Matching the swimming efficiency and agility of fish has remained an elusive goal in underwater robotics. Such locomotion capabilities rely on complex vortex interactions between the robot's body and the surrounding fluid. However, simulating these dynamics, which are governed by coupled ordinary and partial differential equations, is significantly more difficult than the multi-body dynamics of classical rigid robotic systems. We present a differentiable framework for simulating strongly coupled fluid-robot multiphysics as a unified optimization problem. The coupled manipulator and incompressible Navier-Stokes equations are derived together from a single Lagrangian using the principle of least action. We employ discrete variational mechanics to derive a stable, well-conditioned, and physically accurate scheme for jointly simulating articulated bodies and the surrounding fluid. We leverage the implicit function theorem to compute derivatives of the fully coupled dynamics. Using this simulator and its gradients, we realize undulating swimming gaits and optimize a highly dynamic C-start escape maneuver for a bioinspired eel robot. We validate both gaits on physical hardware, demonstrating successful sim-to-real transfer. Simulation code, hardware data, and schematics for the eel robot can be found here: https://unified-fluid-robot-multiphysics.github.io/

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