, while reverting to passivity when energy is high.
Smooth Transition: The method ensures a smooth and continuous transition between passive and non-passive regimes, avoiding the oscillatory behaviors often caused by switching mechanisms in other approaches.
Robustness to Disturbances: The framework explicitly accounts for unknown but bounded external disturbances, proving that both energy levels and system states converge to bounded domains (UUB).
Power Flow Constraints: The approach provides theoretical guarantees on the boundedness of instantaneous power flow, addressing safety concerns related to high-energy transfer rates that are often overlooked in standard PBC.
Finite-Time Convergence: The analysis demonstrates that the energy level converges to the desired operating region within a specific finite settling time.

Results
Numerical simulations were conducted on a two-link robot manipulator subjected to three types of external disturbances: periodic artificial forces, combined viscous/Coulomb friction, and pushing forces aligned with motion.

Tracking Performance: The proposed method successfully tracked a desired circular trajectory under all disturbance scenarios.
Energy Boundedness: The kinetic energy of the closed-loop system converged to the predefined bounded region $[k_a^d - \delta_2, k_a^d + \delta_3]$ within approximately 0.1 seconds.
Error Convergence: Position and velocity tracking errors converged to bounded regions (UUB) within finite time. The size of these bounds and the settling time were shown to be adjustable via control parameters (e.g., $\kappa$ ).
Comparative Analysis:
- Compared to a standard Passive Velocity Field Control (PVFC), the proposed method prevented task failure caused by energy depletion.
- Compared to a switching-based semi-passive method, the proposed approach eliminated discontinuities and transient peaking phenomena, resulting in smoother control torques and better tracking performance.
- The proposed method successfully prevented excessive energy accumulation (safety risk) observed in other methods when subjected to energy-injecting disturbances.

Significance and Claims
The paper claims that the proposed Robust Time-varying SPVFC offers a systematic solution to the trade-off between safety and performance in physical interaction tasks. By relaxing the conservative nature of classical PBC in a controlled manner, the method ensures that mechanical systems can execute intended tasks even under energy-depleted conditions or external disturbances, without sacrificing safety. The theoretical guarantees of bounded energy, UUB state convergence, and bounded power flow provide a rigorous foundation for safe interaction in unstructured environments. The authors emphasize that this approach improves upon preliminary work by addressing external disturbances and power flow constraints, and it avoids the discontinuities inherent in switching-based strategies. Future work is suggested to address actuator saturation and the development of "power valve-like" mechanisms for direct regulation of energy transfer rates.

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