Trajectory optimisation for flapping foils under unsteady inflow conditions

Fish can significantly improve their swimming performance if their kinematics and paths are adequately adapted to the incoming flow. When the optimum path is unknown, the first step is to predict the performance that could be obtained for several route candidates. Next, we can select the trajectory that increases the lift or efficiency. We develop several force models with Koopman-based system identification tools to predict the C_L evolution of a foil executing transitions in its motion inside an unsteady incoming wake. We test the optimum-path selection capabilities by predicting the <span style="font-size:10.8333px">C_L evolution for a set of route candidates, and rank them based on C_L production. We find that adding physically relevant information about the wake in the models helps to find the optimum path, achieving a correlation of 90% with numerical target data. Finally, we optimize a more general form of the transition trajectory to minimize power consumption using the previously developed force models.