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A Tendon-Driven Robotic Jellyfish with Constrained Soft Actuation and Depth Control via Reinforcement Learning

Jiarui Peng, Yutong Wu, Zelong Wang, Ping Deng, Xiaotian Zhang, Xian Chen, Kecheng Qin, Zhongyi Li

arXiv:2609.29132v1cs.RO

TL;DR

Jellyfish-inspired robots face the challenge of achieving large, repeatable deformation and closed-loop control amid coupled body–fluid dynamics. This work combines constrained tendon-driven actuation with a cycle-level reinforcement-learning controller, which improves depth tracking over fixed-amplitude actuation in simulation and transfers directly to the physical robot.

  • Problem

    Jellyfish-inspired robots must combine large, compliant, repeatable deformation, while coupled body–fluid dynamics complicate swimming and closed-loop control.

    Source: §I · p. 1

  • Method

    The robot uses constrained tendon-driven actuators and a simulation-trained, cycle-synchronous PPO policy that selects a common stroke amplitude from depth feedback and transfers without real-world training or fine-tuning.

    Source: §I · p. 1

  • Results

    The cycle-level PPO controller improves depth tracking over fixed-amplitude actuation in simulation and transfers directly to the physical robot.

    Source: §VIII · p. 7

  • Takeaways & Limitations

    Constrained actuator mechanics and a prescribed swimming gait can simplify the control problem while supporting closed-loop depth regulation on the physical robot.

    Source: §VIII · p. 7

    Tank confinement and uninstrumented disturbances limit conclusions about sustained station keeping and disturbance rejection.

    Source: C. Limitations and Future Work · p. 7

Abstract

from arXiv · show

Jellyfish-inspired robots offer a compliant and efficient approach to underwater locomotion, but achieving large deformation together with repeatable actuation and closed-loop control remains challenging. In this work, we present a tendon-driven robotic jellyfish with constrained soft actuation. Each actuator combines a flexible substrate with discrete constraints, enabling bending up to \(150^\circ\) with an approximately linear tendon displacement-bending relationship. Eight actuators driven by four servos allow the robot to perform stable swimming, attitude adjustment, and self-righting. Based on the linear actuation, a reinforcement-learning controller is further developed, enabling closed-loop depth regulation in both simulation and physical experiments. These results show that mechanical constraints can improve the controllability of soft actuation while preserving compliant jellyfish-like motion, providing a route toward manoeuvrable and autonomous jellyfish robots.

I. INTRODUCTION

Jellyfish robots must combine large, repeatable deformation with control despite coupled body–fluid dynamics and the limitations of computationally costly or model-sensitive approaches. This work pairs constrained tendon-driven actuation with cycle-synchronous reinforcement learning, while the related-work review spans soft actuation, robot systems, and modelling and control.

I. INTRODUCTION

  • Soft underwater actuators must combine large deformation, compliance, and repeatability, while predictable deformation is also needed for swimming and closed-loop control.Coupled body–fluid dynamics make direct high-fidelity CFD impractical for real-time use, while simpler controllers can be sensitive to model mismatch or environmental changes.Source: §I · p. 1
  • The robot combines constrained tendon-driven bending, a prescribed contraction–recovery stroke, and a cycle-synchronous reinforcement-learning policy.The prescribed stroke reduces control to selecting a common actuation amplitude once per cycle; the policy is trained in simulation and transferred without additional policy training.Source: §I · p. 1
  • The introduction identifies a constrained soft bending actuator and an eight-actuator, four-servo platform for propulsion, manoeuvring, self-righting, and zero-shot sim-to-real depth control.The actuator combines a flexible TPU substrate with discrete PLA limiting structures for approximately 150° bending and an approximately linear tendon-displacement–bending relationship.Source: §I · p. 1

II. RELATED WORK

  • The related-work review is organised around soft actuation, jellyfish robot systems, and modelling and control.The supplied passage names these perspectives but does not describe their individual studies.Source: §II · p. 2

A. Soft Actuation for Jellyfish

Prior jellyfish robots use varied actuation and modelling strategies, with detailed hydrodynamic models carrying higher computational costs than reduced-order approaches. This work instead builds on tendon-driven bending with a directly characterised displacement–bending relationship and lightweight simulation for policy optimisation and physical transfer.

