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

Abstract

Rapid acceleration and burst maneuvers in underwater robots depend less on maintaining precise resonance and more on force--velocity phase alignment during thrust generation. In this work, we investigate constrained-layer damping (CLD) as a passive mechanism for frequency-selective impedance shaping in soft robotic swimmers. Unlike conventional stiffness-tuning approaches, CLD selectively amplifies the dissipative component of bending impedance while preserving storage stiffness, passively shifting the impedance composition toward dissipative dominance as actuation frequency increases. We characterize this behavior through dry impedance measurements, demonstrate that CLD enhances thrust and alters force--motion phase relationships across Strouhal numbers in constrained propulsion tests, and validate that passive impedance shaping yields a nearly five-fold increase in peak acceleration and a three-fold increase in terminal velocity in unconstrained swimming trials. These results establish phase-oriented passive impedance modulation as a simple, control-free pathway for improving transient propulsion in soft robotic systems.

Figures (5)

• Figure 1: Frequency-dependent passive impedance modulation in a viscoelastic soft fin. (A) A soft robot equipped with a viscoelastic fin can passively modulate its effective mechanical impedance in response to frequency-varying hydrodynamic loading, reducing reliance on precise active stiffness control. (B) The fin incorporates a constrained-layer damping (CLD) element, where shear deformation in the viscoelastic (VE) layer increases with loading frequency, resulting in a shift of the effective impedance composition toward increased damping at higher frequencies.
• Figure 2: CLD module fabrication and frequency-dependent impedance characterization. (A) Exploded view of the symmetric CLD sandwich structure: a PLA base plate (0.5 mm) laminated with a closed-cell acrylic foam viscoelastic core (1 mm) and a PET constraining layer (0.3 mm) on each side. (B) Bender test apparatus. A Teknic ClearPath motor prescribes sinusoidal angular oscillations while an ATI Mini-40 sensor records the resistive torque. (C) Storage modulus $K'$ and loss modulus $K"$ versus actuation frequency. $K"$ increases with frequency, indicating growing dissipative contribution, while $K'$ remains approximately constant. (D) Normalized torque--angle phase portraits. Increasing actuation frequency (light to dark) expands the enclosed loop area, confirming higher energy dissipation per cycle.
• Figure 3: Constrained steady-state propulsion performance. (A) Heaving test setup with four CLD configurations (0%, 16.7%, 33.3%, 66.7% coverage). (B) Mean thrust versus $St$; shaded regions indicate $\pm 1$ standard deviation over three trials. (C) Propulsive efficiency versus $St$; error bars as in (B). (D) Effective impedance composition versus $St$. The baseline remains dissipative-dominant; design c shifts progressively from elastic-dominant toward dissipative dominance. (E) Instantaneous thrust and heave position over one cycle at $St=0.8$.
• Figure 4: Propulsive wake evolution. (A) Phase-resolved PIV flow field at $0.5\pi$ for the baseline and design c, highlighting LEV/TEV structures. (B) Flow field at $1.1\pi$ during heaving reversal, showing vortex development along the foil chord.
• Figure 5: Unconstrained rapid acceleration at $St=0.8$. (A) Design c achieves a peak acceleration of $0.191~\mathrm{m/s^2}$ and terminal velocity of $0.291$ m/s over a $3.8$ s trial. (B) The baseline reaches $0.039~\mathrm{m/s^2}$ acceleration and $0.105$ m/s terminal velocity over the same duration. Yellow traces show the trailing-edge trajectory.