Quadrotor Motion Planning in Stochastic Wind Fields

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 ${{{\mathcal{L}}}_2}$-norm of the UAV thrust, $\left\| f \right\|_{{{{\mathcal{L}}}_2}}^2$. We show that the first two moments of $\left\| f \right\|_{{{{\mathcal{L}}}_2}}^2$ 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.