A. Soft Actuation for Jellyfish

  • Tendon-driven bending with discrete geometric constraints provides a directly characterised tendon displacement–bending relationship, unlike the cited shape-memory-alloy and magnetic-composite approaches.The reviewed work also notes that SoJel swimming performance is sensitive to material and geometric configuration.Source: A. Soft Actuation for Jellyfish · p. 2

B. Jellyfish Robot Systems

  • Jellyfish robots integrate propulsion and manoeuvring through electrohydraulic, pneumatic, and mechanically driven architectures; this work uses four servo-driven tendon channels across eight constrained actuators.The paper describes its architecture as a compact unified system for propulsion, manoeuvring, self-righting, and autonomous depth regulation.Source: B. Jellyfish Robot Systems · p. 2

C. Jellyfish Modelling and Control

  • Detailed CFD and fluid–structure interaction studies resolve hydrodynamics but cost more to model and compute than reduced-order approaches.The reviewed examples include vortex-resolving medusan simulations, flexible-bell FSI, and robotic-jellyfish design and propulsion optimisation.Source: C. Jellyfish Modelling and Control · p. 2
  • Prior control work includes PID depth regulation and reinforcement-learning studies of attitude or jellyfish-robot control; this work uses a lightweight, stateless fluid approximation and evaluates cycle-level depth control through physical transfer.The supplied review passage names the PID and learning-based examples but does not report their outcomes.Source: C. Jellyfish Modelling and Control · p. 2

A. Robot and Actuator Design

The robot integrates eight constrained radial actuators around a compliant bell, with four servos driving neighbouring actuator pairs. Characterisation shows approximately linear bending over the tested range and describes tendon compliance, repeated-use observations, and path-dependent force loading.

A. Robot and Actuator Design

  • Four servomotors each drive a neighbouring pair of the robot’s eight radial actuators, whose coordinated bending contracts and reopens the silicone bell.Ballast is placed to adjust buoyancy and keep the centre of mass below the centre of buoyancy for passive attitude restoration.Source: A. Robot and Actuator Design · p. 2
  • The TPU substrate provides flexibility and elastic recovery, while bonded PLA limiting structures guide bending and restrict local rotation between segments.The current design reaches approximately 150° bending; the tendon offset from the TPU bends the actuator when pulled, and releasing it allows elastic return.Source: A. Robot and Actuator Design · pp. 2–3, Figure 2 · p. 2

B. Actuator Characterisation

  • 29.72 mm of tendon take-up produces approximately 150° of bending, with geometric prediction and physical measurements showing an approximately linear trend over the tested range.This spans the full operating range used in the robot.Source: B. Actuator Characterisation · p. 3, Figure 3 · p. 3
  • After stretch-release preconditioning, tendon compliance measured approximately 0.586 mm N−1; the same eight actuators were used in more than 100 experimental sessions without visually noticeable permanent deformation.The authors state that these observations are not a formal fatigue-life evaluation.Source: B. Actuator Characterisation · p. 3
  • Tendon force follows different paths during contraction and release, and the higher peak in water characterises transmission load rather than propulsive thrust.The passage reports that submerged actuation adds load but provides no thrust measurement.Source: B. Actuator Characterisation · p. 3

IV. OPEN-LOOP SWIMMING GAIT

The prescribed gait synchronises four tendon channels through contraction and elastic recovery, while allowing their amplitudes to vary independently. Equal amplitudes produce symmetric axial propulsion, and amplitude asymmetry supports manoeuvring without changing channel phase.

IV. OPEN-LOOP SWIMMING GAIT

  • Synchronous contraction–recovery actuation supports symmetric propulsion, asymmetric manoeuvring, and self-righting with passive mechanical restoration.Different channel amplitudes change bell deformation without changing relative phase.Source: §IV · p. 3, A. Swimming Gait Generation · p. 4

A. Swimming Gait Generation

  • Each of four servomotors drives a neighbouring pair of radial actuators, and all channels share cycle timing while retaining independently set tendon-retraction amplitudes.The figure presents representative bell configurations and displacement traces across consecutive cycles.Source: Figure 5 · p. 3, A. Swimming Gait Generation · p. 3
  • Contraction occupies the first third of each cycle and recovery the remaining two-thirds, making contraction twice as fast for the same stroke amplitude.Servo speeds are scaled for different amplitudes so channels stay synchronised and reach their stroke limits together.Source: A. Swimming Gait Generation · p. 3
  • During recovery, the servo releases the tendon and actuator elasticity returns the radial members toward their relaxed shape; the servo controls reopening rate rather than actively pushing the bell outward.The paper distinguishes this elastic return from fluid-mediated passive energy recapture.Source: A. Swimming Gait Generation · p. 3
  • In open-loop experiments, pulsation was approximately 0.4 Hz (2.5 s cycle; 0.83 s contraction, 1.67 s recovery), within Aurelia aurita’s reported 0.25–1.00 Hz range [24], with tendon travel capped at 29.72 mm for approximately 150° bending.Source: A. Swimming Gait Generation · p. 4

B. Propulsion and Manoeuvre

Open-loop sequences demonstrate swimming, steering, and mechanically supported righting, while depth regulation uses a cycle-synchronous policy to adjust a shared swimming amplitude. The policy operates on boundary observations of depth error, downward velocity, and the preceding action.

