Geometric Data-Driven Multi-Jet Locomotion Inspired by Salps

TL;DR

This work develops a geometric mechanics framework for salp-inspired multi-jet locomotion where actuation is not restricted to shape axes, and validates it on LandSalp—a land-based proxy for drag-dominated swimming. It advances a data-driven method to learn a Riemannian drag metric from minimal trajectories using Lie-group differentiation, and employs averaging-based gait planning with Lie brackets to achieve omnidirectional motion and shape stability. The approach is demonstrated through simulation and hardware experiments, revealing effective locomotion, shape regulation, and bending capabilities, even in the presence of unmodeled disturbances. Together, these contributions lay a principled foundation for more capable salp-inspired underwater robots and provide a tractable path toward real-world aquatic implementations.

Abstract

Salps are marine animals consisting of chains of jellyfish-like units. Their efficient underwater locomotion by coordinating multi-jet propulsion has aroused great interest in robotics. This paper presents a geometric mechanics framework for salp-inspired robots. We study a new type of geometric mechanics models inspired by salps, in which control inputs are not restricted to the shape axes, analyze nonlinear controllability, and develop motion planning and feedback control methods. We introduce the "LandSalp" robot, which serves as a physical realization of the reduced-order, drag-dominated model of salp swimming, enabling controlled evaluation of locomotion strategies without many confounding factors of underwater experiments. We extend least-squares- and inverse-dynamics-based system identification to learn the Riemannian metric of the drag-dominated model from experimental data using Lie group differentiation. With about three minutes of data, we identify an accurate model of LandSalp. Simulation and hardware experiments demonstrate omnidirectional locomotion, shape regulation, and bending maneuvers, providing a principled pathway toward more capable salp-inspired robots.

Figures (16)

• Figure 1: The LandSalp robot (bottom) and biological salps (top). The LandSalp robot is a land-based physical realization of a reduced-order, drag-dominated model of biological salp, with a minimal but sufficient number of units for studying planning and control of salp-inspired robotic locomotion. The salp picture is reproduced from calliesandiego2024common.
• Figure 2: Schematic comparison of the LandSalp robot (bottom) and the corresponding biological salp with linear-like architectures (top). There are two joints ($\alpha_1$ and $\alpha_2$) connecting the links from left to right. The orientations of the three motor-wheel assemblies used to generate jet thrust and (part of the) viscous drag are $\beta_1$, $\beta_2$, and $\beta_3$, respectively, from left to right, measured relative to the corresponding link axis.
• Figure 3: Control vector fields $B$ for the LandSalp data-driven model. Each row corresponds to each control input. The left column shows the shape velocity resulting from each control input at different shapes, and the right column shows the position velocity resulting from each control input at different shapes, with the linear velocity in the $\dot{x}$ and $\dot{y}$ directions overlaid with the shape axes, and the contours showing the angular velocity $\dot{\theta}$.
• Figure 4: The LandSalp is constructed as a planar chain of links, each link consisting of the following components: 1) passive joints, 2) HEBI X5 series-elastic actuators, whose output torque is a combination of a commanded driving torque and a drag term that simulates fluid friction acting on the link as it moves, 3) omniwheels, 4) ball casters for balancing, 5) rotation mounting slots for adjusting wheel orientation to correspond to different jet directions.
• Figure 5: Data-driven local metrics and corresponding residual gradients. In this paper, we assume that the drag of the wheels and joints is independent, and the principal axes of the local metric are aligned with the wheels. The white grids are unmodeled entries.