A Unified Framework for Simulating Strongly-Coupled Fluid-Robot Multiphysics

We present a framework for simulating fluid-robot multiphysics as a single, unified optimization problem. The coupled manipulator and incompressible Navier-Stokes equations governing the robot and fluid dynamics are derived together from a single Lagrangian using the principal of least action. We then employ discrete variational mechanics to derive a stable, implicit time-integration scheme for jointly simulating both the fluid and robot dynamics, which are tightly coupled by a constraint that enforces the no-slip boundary condition at the fluid-robot interface. Extending the classical immersed boundary method, we derive a new formulation of the no-slip constraint that is numerically well-conditioned and physically accurate for multibody systems commonly found in robotics. We demonstrate our approach's physical accuracy on benchmark computational fluid-dynamics problems, including Poiseuille flow and a disc in free stream. We then design a locomotion policy for a novel swimming robot in simulation and validate results on real-world hardware, showcasing our framework's sim-to-real capability for robotics tasks.