B. Propulsion and Manoeuvre

  • Representative sequences show ascent, asymmetric steering and attitude change, and inversion recovery with passive mechanical righting during continued pulsation.The righting is supported by the calibrated ballast-buoyancy arrangement; these demonstrations establish physical capabilities before learned depth regulation.Source: B. Propulsion and Manoeuvre · p. 4
  • The open-loop capability demonstrations do not provide a matched depth-holding baseline for the learned controller.The learned policy retains the contraction-recovery organisation, with its action mapping and amplitude-dependent cycle timing specified separately.Source: B. Propulsion and Manoeuvre · p. 4

V. REINFORCEMENT LEARNING FOR DEPTH CONTROL

  • The depth controller selects one common amplitude per swimming cycle while retaining the predefined gait and passive attitude restoration.The policy is trained with PPO in simplified simulation and deployed directly on the physical robot.Source: §V · p. 4

A. Cycle-Level Control

  • Cycle-level depth regulation uses a boundary observation containing depth error, estimated downward velocity, and the preceding normalised action.Positive depth error means the robot is deeper than its target; descent is achieved by reducing propulsion under slight negative buoyancy.Source: A. Cycle-Level Control · p. 4

B. Action Mapping and Cyclic Timing

The scalar policy action is mapped to a shared, hover-centred amplitude for the four in-phase quadrants. Cycle duration depends on stroke excursion and prescribed timing rules, with a minimum duration for short strokes.

B. Action Mapping and Cyclic Timing

  • The scalar action adjusts a shared amplitude around the nominal hover setting, with −1, 0, and 1 mapping to the minimum, hover, and maximum amplitudes.The same amplitude is used across all four quadrants, which contract and recover in phase.Source: B. Action Mapping and Cyclic Timing · p. 4
  • The commanded tendon target is set from the relaxed coordinate plus a calibrated gain times amplitude, then constrained by software position limits.The excursion is represented independently of the servo’s internal encoding convention.Source: B. Action Mapping and Cyclic Timing · p. 4
  • Cycle duration combines contraction and recovery travel times with endpoint holds, subject to a controller-imposed minimum.Contraction and recovery use prescribed rate magnitudes of 2ν and ν, respectively; short strokes wait until the minimum duration has elapsed, so cycle duration can vary with amplitude.Source: B. Action Mapping and Cyclic Timing · p. 4

C. Reward and PPO Training

PPO training penalizes depth error, vertical motion, and abrupt action changes, with discounting and the GAE trace factor scaled by cycle duration. A control-oriented simulation trains the actor, which is deployed once per cycle without online policy optimisation.

C. Reward and PPO Training

  • The cycle reward penalizes depth error, vertical velocity, and changes between successive actions, with positive weights setting their relative contributions.Reward evaluation uses the simulated trajectory’s ground-truth error and downward velocity, while both networks receive only the estimated boundary observation.Source: C. Reward and PPO Training · pp. 4–5
  • Discounting and the GAE trace factor account for elapsed physical time through factors scaled by realised cycle duration.Duration scaling of the GAE trace factor is an implementation choice; time-limit truncations retain value bootstrapping, unlike true terminal transitions.Source: C. Reward and PPO Training · p. 5

D. Simulation and Deployment

  • The control-oriented simulation randomises initial depth error, vertical velocity, and small attitude perturbations while keeping mass, buoyancy, drag, and structural parameters fixed.Learning adjusts the strength of an established swimming primitive rather than discovering the gait or coordinating individual quadrants.Source: D. Simulation and Deployment · p. 5
  • At deployment, the actor uses the training observation convention, amplitude mapping, software bounds, and low-level timing, and is evaluated once per cycle with fixed parameters.Simulation rollouts, critic, reward evaluation, and PPO optimisation are training-only components; only the actor is deployed.Source: D. Simulation and Deployment · p. 5, Figure 6 · p. 5

VI. EXPERIMENTAL EVALUATION

The evaluation establishes physical swimming capabilities under prescribed actuation and then assesses depth control against fixed-amplitude actuation in simulation and on the robot. In the ascent test, synchronous pulsation produced sustained upward displacement in a tank with pressure-based depth measurement.

