Exponential attitude and gyro-bias estimation on the Special orthogonal group SO(3)
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- 英文论文题名：Exponential attitude and gyro-bias estimation on the Special orthogonal group SO(3)
- 论文作者：PENG Xiuhui ; SUN Junyong ; GENG Zhiyong
- 英文论文作者：PENG Xiuhui ; SUN Junyong ; GENG Zhiyong ; The State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science ; College of Engineering ; Peking University
- 年：2017
- 作者机构：The State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science,College of Engineering,Peking University;
- 英文论文关键词：Attitude estimator ; Gyro-bias ; Special orthogonal group SO(3) ; Exponential stability ; Singular perturbation method
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O313.3
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：244k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers a nonlinear attitude estimator to estimate the attitude and gyro-bias exponentially for rigid body whose kinematics is evolved on the Special orthogonal group SO(3), which can describe the attitude globally and uniquely.Compared to the asymptotic stabilities which are presented in the previous literature, the estimator presented in this paper has exponential convergence. The exponential stability analysis is demonstrated by singular perturbation method which divide the closed loop system into fast system and slow system. The results can be apply to the vehicles which are equipped with the low-cost inertial measurement unit(IMU) such as gyroscope. Finally, the theoretical results are verified through a numerical simulation.
This paper considers a nonlinear attitude estimator to estimate the attitude and gyro-bias exponentially for rigid body whose kinematics is evolved on the Special orthogonal group SO(3), which can describe the attitude globally and uniquely.Compared to the asymptotic stabilities which are presented in the previous literature, the estimator presented in this paper has exponential convergence. The exponential stability analysis is demonstrated by singular perturbation method which divide the closed loop system into fast system and slow system. The results can be apply to the vehicles which are equipped with the low-cost inertial measurement unit(IMU) such as gyroscope. Finally, the theoretical results are verified through a numerical simulation.
This paper considers a nonlinear attitude estimator to estimate the attitude and gyro-bias exponentially for rigid body whose kinematics is evolved on the Special orthogonal group SO(3), which can describe the attitude globally and uniquely.Compared to the asymptotic stabilities which are presented in the previous literature, the estimator presented in this paper has exponential convergence. The exponential stability analysis is demonstrated by singular perturbation method which divide the closed loop system into fast system and slow system. The results can be apply to the vehicles which are equipped with the low-cost inertial measurement unit(IMU) such as gyroscope. Finally, the theoretical results are verified through a numerical simulation.
引文
[1]J.Crassidis,F.Markley,and Y.Cheng,Survey of nonlinear attitude estimation methods,J.Guid.Control Dynam,30(1):12-28,2007.
[2]X.Peng,Z.Geng and T.Morteza.”Containment control based formation t racking for multi-vehicles on Lie group,”in Proc.Chin.Control Conf.,Chengdu.China,Aug.2016,pp.7751-7756.
[3]N.Chaturvedi,A.Sanyal,and N.Mc Clamroch,Rigid-body attitude control,IEEE Control Syst.Mag,31(3):30-51,2011.
[4]T.H.Mercker and M.Akella,Rigid-body attitude tracking with vector measurements and unknown gyro bias,J.Guid.Control Dynam,34(5):1474-1484,2011.
[5]F.Bullo and A.D.Lewis,Geometric Control of Mechanical Systems.New York,NY,USA:Springer Science+Business Media,2005.
[6]H.Grip,T.Fossen,T.Johansen,and A.Saberi,Attitude estimation using biased gyro and vector measurements with time-varying reference vectors,IEEE Trans.Autom.Control,57(5):1332-1338,2012.
[7]S.Bhat,and D.Bernstein.A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon.Syst.Control Lett.,39(1):63-70,2000.
[8]H.Black,A passive system for determining the attitude of a satellite,AIAA Journal,2(7):1350-1351,1964.
[9]M.Shuster and S.Oh,Three-axis attitude determination from vector observations,J.Guid.Control Dynam,4(1):70-77,1981.
[10]F.Markley,Optimal Attitude Matrix from Two Vector Measurements,J.Guid.Control Dynam,31(3):765-768,2008.
[11]F.Markley and J.Crassidis,Fundamentals of spacecraft attitude determination and control.New York:Springer,2014.
[12]F.L.Markley,R.G.Reynolds,Analytic steady-state accuracy of a spacecraft attitude estimator,AIAA J.Guid.,Control,Dyna,23(6):1065-1067,2000.
