Passive Phase-Oriented Impedance Shaping for Rapid Acceleration in Soft Robotic Swimmers

Fish achieve efficient swimming across varied speeds through active modulation of their body flexibility. To explore the effects of tunable stiffness on swimming performance, we present a bio-inspired freely swimming fish robot with a rapidly tunable particle-jamming body. This design enables rapid stiffness adjustments with negligible changes in shape or volume, achieving a 54% variation in flexural rigidity across vacuum pressures of 0 to -40 kPa. We visualize the midline of the oscillating body under both low- and high-stiffness conditions, and the comparison confirms that the body curvature varies with stiffness. We further experimentally evaluate the tunable stiffness body's effects on swimming performance using velocity and cost of transport (CoT) measurements obtained via a motion tracking system. Results show that active stiffness tuning is essential for sustaining efficient and high-speed swimming across beating frequencies of 1-3 Hz. At low frequencies (1-1.5 Hz), a softer body (0 kPa) maximizes velocity and minimizes CoT, whereas at high frequencies (2.5-3 Hz), a stiffer body (-40 kPa) delivers superior velocity and reduced transport cost. These findings highlight stiffness modulation as a key strategy for adaptive and efficient propulsion in bio-inspired robotic swimmers.

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.

Bio-inspired aquatic propulsion offers high thrust and maneuverability but is prone to destabilizing forces such as lift fluctuations, which are further amplified by six-degree-of-freedom (6-DoF) fluid coupling. We formulate quadrupedal swimming as a constrained optimization problem that maximizes forward thrust while minimizing destabilizing fluctuations. Our proposed framework, Accelerated Constrained Proximal Policy Optimization with a PID-regulated Lagrange multiplier (ACPPO-PID), enforces constraints with a PID-regulated Lagrange multiplier, accelerates learning via conditional asymmetric clipping, and stabilizes updates through cycle-wise geometric aggregation. Initialized with imitation learning and refined through on-hardware towing-tank experiments, ACPPO-PID produces control policies that transfer effectively to quadrupedal free-swimming trials. Results demonstrate improved thrust efficiency, reduced destabilizing forces, and faster convergence compared with state-of-the-art baselines, underscoring the importance of constraint-aware safe RL for robust and generalizable bio-inspired locomotion in complex fluid environments.