Energy-storing analysis and fishtail stiffness optimization for a wire-driven elastic robotic fish

TL;DR

This work tackles motor power fluctuations in wire-driven elastic robotic fish by introducing an active-segment elastic spine (AES) made of spring steel to store and release energy within each fishtail swing. A Lagrangian dynamic model paired with a cantilever-beam analysis is used to derive the system dynamics and formulate a nonlinear stiffness-optimization problem that minimizes the motor power variance while accounting for the passive-segment elastic spine (PES). Key findings show that AES energy-storing does not change the mean motor power but can dramatically reduce power variance and enable higher swing frequencies, with optimal AES stiffness increasing with drive frequency and PES stiffness; compared to an active-segment rigid spine (ARS), the AES can increase maximum motor frequency by about 4.1% and peak thrust by ~0.06 N, while lowering peak power. The results offer a practical pathway to more reliable, higher-speed swimming robotic fish through tunable energy storage in the AES, and suggest future work on coordinated stiffness optimization and online adaptivity for AES and PES.

Abstract

The robotic fish with high propulsion efficiency and good maneuverability achieves underwater fishlike propulsion by commonly adopting the motor to drive the fishtail, causing the significant fluctuations of the motor power due to the uneven swing speed of the fishtail in one swing cycle. Hence, we propose a wire-driven robotic fish with a spring-steel-based active-segment elastic spine. This bionic spine can produce elastic deformation to store energy under the action of the wire driving and motor for responding to the fluctuations of the motor power. Further, we analyze the effects of the energy-storing of the active-segment elastic spine on the smoothness of motor power. Based on the developed Lagrangian dynamic model and cantilever beam model, the power-variance-based nonlinear optimization model for the stiffness of the active-segment elastic spine is established to respond to the sharp fluctuations of motor power during each fishtail swing cycle. Results validate that the energy-storing of the active-segment elastic spine plays a vital role in improving the power fluctuations and maximum frequency of the motor by adjusting its stiffness reasonably, which is beneficial to achieving high propulsion and high speed for robotic fish. Compared with the active-segment rigid spine that is incapable of storing energy, the energy-storing of the active-segment elastic spine is beneficial to increase the maximum frequency of the motor and the average thrust of the fishtail by 0.41 Hz, and 0.06 N, respectively.

Figures (19)

• Figure 1: Overview design of the wire-driven elastic robotic fish.
• Figure 2: Definition of coordinate frames. The green dotted curve denotes the AES. The two orange solid lines represent the chord of the AES and the caudal fin, respectively. The PES is simplified as the torsion spring.
• Figure 3: Swing analysis of fishtail in one cycle. The swing cycle of fishtail includes (a) drive stroke and (b) recovery stroke. The drive stroke is defined as the duration when the fishtail swings from the middle to the sides, and the recovery stroke is opposite to the drive stroke. The $F_{tail}$ and $F_{fin}$ represent the hydrodynamic forces of the fishtail and caudal fin, respectively.
• Figure 4: The real-time curves of motor torque $T_m$ and power $P_m$. The $f$, $\kappa_{1}$, and $\kappa_{2}$ are 4 Hz, 0.15 N$\cdot$m, and 1.31 N$\cdot$m, respectively.
• Figure 5: The curves of $\theta_1$, $\theta_2$ and $\theta_s$. The $f$, $\kappa_{1}$, and $\kappa_{2}$ are 4 Hz, 0.15 N$\cdot$m, and 1.31 N$\cdot$m, respectively. The three curves follow the sine-like curve, which is in line with the swing rule of the fishtail.