Time-optimal quadrotor flight

Solving the time-optimal path planning problem, where a system is brought from an initial to terminal state in minimal time while obeying geometric and dynamic constraints, has been an active area of research for many years. Very often the problem is divided into a high-level path planning stage where a feasible geometric path is determined and a low-level path following stage where system dynamics are taken into account. This paper combines both approaches for differentially flat systems into a single optimization problem. The geometric path is represented as a convex combination of two or more feasible paths and the dynamics of the system can subsequently be projected onto the path which leads to a single input system. The resulting optimization problem is transformed into a fixed end-time optimal control problem that can be initialized easily. Throughout the paper, the quadrotor, a challenging non-linear system, is used to illustrate the proposed approach.