Riding the interface: differentiable physics for wave-driven locomotion
A small robot sitting on water can propel itself forward without paddles, fins, or jets: by vibrating. The vibration radiates surface waves, and if those waves are directionally asymmetric, their momentum imbalance generates a net thrust. The SurferBot (Rhee et al., 2022) demonstrated this experimentally; our work builds a simulator where every design choice can be optimized directly.
At an air–water interface, surface tension, gravity waves, and added-mass effects govern the interface dynamics. Performance depends on coupled choices: body shape, mass distribution, motor location, drive frequency, waveform, and fluid properties, all of which are expensive to explore by experiment. We model the robot as a buoyant, possibly flexible body constrained to the interface and driven by a time-varying actuator, with the surrounding fluid described by an interface-resolving small-amplitude free-surface theory (Benham et al., 2024). The simulator is differentiable with respect to all design parameters $\theta$: state updates use linear and nonlinear solves $A(\theta)\,y=b(\theta)$ with custom reverse-mode rules, so $\nabla_\theta \mathcal{L}$ follows from two linear solves (forward and adjoint) per time step, keeping memory bounded and gradients stable across the full trajectory.
With these gradients, multi-start optimization explores hull geometries, actuator placements, and drive waveforms; Bayesian optimization handles global search under power-budget and manufacturability constraints.
References
2024
Arxiv
On wave-driven propulsion
Graham P. Benham, Olivier Devauchelle, and Stuart J. Thomson
@article{Benham_Devauchelle_Thomson_2024,title={On wave-driven propulsion},volume={987},doi={10.1017/jfm.2024.352},journal={Journal of Fluid Mechanics},author={Benham, Graham P. and Devauchelle, Olivier and Thomson, Stuart J.},year={2024},pages={A44}}
2022
SurferBot: a wave-propelled aquatic vibrobot
Eugene Rhee, Robert Hunt, Stuart J Thomson, and 1 more author
Nature has evolved a vast array of strategies for propulsion at the air-fluid interface. Inspired by a survival mechanism initiated by the honeybee (Apis mellifera) trapped on the surface of water, we here present the SurferBot: a centimeter-scale vibrating robotic device that self-propels on a fluid surface using analogous hydrodynamic mechanisms as the stricken honeybee. This low-cost and easily assembled device is capable of rectilinear motion thanks to forces arising from a wave-generated, unbalanced momentum flux, achieving speeds on the order of centimeters per second. Owing to the dimensions of the SurferBot and amplitude of the capillary wave field, we find that the magnitude of the propulsive force is similar to that of the honeybee. In addition to a detailed description of the fluid mechanics underpinning the SurferBot propulsion, other modes of SurferBot locomotion are discussed. More broadly, we propose that the SurferBot can be used to explore fundamental aspects of active and driven particles at fluid interfaces, as well as in robotics and fluid mechanics pedagogy.
@article{Rhee_2022,doi={10.1088/1748-3190/ac78b6},url={https://dx.doi.org/10.1088/1748-3190/ac78b6},year={2022},month=jul,publisher={IOP Publishing},volume={17},number={5},pages={055001},author={Rhee, Eugene and Hunt, Robert and Thomson, Stuart J and Harris, Daniel M},title={SurferBot: a wave-propelled aquatic vibrobot},journal={Bioinspiration & Biomimetics}}