VI. EXPERIMENTAL EVALUATION

  • The evaluation first tested prescribed-actuation ascent, steering, and righting, then compared RL depth control with fixed-amplitude actuation in simulation and after physical transfer.Source: §VI · p. 5

A. Environment Setup

  • Tests used a glass tank with approximately 60 cm of water, and vertical motion was estimated from hydrostatic pressure relative to the initial measurement.The robot was ballasted to reduce static roll and pitch bias while retaining its centre of mass below its centre of buoyancy; slack cables provided no mechanical support.Source: A. Environment Setup · p. 5

B. Open-Loop Ascent

  • All four channels were driven synchronously at 0.4 Hz using nominal tendon excursions of approximately 15.7 mm.Tendon compliance reduced the realised excursion slightly, to approximately 15.4 mm.Source: B. Open-Loop Ascent · p. 5
  • Repeated synchronous pulsation produced sustained upward displacement, showing that compliant-bell deformation supported unsupported swimming.The representative ascent trace extends beyond the photographed interval.Source: B. Open-Loop Ascent · p. 5

C. Steering and Self-Righting

The experiments demonstrate open-loop steering and mechanically supported righting, then assess simulated and physical depth regulation. The PPO controller reduced aggregate simulated depth error relative to fixed-amplitude actuation, and its transferred policy maintained depth on the robot.

C. Steering and Self-Righting

  • Asymmetric bell deformation produced open-loop steering, while continued pulsation returned the inverted robot towards upright and resumed upward swimming.The illustrated steering angles are zero-referenced, so their relative evolution—not absolute initial values—is interpreted; righting did not use learned attitude control.Source: C. Steering and Self-Righting · p. 5, Figure 7 · p. 6

D. Depth Control in Simulation

E. Depth Control on the Robot

  • After transfer, the policy varied a common stroke amplitude with measured vertical state and maintained depth despite residual ballast-buoyancy imbalance.The figure shows representative simulated and physical trajectories; its annotated RMSEs are not multi-trial aggregates.Source: E. Depth Control on the Robot · p. 6, Figure 8 · p. 6
  • Simulation-to-physical discrepancies may reflect fluid approximation, fabrication and buoyancy mismatch, tendon compliance, and confined-tank hydrodynamics, but their individual contributions were not isolated.Source: E. Depth Control on the Robot · p. 6
  • Manual-displacement and large-attitude-perturbation trials showed repeated recovery qualitatively, but uninstrumented forces and moments preclude quantitative disturbance-rejection results.Passive mechanical trim remains the principal attitude-restoring mechanism.Source: E. Depth Control on the Robot · pp. 6–7

VII. DISCUSSION

The discussion presents local structural constraints as a way to organise compliant deformation and separates the robot’s mechanical attitude restoration, swimming strokes, and depth regulation. It also identifies design dimensions that could be customised.

A. Constrained Compliance and Passive Stabilisation

  • Bending is concentrated mainly in thin PLA links between ossicles, while the TPU substrate accommodates extension and provides elastic recovery.Source: A. Constrained Compliance and Passive… · p. 7
  • The bend range reflects body dimensions rather than an intrinsic architectural limit, so total bending angle, actuator length, and curvature can be customised.Source: A. Constrained Compliance and Passive… · p. 7
  • Non-uniform ossicle spacing, dimensions, and contact angles could enable geometrically programmed curvature distributions through mechanics-based optimisation, subject to strain and contact constraints.Source: A. Constrained Compliance and Passive… · p. 7
  • Mechanical trim restores attitude, prescribed strokes generate swimming, and the policy regulates depth without observing or commanding individual segment deformations.The discussion frames this restricted learning interface as using morphology to reduce active-control requirements.Source: A. Constrained Compliance and Passive… · p. 7

B. Sim-to-Real Transfer

The policy improves depth tracking in simulation and transfers to the physical robot, but the evidence does not establish hydrodynamic equivalence or broad robustness.

B. Sim-to-Real Transfer

  • The simulation uses instantaneous fluid loads without resolving evolving wakes, so its trajectories cannot establish physical thrust mechanisms or propulsion efficiency.The transfer demonstrates useful feedback despite model mismatch, not hydrodynamic equivalence.Source: B. Sim-to-Real Transfer · p. 7
  • Simulation gains and hardware depth correction are distinct evidence; they do not establish equal performance across environments or consistently precise hovering.History-dependent force surrogates informed by CFD or physical measurements are proposed, with validation across stroke conditions.Source: B. Sim-to-Real Transfer · p. 7

C. Limitations and Future Work

  • Tendon wear and occasional breakage motivate abrasion-resistant lines and improved guides, while submerged trim can change with trapped air or water ingress.Preconditioning and post-immersion trim checks remain important; replacement tendons require reassessment of compliance and overload behaviour.Source: C. Limitations and Future Work · p. 7
  • Tank confinement and uninstrumented disturbances limit conclusions about sustained station keeping and disturbance rejection.Longer trials in a larger volume, independent motion measurements, calibrated disturbances, and conventional feedback baselines are proposed before broader robustness claims.Source: C. Limitations and Future Work · p. 7

VIII. CONCLUSION

  • The cycle-level PPO controller improves depth tracking over fixed-amplitude actuation in simulation and transfers directly to the physical robot.Constraining actuator mechanics and prescribing the swimming gait lets learning focus on depth regulation rather than gait generation or individual actuator coordination.Source: §VIII · p. 7
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