Relative motion coupled control based on dual quaternion

Abstract Coordinated control problem of translation and rotation between two spacecraft is investigated in this paper. Using dual quaternion, we establish the relative coupled dynamic model in which the coupling effect between translational and rotational motion is indicated. Based on the logarithm of dual quaternion, a model-independent PD-like controller is proposed for spacecraft tracking control problem. The convergence of the closed loop system in the presence of external disturbances is proven theoretically. The validity of the proposed approach is demonstrated by numerical simulations. The advantages of the proposed controller are displayed by comparing with others.

[1]  K. Zindler.  Geometrie der Dynamen , 1903 .

[2]  Moshe Shoham,et al.  Dual numbers representation of rigid body dynamics , 1999 .

[3]  Sebastian Gaulocher.  Modeling the Coupled Translational and Rotational Relative Dynamics for Formation Flying Control , 2005 .

[4]  J. Wen,et al.  The attitude control problem , 1991 .

[5]  Clifford,et al.  Preliminary Sketch of Biquaternions , 1871 .

[6]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[7]  V. Kapila,et al.  Output feedback control for spacecraft formation flying with coupled translation and attitude dynamics , 2005, Proceedings of the 2005, American Control Conference, 2005..

[8]  Sung-yong Shin,et al.  A Compact Differential Formula for the First Derivative of a Unit Quaternion Curve , 1996 .

[9]  D. Hu,et al.  Strapdown inertial navigation system algorithms based on dual quaternions , 2005 .

[10]  Qing Wei,et al.  Control of Oriented Mechanical systems: A Method Based on Dual Quaternion , 2008 .

[11]  D. T. Stansbery,et al.  Position and attitude control of a spacecraft using the state-dependent Riccati equation technique , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[12]  Jan Tommy Gravdahl,et al.  Spacecraft coordination control in 6DOF: Integrator backstepping vs passivity-based control , 2008, Autom..

[13]  Baoqun Zhang,et al.  Asymptotical stability analysis of “PD+” controller for spacecraft attitude tracking system* , 2010, 2010 8th World Congress on Intelligent Control and Automation.

[14]  Scott Evan Lennox,et al.  Coupled Attitude And Orbital Control System Using Spacecraft Simulators , 2004 .

[15]  J. Michael McCarthy,et al.  Dual quaternion synthesis of constrained robotic systems , 2003 .

[16]  S. Ploen,et al.  Rigid body equations of motion for modeling and control of spacecraft formations. Part 1: Absolute equations of motion , 2004, Proceedings of the 2004 American Control Conference.

[17]  Ian S. Fischer,et al.  Dual-Number Methods in Kinematics, Statics and Dynamics , 1998 .

[18]  John L. Junkins,et al.  Application of the cayley form to general spacecraft motion , 2006 .

[19]  Per Johan Nicklasson,et al.  Spacecraft formation flying: A review and new results on state feedback control , 2009 .

[20]  S. Qiao,et al.  Dual quaternion-based inverse kinematics of the general spatial 7R mechanism , 2008 .