Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy measurements. Proposed estimator considers all the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on SE(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.

[1]  Kamel Kara,et al.  State vector estimation using extended filter kalman for the sliding mode controlled quadrotor helicopter in vertical flight , 2013, 2013 8th International Conference on Electrical and Electronics Engineering (ELECO).

[2]  Taeyoung Lee,et al.  Robust Adaptive Attitude Tracking on ${\rm SO}(3)$ With an Application to a Quadrotor UAV , 2013, IEEE Transactions on Control Systems Technology.

[3]  Taeyoung Lee,et al.  Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) , 2013 .

[4]  Daewon Lee,et al.  Geometric control of a quadrotor UAV transporting a payload connected via flexible cable , 2014, 1407.8164.

[5]  Fikret Caliskan,et al.  Actuator and sensor fault detection and diagnosis of quadrotor based on Two-Stage Kalman Filter , 2015, 2015 5th Australian Control Conference (AUCC).

[6]  S. Bhat,et al.  A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , 2000 .

[7]  Vijay Kumar,et al.  Cooperative Grasping and Transport Using Multiple Quadrotors , 2010, DARS.

[8]  Shaohua Wang,et al.  Quadrotor aircraft attitude estimation and control based on Kalman filter , 2012, Proceedings of the 31st Chinese Control Conference.

[9]  Emre Kiyak,et al.  An integrated navigation system design for Quadrotors , 2015, 2015 Sensor Data Fusion: Trends, Solutions, Applications (SDF).

[10]  Daewon Lee,et al.  Geometric Adaptive Tracking Control of a Quadrotor Unmanned Aerial Vehicle on SE(3) for Agile Maneuvers , 2015 .

[11]  Daewon Lee,et al.  Geometric nonlinear PID control of a quadrotor UAV on SE(3) , 2013, 2013 European Control Conference (ECC).

[12]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[13]  D. Candidate MAE.  Geometric Adaptive Tracking Control of a Quadrotor UAV on SE ( 3 ) for Agile Maneuvers , 2014 .

[14]  Seungwon Choi,et al.  Aerial manipulation using a quadrotor with a two DOF robotic arm , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  M. Akella,et al.  Differentiator-Free Nonlinear Proportional-Integral Controllers for Rigid-Body Attitude Stabilization , 2004 .

[16]  Yan Zhuang,et al.  Real-time pose estimation and motion control for a quadrotor UAV , 2014, Proceeding of the 11th World Congress on Intelligent Control and Automation.

[17]  Anthony Tzes,et al.  Model predictive quadrotor indoor position control , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[18]  Daewon Lee,et al.  Geometric stabilization of a quadrotor UAV with a payload connected by flexible cable , 2013, 2014 American Control Conference.

[19]  Hyo-Sung Ahn,et al.  Extended Kalman filter with multi-frequency reference data for quadrotor navigation , 2015, 2015 15th International Conference on Control, Automation and Systems (ICCAS).

[20]  Torsten Bertram,et al.  Attitude estimation and control of a quadrocopter , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  Farhad A. Goodarzi.  Geometric Nonlinear Controls for Multiple Cooperative Quadrotor UAVs Transporting a Rigid Body , 2015, 1508.03789.

[22]  Jyh-Ching Juang,et al.  Spacecraft robust attitude tracking design: PID control approach , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[23]  Kamesh Subbarao,et al.  Nonlinear PID-Like Controllers for Rigid-Body Attitude Stabilization , 2004 .

[24]  Taeyoung Lee,et al.  Dynamics and control of quadrotor UAVs transporting a rigid body connected via flexible cables , 2015, 2015 American Control Conference (ACC).

[25]  J. Butcher.  The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[26]  Francesco Bullo,et al.  Simple mechanical control systems , 2005 .