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.

翻译：多旋翼的时间最优控制因其动力学存在的欠驱动和非线性特性，使得直接求解该问题较为困难，因此至今仍是一个开放性问题。本文研究了多旋翼的时间最优控制问题。首先，提出了一种推力极限最优分解方法，该方法能够根据当前状态与目标状态，将有限的推力合理分解到三个方向上，从而将推力极限约束转化为线性约束。基于线性约束与解耦后的动力学，可获得一条时间最优引导轨迹。然后，基于该时间最优引导轨迹定义了一个成本函数，该函数具有二次形式，可用于评估系统输出的时间最优性能。最后，基于该成本函数，将时间最优控制问题重新表述为一个模型预测控制问题。实验结果验证了所提出方法的可行性与有效性。