💻 computer science

Real-time Estimator of Actuator Control and Health (REACH) on an Eel-Inspired Soft Robot

This paper presents REACH, a real-time algorithm that utilizes a soft robot model, sigma point filter, and statistical hypothesis testing to accurately estimate actuator health and degradation in eel-inspired underwater robots across various swimming gaits and sensor configurations.

Original authors: Zhangjingyi Jiang, Myungsun Park, Michael T. Tolley, Mark Campbell

Published 2026-08-18

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CC BY 4.0

Original authors: Zhangjingyi Jiang, Myungsun Park, Michael T. Tolley, Mark Campbell

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

Deep beneath the surface, where sunlight fades and pressure mounts, autonomous machines are tasked with exploring the unknown. These underwater vehicles, designed to operate without human guidance, face a unique challenge: the very materials that make them flexible and adaptable are also their weakest link. Unlike rigid metal robots, soft robots are built from pliable substances that can bend and twist like living creatures, allowing them to slip through tight spaces and move quietly. However, these soft materials are prone to wear, tearing, or simply losing their strength over time. If an underwater robot cannot tell that its muscles are failing, it may drift off course or become stranded, unable to return to safety. The critical question for engineers is how to give these machines a sense of their own internal health, allowing them to detect damage instantly and adjust their movements to survive.

Researchers have developed a new system called REACH to solve this problem for a specific type of underwater robot designed to swim like an eel. This robot, built by a team from Cornell University and the University of California San Diego, mimics the undulating motion of an eel, using a series of soft, water-filled chambers that expand and contract to propel it forward. The researchers created a digital twin of this robot, a sophisticated simulation that predicts how the machine should move under perfect conditions. They then built a real-world version of the robot and placed it in a water tank to test if they could use the difference between the expected movement and the actual movement to figure out when an actuator—the robot's "muscle"—was failing. The system works by constantly comparing what the robot is doing against what it should be doing, using a statistical method that can handle the messy, unpredictable nature of fluid dynamics and soft materials.

To make this system work, the team had to decide which sensors would provide the best data. They tested three different types of measurement tools: a global positioning system to track location, an inertial measurement unit to sense acceleration and orientation, and flexible bend sensors attached directly to the robot's body. The results were clear and surprising. The global positioning system, often the go-to for navigation, proved useless for this specific task. Because the robot moves slowly and the water environment is complex, the position data was too slow to react to sudden failures. In contrast, the bend sensors and the inertial measurement units performed exceptionally well. The bend sensors, which measure how much the robot's body curves, were able to detect a failure almost immediately, while the inertial units, which sense how the robot shakes and turns, were nearly as effective.

The researchers also investigated how many sensors were actually needed to keep the robot safe. They found that for the inertial measurement units, placing just two sensors on the robot was enough to accurately diagnose the health of all its muscles. For the bend sensors, which are more localized and only "see" the part of the robot they are attached to, three sensors were required to get a complete picture of the robot's condition. This distinction is vital for future designs, as adding too many sensors can make a robot heavy and expensive, while too few leaves it blind to damage. The team tested the system under three different swimming styles: swimming straight, making wide turns, and executing tight, sharp turns. In every scenario, the system successfully identified when a muscle failed, regardless of how the robot was moving.

Finally, the team took the system out of the computer and into the water with a physical robot fish. They deliberately degraded the performance of the robot's muscles by reducing the water flow to specific chambers, simulating a tear or a pump failure. The system, using data from the bend sensors, was able to detect these changes in real-time. While the estimates were not always perfectly precise in the first few seconds—likely due to the time it took for the water pumps to ramp up—the system quickly stabilized and correctly identified which muscles were damaged and to what extent. The study demonstrates that by combining a realistic simulation with the right mix of sensors, soft robots can be given the ability to monitor their own health, ensuring they can complete their missions and return home even when parts of their bodies begin to fail.

Technical Summary: Real-time Estimator of Actuator Control and Health (REACH) on an Eel-Inspired Soft Robot

Problem Statement
Autonomous underwater vehicles (AUVs) operating in harsh environments face significant challenges regarding material degradation and actuator failure, particularly when utilizing soft robotics. Soft robots, while advantageous for their flexibility, adaptability, and low drag, suffer from compliant materials prone to degradation (e.g., Mullins effect) and tears. Unlike rigid actuators, where health monitoring often relies on binary model-based logic or discrete machine learning classifications, soft actuators exhibit complex, continuous nonlinear behaviors. Current methods are insufficient for capturing the gradual degradation and continuous fault states of soft actuators. There is a critical need for an estimation system that can accurately and rapidly predict actuator health to enable mission adaptation and safe return-to-base capabilities without human intervention.

