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

Abstract

We present Aquarium, a differentiable fluidstructure interaction solver for robotics that offers stable simulation, accurate coupled robot-fluid physics, and full differentiability with respect to fluid states, robot states, and shape parameters. Aquarium achieves stable simulation with accurate flow physics by integrating over the discrete, incompressible Navier-Stokes equations directly using a fully-implicit Crank-Nicolson scheme with a second-order finite-volume spatial discretization. The robot and fluid 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 fluidstructure 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. The derivatives can then be passed to a gradientbased optimization or learning framework. We demonstrate Aquarium's ability to accurately simulate coupled fluid-solid physics with numerous examples, including a cylinder in free stream and a soft robotic tail with hardware validation. We also demonstrate Aquarium's ability to provide full, analytical gradients by performing both shape and gait optimization of a robotic fish tail to maximize generated thrust.