Dual-quaternion-based finite-time control for spacecraft tracking in six degrees of freedom

Abstract

This article investigates the tracking control problem for the six-degree-of-freedom motion of a follower spacecraft relative to a leader spacecraft. Employing dual quaternion representation, the model of the six-degree-of-freedom relative motion between the two spacecraft is derived. Taking into account the model uncertainties and external disturbances, two robust fast sliding mode control laws are proposed to guarantee the finite-time convergence of the tracking errors, where the second control law can solve the dual-equilibrium problem that exists in the first one. In order to alleviate chattering phenomenon, continuous saturation function is introduced into the controller and a softening control strategy is developed. It is worth pointing out that the convergence rate of the proposed fast sliding mode control is faster than that of the linear sliding mode control and terminal sliding mode control. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approaches.

Keywords

Finite-time control fast sliding mode control dual quaternion six-degrees-of-freedom tracking control

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References

Subbarao

. Nonlinear control of motion synchronization for satellite proximity operations. J Guid Control Dyn 2008; 31(5): 1284–1294.

Bristow J, Folta D and Hartman K. A formation flying technology vision. In: Proceedings of the AIAA space 2000 conference and exposition, Long Beach, CA, 19–21 September 2000, paper no. AIAA-2000-5194. Reston, VA: AIAA.

Xin

Pan

. Nonlinear optimal control of spacecraft approaching a tumbling target. Aerosp Sci Technol 2011; 15: 79–80.

Tsuda

Nakasuka

. New attitude motion following control algorithm for capturing tumbling object in space. Acta Astronaut 2003; 53: 847–861.

Pan H and Kapila V. Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics. In: Proceedings of the 40th IEEE conference on decision and control, Orlando, FL, 4–7 December 2001, vol. 3, pp.2057–2062. New York, NY: Institution of Electrical and Electronics Engineers.

Wong H, Pan H and Kapila V. Output feedback control for spacecraft formation flying with coupled translation and attitude dynamics. In: Proceedings of the 2005 American control conference, Portland, OR, USA, 8–10 June 2005, vol. 4, pp.2419–2426. Piscataway, NJ: IEEE.

Kristiansen

Nicklasson

Gravdahl

. Spacecraft coordination control in 6DOF: Integrator backstepping vs passivity-based control. Automatica 2008; 44(11): 2896–2901.

Clifford

. Preliminary sketch of bi-quaternions. Proc London Math Soc 1873; 4: 381–395.

Study

. Von den bewegungen und umlegungen. Math Ann 1891; 39: 441–556.

10.

Brodsky

Shoham

. Dual numbers representation of rigid body dynamics. Mech Mach Theory 1999; 34(5): 693–718.

11.

Y-L

Luh

JYS

. Dual-number transformation and its applications to robotics. IEEE J Rob Autom 1987; 3(6): 615–623.

12.

. Strapdown inertial navigation system algorithms based on dual quaternions. Aerosp Electron Syst 2005; 41(1): 110–132.

13.

Gan

Liao

Wei

. Dual quaternion-based inverse kinemics of the general spatial 7R mechanism. Proc Inst Mech Eng Part C J Mech Eng Sci 2008; 222(8): 1593–1598.

14.

Perez

McCarthy

. Dual quaternion synthesis of constrained robotic systems. J Mech Des 2004; 126(3): 425–435.

15.

Han D, Wei Q, Li Z, et al. Control of oriented mechanical systems: a method based on dual quaternion. In: Proceedings of the 17th world congress, Seoul, Korea, 6–11 July 2008, pp.3836–3841. Natick, MA: The International Federation of Automatic Control.

16.

S-C

Chen

Y-P

. Smooth sliding-mode control for spacecraft attitude tracking maneuvers. J Guid Control Dyn 1995; 18(6): 1345–1349.

17.

Robinetti

Parker

. Spacecraft euler parameters tracking of large angle maneuvers via sliding mode control. J Guid Control Dyn 1996; 19(3): 702–703.

18.

Cao

Zhang

. Robust backstepping sliding mode attitude tracking and vibration damping of flexible spacecraft with actuator dynamics. J Aerosp Eng 2009; 22(2): 139–152.

19.

Zhu

Xia

. Adaptive sliding mode control for attitude stabilization with actuator saturation. IEEE Trans Ind Electron 2011; 58(10): 4898–4907.

20.

Liu

Hexi

. Sliding mode control for low-thrust Earth-orbiting spacecraft formation maneuvering. Aerosp Sci Technol 2006; 10: 636–643.

21.

Godard Kumar

. Fault tolerant reconfigurable satellite formations using adaptive variable structure techniques. J Guid Control Dyn 2010; 33(3): 969–984.

22.

Jin

Sun

. Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control. Aerosp Sci Technol 2008; 12: 324–330.

23.

Zou

A-M

Kumar

Hou

Z-G

. Finite-time attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network. IEEE Trans Syst Man Cybern Part B Cybern 2011; 41(4): 950–963.

24.

Liu

. Terminal sliding mode control for spacecraft formation flying. IEEE Trans Aerosp Electron Syst 2009; 45(3): 835–846.