Abstract：Regarding the autonomous flight control for unmanned aerial vehicle (UAV) in global positioning system denied environments, an error state Kalman filter (ESKF) framework is designed to fuse the vision and IMU (inertial measurement unit). On this basis, a novel input saturated control approach is proposed to further alleviate those issues due to motion blur and the field of view constraint. Different from the traditional extended Kalman filter (EKF) framework, the designed filter framework updates and corrects the error state rather than directly estimates the system state. Since the error state is a small variable with good linearity, the model error caused by its local linearization is smaller than that of the system state. Hence, the state estimation accuracy can be improved by using the error state. Based on the full state estimation in the ESKF framework, a novel hybrid linear and hyperbolic tangent saturation function is proposed to design the input saturated control approach. And it is shown that the equilibrium of the closed-loop system is asymptotically stable in the Lyapunov sense. Finally, comparative experimental results on the rotorcraft unmanned aerial vehicle (RUAV) demonstrate that the state estimation based on the proposed ESKF approach is more accurate. In addition, the proposed input saturated control method can help to keep the visual features in the field of view, and it has better transient and steady-state performances compared with the bounded integral control method.
 Tian B L, Cui J, Lu H C, et al. Adaptive finite-time attitude tracking of quadrotors with experiments and comparisons[J]. IEEE Transactions on Industrial Electronics, 2019, 66(12):9428-9438.  张广玉,何玉庆,代波,等.面向抓取作业的飞行机械臂系统及其控制[J].机器人,2019, 41(1):19-29.Zhang G Y, He Y Q, Dai B, et al. Towards grasping task:System and control of an aerial manipulator[J]. Robot, 2019, 41(1):19-29.  韩晓薇, 鲜斌, 杨森.无人机吊挂空运系统的自适应控制设计[J].控制理论与应用,2019.DOI:10.7641/CTA.2019. 90181.Han X W, Xian B, Yang S. Adaptive controller design for an unmanned quadrotor transportation system[J]. Control Theory and Applications, 2019. DOI:10.7641/CTA.2019.90181.  代波,何玉庆,谷丰,等.基于加速度反馈增强的旋翼无人机抗风扰控制[J].机器人,2020,42(1):79-88.Dai B, He Y Q, Gu F, et al. Acceleration feedback enhanced controller for wind disturbance rejection of rotor unmanned aerial vehicle[J]. Robot, 2020, 42(1):79-88.  张广玉,何玉庆,代波,等.面向自由飞行目标捕获的四旋翼最优轨迹规划[J].信息与控制,2019,48(4):469-476,485.Zhang G Y, He Y Q, Dai B, et al. Optimal trajectory planning of a quadrotor toward free flying target catching[J]. Information and Control, 2019, 48(4):469-476, 485.  鲜斌,刘洋,张旭,等.基于视觉的小型四旋翼无人机自主飞行控制[J].机械工程学报,2015,51(9):58-63.Xian B, Liu Y, Zhang X, et al. Autonomous control of a micro quadrotor unmanned aerial vehicle using optical flow[J]. Journal of Mechanical Engineering, 2015, 51(9):58-63.  Zhang X T, Fang Y C, Zhang X B, et al. A novel geometric hierarchical approach for dynamic visual servoing of quadrotors[J]. IEEE Transactions on Industrial Electronics, 2020, 67(5):3840-3849.  Wang H S, Zheng D L, Wang J, et al. Ego-motion estimation of a quadrotor based on nonlinear observer[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(3):1138-1147.  周璠,郑伟,汪增福.基于多异类传感器信息融合的微型多旋翼无人机实时运动估计[J].机器人,2015, 37(1):94-101.Zhou F, Zheng W, Wang Z F. Real-time motion estimation for UAVs based on dissimilar multi-sensor data fusion[J]. Robot, 2015, 37(1):94-101.  Sabatelli S, Galgani M, Fanucci L, et al. A double-stage Kalman filter for orientation tracking with an integrated processor in 9-D IMU[J]. IEEE Transactions on Instrumentation and Measurement, 2013, 62(3):590-598.  Julier S J, Uhlmann J K. New extension of the Kalman filter to nonlinear systems[C]//Proceedings of the SPIE, Vol.3068. Bellingham, USA:SPIE, 1997.  Madyastha V K, Ravindra V C, Mallikarjunan S, et al. Extended Kalman filter vs. error state Kalman filter for aircraft attitude estimation[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston, USA:AIAA, 2011.  Qin T, Li P L, Shen S J. VINS-Mono:A robust and versatile monocular visual-inertial state estimator[J]. IEEE Transactions on Robotics, 2018, 34(4):1004-1020.  Zhang X B, Wang R H, Fang Y C, et al. Acceleration-level pseudo-dynamic visual servoing of mobile robots with backstepping and dynamic surface control[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2019, 49(10):2071-2081.  Li B Q, Zhang X B, Fang Y C, et al. Visual servoing of wheeled mobile robots without desired images[J]. IEEE Transactions on Cybernetics, 2019, 49(8):2835-2844.  Cabecinhas D, Brá S, Cunha R, et al. Integrated visual servoing solution to quadrotor stabilization and attitude estimation using a pan and tilt camera[J]. IEEE Transactions on Control Systems Technology, 2019, 27(1):14-29.  Tee K P, Ge S S, Tay E H. Barrier Lyapunov control functions for the control of output-constrained nonlinear systems[J]. Automatica, 2009, 45(4):918-927.  Romdlony M Z, Jayawardhana B. Stabilization with guaranteed safety using control Lyapunov-barrier function[J]. Automatica, 2016, 66: 39-47.  Dasgupta R, Roy S B, Patil O S, et al. A singularity-free hierarchical nonlinear quad-rotorcraft control using saturation and barrier Lyapunov function[C]//American Control Conference. Piscataway, USA: IEEE, 2019: 3075-3080.  Wang Y Q, Ren B B, Zhong Q C. Bounded UDE-based controller for systems with input constraints[C]//IEEE Conference on Decision and Control. Piscataway, USA:IEEE, 2018:2976-2981.  Wang Y F, Wang Y Q, Dong Y T, et al. Bounded UDE-based control for a SLAM equipped quadrotor with input constraints[C]//American Control Conference. Piscataway, USA:IEEE, 2019:3117-3122.  Xie H, Lynch A F. Input saturated visual servoing for unmanned aerial vehicles[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(2):952-960.  Jabbari Asl H, Yoon J. Robust image-based control of the quadrotor unmanned aerial vehicle[J]. Nonlinear Dynamics, 2016, 85(3):2035-2048.  Jabbari Asl H. Robust vision-based tracking control of VTOL unmanned aerial vehicles[J]. Automatica, 2019, 107:425-432.  Cao N, Lynch A F. Inner-outer loop control for quadrotor UAVs with input and state constraints[J]. IEEE Transactions on Control Systems Technology, 2016, 24(5):1797-1804.  Teel A R. Global stabilization and restricted tracking for multiple integrators with bounded controls[J]. Systems and Control Letters, 1992, 18(3):165-171.  Moreno-Valenzuela J, Perez-Alcocer R, Guerrero-Medina M, et al. Nonlinear PID-type controller for quadrotor trajectory tracking[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(5):2436-2447.  Zhang X T, Fang Y C, Zhang X B, et al. Dynamic image-based output feedback control for visual servoing of multirotors[J]. IEEE Transactions on Industrial Informatics, 2020. DOI:10.1109/TII.2020.2974485.  Zhang X T, Jiang J Q, Fang Y C, et al. Enhanced fiducial marker based precise landing for quadrotors[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Pisactaway, USA:IEEE, 2019:1353-1358.