Three challenges, however, can hinder the application of Feedback Linearization: over-intensive control signals, singular decoupling matrix, and saturation. Activating any of these three issues can challenge the stability proof. To solve these three challenges, first, this research proposed the drone gait plan. The gait plan was initially used to figure out the control problems in quadruped (four-legged) robots; applying this approach, accompanied by Feedback Linearization, the quality of the control signals was enhanced. Then, we proposed the concept of unacceptable attitude curves, which are not allowed for the tiltrotor to travel to. The Two Color Map Theorem was subsequently established to enlarge the supported attitude for the tiltrotor. These theories were employed in the tiltrotor tracking problem with different references. Notable improvements in the control signals were witnessed in the tiltrotor simulator. Finally, we explored the control theory, the stability proof of the novel mobile robot (tilt vehicle) stabilized by Feedback Linearization with saturation. Instead of adopting the tiltrotor model, which is over-complicated, we designed a conceptual mobile robot (tilt-car) to analyze the stability proof. The stability proof (stable in the sense of Lyapunov) was found for a mobile robot (tilt vehicle) controlled by Feedback Linearization with saturation for the first time. The success tracking result with the promising control signals in the tiltrotor simulator demonstrates the advances of our control method. Also, the Lyapunov candidate and the tracking result in the mobile robot (tilt-car) simulator confirm our deductions of the stability proof. These results reveal that these three challenges in Feedback Linearization are solved, to some extents.

翻译：然而，反馈线性化在实际应用中面临三大挑战：控制信号过强、解耦矩阵奇异以及饱和问题。这三个问题中的任何一个被激活，都会增加稳定性证明的难度。为解决这些问题，本研究首先提出了无人机步态规划方法。该规划方法最初用于解决四足机器人的控制问题；将此方法与反馈线性化相结合，可有效提升控制信号质量。随后，我们提出了不可接受姿态曲线的概念——倾转旋翼机被禁止进入的姿态区域，并建立了双色映射定理以扩大倾转旋翼机可支持的姿态范围。将这些理论应用于不同参考轨迹的倾转旋翼跟踪问题，在倾转旋翼机仿真器中观察到控制信号的显著改善。最后，我们深入研究了基于饱和反馈线性化的新型移动机器人（倾转载具）控制理论与稳定性证明。为避免使用过于复杂的倾转旋翼机模型，我们设计了概念性移动机器人（倾转小车）来分析稳定性证明，并首次获得了饱和约束下反馈线性化控制的移动机器人（倾转载具）的Lyapunov稳定性证明。倾转旋翼机仿真器中成功的跟踪结果与优化的控制信号验证了所提控制方法的先进性，而移动机器人（倾转小车）仿真器中的Lyapunov函数选取与跟踪结果则证实了稳定性证明的正确推导。这些结果表明，反馈线性化的三大难题已得到一定程度的解决。