Methodology
The paper proposes REACH (Real-time Estimator of Actuator Control and Health), a novel architecture designed to estimate the health of an eel-inspired soft swimming robot. The system defines actuator health ( $H$ ) as the ratio of actual to desired actuator torque output, where $H=0$ represents full failure and $H=1$ represents full functionality.

The core methodology integrates three primary components:

Prediction Model: The system utilizes the Anguilliform Swimming Soft Robot Simulation Platform (ASSRSimP). This platform employs a Finite Element Method (FEM) model of a free-floating elastic beam coupled with a nonlinear hydrodynamics model. The control approach generates swimming gaits (linear, turning, braking) by modulating torque inputs. To simulate degradation, the torque input for each actuator is multiplied by its health value ( $H_i$ ).
Estimation Algorithm: A Sigma Point Kalman Filter (SPKF) is employed to handle the nonlinearities of the hydrodynamic model without requiring analytical Jacobians. The actuator health vector is appended to the state vector, allowing the filter to estimate health alongside the robot's physical state.
Validation and Tuning: A formal statistical hypothesis test is used to validate filter consistency. The average normalized innovation squared ( $\lambda_{KF}$ ) is calculated over a time window and compared against Chi-squared thresholds to ensure the filter is neither biased nor overly conservative. This method is used to tune process and measurement noise statistics.

Key Contributions
The paper presents three primary contributions:

REACH Architecture: A complete system comprising sensors, an SPKF estimator, and a formal hypothesis test to estimate actuator degradation in eel-inspired soft robots.
Sensor Comparative Study: A rigorous evaluation of internal bend sensors versus inertial measurement units (IMU) and GPS for health estimation, analyzing both sensor types and optimal placement strategies.
Experimental Validation: The validation of the actuator health estimator using a physical three-actuator soft robot fish swimming underwater, demonstrating the algorithm's performance with noisy real-world data and manufacturing variations.

Results
The performance of REACH was evaluated through simulation and physical experiments using metrics of RMS error (accuracy) and rise time (timeliness).

Sensor Comparison:
- GPS: Proven unsuitable for this application due to long rise times and unreliable convergence; it failed to detect failures within the required timeframe.
- IMU and Bend Sensors: Both were deemed adequate. IMUs generally demonstrated lower rise times for failures in the first four actuators, while bend sensors showed lower RMS errors for most cases and faster detection for the fifth actuator.
- Sensor Quantity and Placement: Simulation results indicated that two IMUs (placed at actuators A1 and A4) are sufficient for excellent health estimation. In contrast, three bend sensors (placed at A2, A4, and A5) are required for equivalent performance, as bend sensors are more local and struggle to estimate the health of uninstrumented actuators.
Gait Performance: REACH successfully predicted actuator health across three swimming gaits (linear swimming, wide turning, and tight turning) with minimal performance differences between them.
Filter Consistency: The statistical validation method confirmed that the filter is consistent, with the normalized innovation squared falling within the calculated bounds approximately 95% of the time.
Experimental Outcomes: Using data from a physical UCSD robot fish, REACH successfully estimated actuator health for various degradation scenarios (partial and total failure). While the algorithm accurately predicted failure events, some trials showed slight offsets in exact health values for partially functioning actuators, attributed to fluid pump ramp-up times and slight delays in measurement data.

Significance and Claims
The paper claims that REACH provides a statistically consistent and robust method for monitoring soft robot actuator health in real-time. By moving beyond binary failure detection to continuous health estimation, the system enables soft AUVs to adapt to material degradation and faults, thereby extending mission duration and safety. The study establishes that while IMUs offer a more compact solution for global health estimation, bend sensors provide high-fidelity local data, and that the proposed architecture is effective even in the presence of manufacturing variances and noisy experimental data. The work demonstrates that accurate, timely health estimation is achievable for complex, nonlinear soft swimming robots, addressing a key barrier to their long-term autonomous operation.

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