Aquarium: A Fully Differentiable Fluid-Structure Interaction Solver for Robotics Applications

We present Aquarium, a differentiable fluid- structure interaction solver for robotics that offers stable simulation, accurately coupled fluid-robot physics in two dimen- sions, and full differentiability with respect to fluid and robot states and parameters. Aquarium achieves stable simulation with accurate flow physics by directly integrating over the incompressible Navier-Stokes equations using a fully implicit Crank-Nicolson scheme with a second-order finite-volume spa- tial discretization. The fluid and robot physics are coupled using the immersed-boundary method by formulating the no- slip condition as an equality constraint applied directly to the Navier-Stokes system. This choice of coupling allows the fluid- structure interaction to be posed and solved as a nonlinear optimization problem. This optimization-based formulation is then exploited using the implicit-function theorem to compute derivatives. Derivatives can then be passed to downstream gradient-based optimization or learning algorithms. We demon- strate Aquarium’s ability to accurately simulate coupled fluid- robot physics with numerous 2D examples, including a cylinder in free stream and a soft robotic fish tail with hardware validation. We also demonstrate Aquarium’s ability to provide analytical gradients by performing gradient-based shape-and- gait optimization of an oscillating diamond foil to maximize its generated thrust.