Performance benchmarking of quadrotor systems using time-optimal control

Frequently hailed for their dynamical capabilities, quadrotor vehicles are often employed as experimental platforms. However, questions surrounding achievable performance, influence of design parameters, and performance assessment of control strategies have remained largely unanswered. This paper presents an algorithm that allows the computation of quadrotor maneuvers that satisfy Pontryagin's minimum principle with respect to time-optimality. Such maneuvers provide a useful lower bound on the duration of maneuvers, which can be used to assess performance of controllers and vehicle design parameters. Computations are based on a two-dimensional first-principles quadrotor model. The minimum principle is applied to this model to find that time-optimal trajectories are bang-bang in the thrust command, and bang-singular in the rotational rate control. This paper presents a procedure allowing the computation of time-optimal maneuvers for arbitrary initial and final states by solving the boundary value problem induced by the minimum principle. The usage of the computed maneuvers as a benchmark is demonstrated by evaluating quadrotor design parameters, and a linear feedback control law as an example of a control strategy. Computed maneuvers are verified experimentally by applying them to quadrocopters in the ETH Zurich Flying Machine Arena testbed.