A fixed-time trajectory following problem for quadrotors via output feedback is concerned. Based on the inner–outer separation design philosophy, the under-actuated quadrotor is formulated as a hierarchical structure composed by position and attitude dynamics. With an emphasis on removing the demand on unmeasured velocity and eliminating the negative effect of disturbances, fixed-time extended state observers utilizing two kinds of polynomial feedback terms are proposed to simultaneously identify unavailable velocity states and unknown uncertainties with a fixed-time estimation capability. With these observation results, a velocity free fixed-time control protocol is synthesized to enable a satisfied trajectory regulation with a uniform convergence time independent of initial positions, such that a prescribed fixed-time stability and enhanced robustness can be obtained with chattering-free inputs. By virtue of bi-limit homogeneity properties, all error variables of the resultant quadrotor system are demonstrated to be fixed-time convergent. Eventually, the benefits of developed algorithm are illustrated via simulations

通过输出反馈对四旋翼飞机的固定时间轨迹跟随问题进行了研究。基于内外分离设计理念，欠驱动四旋翼被公式化为由位置和姿态动力学组成的分层结构。为了消除对测速的需求并消除干扰的负面影响，提出了利用两种多项式反馈项的固定时间扩展状态观测器，以固定时间估计能力同时识别不可用的速度状态和未知不确定性。利用这些观察结果，可以合成无速度的固定时间控制协议，从而以独立于初始位置的均匀收敛时间实现令人满意的轨迹调节，这样就可以使用无抖动输入获得规定的固定时间稳定性和增强的鲁棒性。由于具有双极限同质性，所产生的四旋翼系统的所有误差变量都被证明是固定时间收敛的。最终，通过仿真说明了开发算法的好处