Optimal Visual Servoing for differentially flat underactuated systems

This work introduces a hybrid visual servoing technique for differentially flat, underactuated systems that is well suited for aggressive dynamics. Standard Position-Based Visual Servoing (PBVS) and Image-Based Visual Servoing (IBVS) approaches for underactuated systems, such as quadrotors, oftentimes do not explicitly ensure that the relevant image features stay in the camera's field of view, especially while the system is performing agile maneuvers. We present a control technique that is designed to mitigate this issue and that results in increased robustness. Given a goal image, we first solve a constrained Perspective-n-Point (PnP) problem to find an equilibrium pose which aligns the camera with the goal. We then formulate the task of navigating to the goal pose as an optimal control problem, where a cost over the resulting image feature tracks along the trajectory is minimized which implicitly keeps features in the field of view over the course of the trajectory. The optimization is performed over a polynomial parametrization of the flat outputs of the system to decrease the dimensionality of the optimization. Simulations and physical experiments are performed with a quadrotor system to benchmark the algorithm's performance against a typical PBVS approach.