Nonlinear Control of Motion Synchronization for Satellite Proximity Operations

This paper considers the problem of motion synchronization of free-flying robotic spacecraft and serviceable floating objects in space. The synchronization maneuvers are a combination of relative position tracking and attitude reorientation. Control laws are developed that ensure that the relative position vector between a pursuer and target spacecraft is always directed toward the docking port of the target. The tracking-error reference signals are generated based on a novel "virtual target" construction. Also, the attitude reorientation of the pursuer is achieved by constructing a desired attitude from the virtual target, and the control law seeks to nullify the errors between the current and desired attitude parameters. The control law synthesis proceeds along familiar, established procedures motivated by feedback-linearization-based approaches. Disturbance torques due to gravity gradient and other unknown but bounded disturbances are accounted for using an adaptive control formulation. The stability of the control laws are demonstrated via Lyapunov analysis and Matrosov's theorem Numerical simulations are performed to demonstrate the efficacy of this control formulation.

[1]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .

[2]  M. Shuster.  A survey of attitude representation , 1993 .

[3]  Vikram Kapila,et al.  Adaptive tracking control using synthesized velocity from attitude measurements , 2001, Autom..

[4]  Shinichi Nakasuka,et al.  New attitude motion following control algorithm for capturing tumbling object in space , 2003 .

[5]  Steven Dubowsky,et al.  State, shape, and parameter estimation of space objects from range images , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[6]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[7]  Chi Zhu,et al.  Planning of Safe Kinematic Trajectories for Free Flying Robots Approaching an Uncontrolled Spinning Satellite , 2002 .

[8]  Sergei Tanygin.  Generalization of Adaptive Attitude Tracking , 2002 .

[9]  Dennis S. Bernstein,et al.  Adaptive Asymptotic Tracking of Spacecraft Attitude Motion with Inertia Matrix Identification , 1998 .

[10]  Liu Guo-rong.  Adaptive Control for a Class of Nonlinear Systems , 2007 .

[11]  Brad Paden,et al.  Globally asymptotically stable ‘PD+’ controller for robot manipulators , 1988 .

[12]  John L. Junkins,et al.  Adaptive Control of Nonlinear Attitude Motions Realizing Linear Closed Loop Dynamics , 2001 .

[13]  Antonio Loría,et al.  A nested Matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems , 2005, IEEE Transactions on Automatic Control.

[14]  E. Wong,et al.  Inertial attitude determination for a dual-spin planetary spacecraft , 1983 .

[15]  S. Di Gennaro,et al.  Adaptive robust tracking for flexible spacecraft in presence of disturbances , 1998 .

[16]  N. Rouche,et al.  Stability Theory by Liapunov's Direct Method , 1977 .

[17]  Kamesh Subbarao,et al.  Adaptive Output Feedback Control for Spacecraft Rendezvous and Docking Under Measurement Uncertainty , 2006 .

[18]  Kamesh Subbarao.  The attitude control problem, re-visited , 2003 .

[19]  Yoshiaki Ohkami,et al.  Satellite capturing strategy using agile Orbital Servicing Vehicle, Hyper-OSV , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[20]  Kamesh Subbarao,et al.  Structured Model Reference Adaptive Control for a Class of Nonlinear Systems , 2003 .

[21]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[22]  John L. Junkins,et al.  Adaptive realization of linear closed loop tracking dynamics in the presence of large system model errors , 1999 .

[23]  Kamesh Subbarao.  Structured adaptive model inversion (SAMI): Theory and applications to trajectory tracking for non-linear dynamical systems , 2001 .

[24]  Ralph E. Bach,et al.  Attitude control with realization of linear error dynamics , 1993 .

[25]  Toru Kasai,et al.  Result of Autonomous Rendezvous Docking Experiment of Engineering Test Satellite-VII , 2001 .