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：我们提出Aquarium——一种面向机器人领域的可微分流固耦合求解器，可实现稳定仿真、二维流体-机器人物理的精确耦合，以及对流体与机器人状态及参数的全微分特性。Aquarium通过采用全隐式Crank-Nicolson格式与二阶有限体积空间离散方法直接对不可压缩Navier-Stokes方程进行积分，从而在精确流体物理模拟基础上实现稳定仿真。通过将无滑移条件构建为直接施加于Navier-Stokes系统的等式约束，利用浸入边界方法实现流体与机器人物理的耦合。这种耦合方式使流固相互作用被构建为非线性优化问题并求解。进而借助隐函数定理利用该优化公式计算导数，所得导数可传递至下游基于梯度的优化或学习算法。我们通过包括自由来流圆柱体与通过硬件验证的软体机器人鱼尾在内的多个二维示例，验证了Aquarium准确模拟流体-机器人耦合物理的能力。同时通过对振荡菱形箔进行基于梯度的形状-步态联合优化来最大化其推进力，展示了Aquarium提供解析梯度的能力。