Minimum-Time Trajectory Generation for Quadrotors in Constrained Environments

In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing reformulation. Transverse coordinates, expressing the distance from a frame path, are used to parameterize the vehicle position and a spatial parameter is used as independent variable. This reformulation allows us to: (1) obtain a fixed horizon problem and (2) easily formulate (fairly complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios. Moreover, the optimal trajectory generated in the second scenario is experimentally executed with a real nanoquadrotor in order to show its feasibility.