  Time-optimal control of a multi-rotor remains an open problem due to the
under-actuation and nonlinearity of its dynamics, which make it difficult to
solve this problem directly. In this paper, the time-optimal control problem of
the multi-rotor is studied. Firstly, a thrust limit optimal decomposition
method is proposed, which can reasonably decompose the limited thrust into
three directions according to the current state and the target state. As a
result, the thrust limit constraint is decomposed as a linear constraint. With
the linear constraint and decoupled dynamics, a time-optimal guidance
trajectory can be obtained. Then, a cost function is defined based on the
time-optimal guidance trajectory, which has a quadratic form and can be used to
evaluate the time-optimal performance of the system outputs. Finally, based on
the cost function, the time-optimal control problem is reformulated as an MPC
(Model Predictive Control) problem. The experimental results demonstrate the
feasibility and validity of the proposed methods.
