We present Aquarium, a differentiable fluid-structure interaction solver for robotics that offers stable simulation, accurately coupled fluid-robot physics in two dimensions, 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 spatial 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 demonstrate 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.

翻译：我们展示了水族馆,这是机器人的一种不同的流体结构互动求解器,它提供稳定的模拟、精确结合的液态机器人物理学的两个维度,以及流体和机器人状态和参数方面的完全差异性。水族馆通过直接结合不压缩的纳维-斯托克斯方程式,利用完全隐含的Crank-Nicolson 方程式和二级有限空间离散。流体和机器人物理学同时使用浸入式边界法,将无滑动状态作为直接适用于纳维-斯托克斯系统的平等制约。这种组合式选择使流体结构互动得以形成,并作为一种非线性优化问题加以解决。然后利用这种优化式配方程式利用隐含功能的标语来计算衍生衍生物。然后可以传递到下游的梯度优化或学习算法。我们展示了水族馆准确模拟混合液态物理学的能力,并以许多2D示例直接适用于纳维-斯托克斯系统。这种选择使流体结构互动得以形成,并作为非线性优化问题解决。然后利用隐含功能的电流和软机层尾质级软体结构的硬体结构验证,我们提供了一种磁级的磁级的磁级的磁度的磁度,以演示。</s>