Geometric Design and Gait Co-Optimization for Soft Continuum Robots Swimming at Low and High Reynolds Numbers

Abstract

Recent advancements in soft actuators have enabled soft continuum swimming robots to achieve higher efficiency and more closely mimic the behaviors of real marine animals. However, optimizing the design and control of these soft continuum robots remains a significant challenge. In this paper, we present a practical framework for the co-optimization of the design and control of soft continuum robots, approached from a geometric locomotion analysis perspective. This framework is based on the principles of geometric mechanics, accounting for swimming at both low and high Reynolds numbers. By generalizing geometric principles to continuum bodies, we achieve efficient geometric variational co-optimization of designs and gaits across different power consumption metrics and swimming environments. The resulting optimal designs and gaits exhibit greater efficiencies at both low and high Reynolds numbers compared to three-link or serpenoid swimmers with the same degrees of freedom, approaching or even surpassing the efficiencies of infinitely flexible swimmers and those with higher degrees of freedom.

Figures (6)

• Figure 1: Schematic diagram of the co-optimization of design and control for soft continuum robots based on geometric mechanics. Starting with an initial guess for the design and gait of the soft continuum robot, we apply geometric mechanics principles to model continuum swimming to obtain the gradients of displacement and power consumption relative to the design and gait. These gradients are then used in variational optimization to determine the optimal design and gait for the soft continuum swimming robot.
• Figure 2: Demonstration of the deformation of soft continuum robots parameterized by curvature functions. (Top left): The curvature of a two-shape-mode swimmer, where the curvature is a sum of two shape modes. The shape modes are visualized by black and grey curves at $t = 1$, with shape variables represented by dashed lines at $s = 0$. (Top right): Snapshots of the two-shape-mode swimmer’s configuration corresponding to the black curves in the top left subfigure, with curvature indicated by a red-white-black color scheme. Each shape mode is also visualized as a solid black and grey swimmer on the sides. (Bottom left): The curvature of an infinitely flexible swimmer, parameterized by unit shape modes distributed along the arclength. The unit shape modes, scaled by the shape variables, are visualized by the red-white-black curves. (Bottom right): Snapshots of the infinitely flexible swimmer’s configuration corresponding to the black curves in the bottom left subfigure.
• Figure 3: Geometric mechanics-based locomotion analysis of soft continuum swimmers. (Left): The local connections in the $x$ direction for a two-shape-mode high-Re swimmer with an optimal design and gait, represented by arrows at each time and arclength. The magnitude of the local connection at each time is scaled to match the tangent vector of the curvature surface in the time direction. (Right): The gradients of displacement in the $x$ direction relative to the magnitude of curvature at each arclength and time for a three-link high-Re swimmer with an optimal gait, represented by arrows. The magnitude of each arrow indicates the increase in displacement for a unit increase in curvature at the arrow's position. The two insets illustrate the concepts of local connection and gradient in gait space.
• Figure 4: Comparison of the optimal design-and-gait efficiencies of different continuum swimmers swimming forward at low and high Re. In both plots, efficiency is normalized by the maximum efficiency. The low Re swimmers use dissipated power metrics based on the Riemannian metrics of the system's shape velocity, while the high Re swimmer uses the covariant acceleration metric related to the square of the active force.
• Figure 5: Comparison of the optimal forward swimming deformation for determined by the design and gait of the two-shape-mode swimmer with other swimmers at low and high Re. (Left): Comparison of the curvature between the optimal design and gait of the two-shape-mode swimmer and the optimal gait of the infinitely flexible swimmer at low Re. (Right): Comparison of the curvature between the optimal design and gait of the two-shape-mode swimmer and the three-shape-mode swimmer at high Re.