[13]J.Hashmall,M.Radomski,and J.Sedlak,On-orbit calibration of satellite gyroscopes,in Proceedings of the AIAA/AAS Astrodynamics Specialist Conference,2000:13-17.
[14]J.Thienel and R.Sanner.A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise.IEEE Trans.on Automatic Control,48(11):2011-2014,2003.
[15]R.Mahony,T.Hamel and J.-M.Pflimlin,Nonlinear complementary filters on the special orthogonal group,IEEE Trans.on Automatic Control,53(5):1203-1218,2008.
[16]M.Krstic,I.Kanellakopoulos and P.V.Kokotovic,Nonlinear and adaptive control design.Wiley,1995.
[17]H.K.Khalil and J.Grizzle Nonliear systems.Printice Hall,New Jersey,1996.
[18]T.Lee,Robust adaptive attitude tracking on with an application to a quadrotor uav,IEEE Trans.Control Syst.Technol,21(5):1924-1930,2013.
[19]D.Zlotnik,J.Forbes.Exponential convergence of a nonlinear attitude estimator.Automatica,72:11-18,2016.
[20]L.Markley.Attitude determination using vector observations and the singular value decomposition.The Journal of the Astronautical Sciences,36(3):245C258,1988.
[2]X.Peng,Z.Geng and T.Morteza.”Containment control based formation t racking for multi-vehicles on Lie group,”in Proc.Chin.Control Conf.,Chengdu.China,Aug.2016,pp.7751-7756.
[3]N.Chaturvedi,A.Sanyal,and N.Mc Clamroch,Rigid-body attitude control,IEEE Control Syst.Mag,31(3):30-51,2011.
[4]T.H.Mercker and M.Akella,Rigid-body attitude tracking with vector measurements and unknown gyro bias,J.Guid.Control Dynam,34(5):1474-1484,2011.
[5]F.Bullo and A.D.Lewis,Geometric Control of Mechanical Systems.New York,NY,USA:Springer Science+Business Media,2005.
[6]H.Grip,T.Fossen,T.Johansen,and A.Saberi,Attitude estimation using biased gyro and vector measurements with time-varying reference vectors,IEEE Trans.Autom.Control,57(5):1332-1338,2012.
[7]S.Bhat,and D.Bernstein.A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon.Syst.Control Lett.,39(1):63-70,2000.
[8]H.Black,A passive system for determining the attitude of a satellite,AIAA Journal,2(7):1350-1351,1964.
[9]M.Shuster and S.Oh,Three-axis attitude determination from vector observations,J.Guid.Control Dynam,4(1):70-77,1981.
[10]F.Markley,Optimal Attitude Matrix from Two Vector Measurements,J.Guid.Control Dynam,31(3):765-768,2008.
[11]F.Markley and J.Crassidis,Fundamentals of spacecraft attitude determination and control.New York:Springer,2014.
[12]F.L.Markley,R.G.Reynolds,Analytic steady-state accuracy of a spacecraft attitude estimator,AIAA J.Guid.,Control,Dyna,23(6):1065-1067,2000.
[13]J.Hashmall,M.Radomski,and J.Sedlak,On-orbit calibration of satellite gyroscopes,in Proceedings of the AIAA/AAS Astrodynamics Specialist Conference,2000:13-17.
[14]J.Thienel and R.Sanner.A coupled nonlinear spacecraft attitude controller and observer with an unknown constant gyro bias and gyro noise.IEEE Trans.on Automatic Control,48(11):2011-2014,2003.
[15]R.Mahony,T.Hamel and J.-M.Pflimlin,Nonlinear complementary filters on the special orthogonal group,IEEE Trans.on Automatic Control,53(5):1203-1218,2008.
[16]M.Krstic,I.Kanellakopoulos and P.V.Kokotovic,Nonlinear and adaptive control design.Wiley,1995.
[17]H.K.Khalil and J.Grizzle Nonliear systems.Printice Hall,New Jersey,1996.
[18]T.Lee,Robust adaptive attitude tracking on with an application to a quadrotor uav,IEEE Trans.Control Syst.Technol,21(5):1924-1930,2013.
[19]D.Zlotnik,J.Forbes.Exponential convergence of a nonlinear attitude estimator.Automatica,72:11-18,2016.
[20]L.Markley.Attitude determination using vector observations and the singular value decomposition.The Journal of the Astronautical Sciences,36(3):245C258,1988.