Abstract:

In this paper, we propose a motion planner for quadrotors in windy environments. We extend a well-known convex polynomial optimization (CPO) method to incorporate known stochastic input uncertainties. In particular, we focus on a quadrotor unmanned aerial vehicle (UAV), and propose a new objective for direct minimization of the squared L2- norm of the UAV thrust, ‖f ‖2 L2 . We show that the first two moments of ‖f ‖2 L2 are convex in the optimization variables of the CPO problem, and can be minimized directly. Furthermore, we demonstrate that a constrained CPO approach can be used in this setting, contrary to the more popular unconstrained approaches. We provide examples demonstrating: (i) that inclusion of wind can yield significant improvements in the considered cost; (ii) that re-planning of complex paths at can be done at rates exceeding 100 Hz; and (iii) that the proposed method facilitates online re-planning leveraging wind in free- space defined as the union of convex sets.