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

cs.ROSep 24, 2026

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

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

Organizations: Hong Kong Embodied AI Lab, Hong Kong SAR, China · The Chinese University of Hong Kong, Hong Kong SAR, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China

Abstract

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.

Figures & tables

Fig. 1: Biological inspiration and robotic implementation. (A) Cross jelly ( Mitrocoma cellularia ), showing the compliant bell, radial canals, and densely distributed marginal tentacles. (B) Proposed tendon-driven jellyfish-inspired robot, with eight radial members supporting the compliant silicone bell. Scale bar: 10 cm.

Fig. 2: Mechanical architecture and actuator construction. (A) Robot 3D design model showing the bell, servomotors, radial members, electronics, and ballast. (B) Laminated radial member with a TPU 90A substrate [ 19 ] , a PLA Basic ossicle strip [ 20 ] , and a distal membrane clip. (C) Flexural links and contact geometry; scale bar: 4 mm. The laminate combines localised bending with elastic recovery and geometric rotation limits.

Fig. 3: Bending geometry and characterisation. (A) Total bend angle $\theta$ and start-to-tip angle $\phi$ versus motor take-up, with geometric definitions. Central curves follow the 3D design model, while the accompanying deviations reflect physical measurements. (B) Representative configurations spanning $0$ to $29.72\,\mathrm{mm}$ take-up and $0^{\circ}$ to approximately $150^{\circ}$ total bend. The geometry and measurements support a quasi-linear displacement-bending relationship.

Fig. 4: Tendon force during contraction and recovery in water and air. Shading indicates one standard deviation about the mean. The largest recorded forces were $27.6\,\mathrm{N}$ in water and $24.5\,\mathrm{N}$ in air, a $3.1\,\mathrm{N}$ increase (approximately $13\%$ ). The comparison highlights path-dependent loading and the higher peak load during submerged actuation.

Fig. 5: Prescribed open-loop actuation organisation and swimming cycle. (A) Four servomotors each actuate a neighbouring pair of radial members. (B) Representative bell configurations and schematic displacement traces during consecutive cycles. Shared stroke timing permits amplitude asymmetry while preserving phase synchronisation.

Fig. 6: Cycle-synchronous RL-based depth control. Depth and inertial feedback provide the observation $\mathbf{o}_{k}$ ; the actor selects $u_{k}$ , which is mapped to a common amplitude $A_{k}$ for four synchronous servomotors and held throughout the stroke. Both networks share the same observation during training. Simulation rollouts, the critic, reward evaluation, and PPO optimisation are training-only components; only the actor is deployed.

Fig. 7: Physical swimming behaviours under prescribed open-loop actuation. (A) Representative synchronous ascent sequence. (B) Pressure-derived upward displacement during the representative ascent trial. (C) Representative asymmetric steering sequence. (D) Zero-referenced roll, pitch, and yaw evolution during the illustrated manoeuvre. (E) Recovery from inversion followed by upward motion. (F) Self-righting swimming. Righting occurred during continued pulsation without learned attitude control.

Fig. 8: Representative closed-loop depth-control behaviour using the common-amplitude PPO policy. (A) Simulated swimming sequence. (B) Corresponding simulated depth. (C) Physical deployment of the same policy. (D) Corresponding pressure-derived physical depth response. Annotated RMSEs refer to the illustrated trajectories rather than multi-trial aggregates. These examples show closed-loop depth regulation in simulation and after transfer to the physical robot.

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Soft Robotics Learning-Based Control Embodied Artificial Intelligence Oscillatory Dynamics

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Soft robots are valuable robophysical platforms for studying body-caudal undulatory locomotion, but their compliant bodies are difficult to control precisely under changing hydrodynamic loading. Conventional proportional-integral-derivative (PID) feedback stabilizes periodic undulation in static water, but can accumulate flow-dependent tracking delay and increasing inter-trial variability when environmental flow becomes non-trivial. Here, we evaluate whether augmenting PID control with a Linear Repetitive Learning Estimation Scheme (PID-LRLES) recovers tracking accuracy and repeatability under dynamic flow. The LRLES generalizes classical integral action from constant to periodic, non-constant references, while using a stable transfer-function realization whose poles have negative real parts to avoid the long-term instability issues of classical repetitive control. Closed-loop experiments were carried out in a recirculating flow tank at five bulk flow speeds spanning 0 to 32.6 cm s^-1, using an embedded soft capacitive bending sensor at a 1 kHz control-loop rate. With controller gains tuned once in static water and then held fixed across all conditions, PID-LRLES tracked the periodic bending-envelope reference more closely than the PID baseline and significantly reduced the inter-trial spread of the per-trial RMSE (paired Wilcoxon signed-rank test, p = 1.8 x 10^-4, n = 25). Embedded soft proprioception and cycle-to-cycle learning act as complementary contributors to robustness: the sensor exposes the periodic hydrodynamic bias in body deformation, while the learning term absorbs it over recent oscillation cycles. By reducing flow-dependent control-induced variability, the approach provides an enabling layer for future robophysical studies seeking to isolate the effects of morphology, sensing, and environmental flow on aquatic locomotion.

Abstract

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