Two-Stage Trajectory Optimization for Flapping Flight with Data-Driven Models

Underactuated robots often require involved routines for trajectory planning due to their complex dynamics. Flapping-wing aerial vehicles have unsteady aerodynamics and periodic gaits that complicate the planning procedure. In this paper, we improve upon existing methods for flight planning by introducing a two-stage optimization routine to plan flapping flight trajectories. The first stage solves a trajectory optimization problem with a data-driven fixed-wing approximation model trained with experimental flight data. The solution to this is used as the initial guess for a second stage optimization using a flapping-wing model trained with the same flight data. We demonstrate the effectiveness of this approach with a bat robot in both simulation and experimental flight results. The speed of convergence, the dependency on the initial guess, and the quality of the solution are improved, and the robot is able to track the optimized trajectory of a dive maneuver.