A free-floating space robot with four linkages, two flexible arms and a rigid end-effector that are mounted on a rigid spacecraft; is studied in this paper. The governing equations are derived using Kane’s method. The powerful tools of Kane’s approach in incorporating motion constraints have been applied in the dynamic model. By including the motion constraints in the kinematic and dynamic equations, a two way coupling between the spacecraft motion and manipulator motion is achieved. The assumed mode method is employed to express elastic displacements, except that the associated admissible functions are supplanted by quasicomparison functions. By a perturbation approach, the resulting nonlinear problem is separated into two sets of equations: one for rigid-body maneuvering of the robot and the other for elastic vibrations suppression and rigid-body perturbation control. The kinematic redundancy of the manipulator system is removed by exploiting the conservation of angular momentum law that makes the rigid manipulator system nonholonimic. Nonholonomic constraints, resulted from the nonintegrability of angular momentum, in association with equations obtained from conservation of linear momentum and direct differential kinematics generate a set of ordinary differential equations that govern the motion tracking of the robot. The digitalized linear quadratic regulator (LQR) with prescribed degree of stability is used as the feedback control scheme to suppress vibrations. A numerical example is presented to show the numerical preferences of using Kane’s method in deriving the equations of motion and also the efficacy of the control scheme. Acquiring a zero magnitude for spacecraft attitude control moment approves the free-floating behavior of the space robot in which considerable amount of energy is saved.

References

References
1.
Dubowsky
,
S.
, and
Papadopoulos
,
E.
, 1993, “
The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems
,”
IEEE Trans. Rob. Autom.
,
9
(
5
), pp.
531
543
.
2.
Umetani
,
Y.
, and
Yoshida
,
K.
, 1987, “
Continuous Path Control of Space Manipulators Mounted on OMV
,”
Acta Astronaut.
,
15
, pp.
981
986
.
3.
Vafa
,
Z.
, and
Dubowsky
,
S.
, 1987, “
On the Dynamics of Manipulators in Space Using the Virtual Manipulator Approach
,”
Proceedings of IEEE International Conference on Robotics and Automation
, pp.
579
585
.
4.
Nakamura
,
Y.
, and
Mukherjee
,
R.
, 1991, “
Nonholonomic Path Planning of Space Robots Via Bidirectional Approach
,”
IEEE Trans. Rob. Autom.
,
7
(
4
), pp.
500
514
.
5.
Papadopoulos
,
E.
, and
Dubowsky
,
S.
, 1993, “
Dynamic Singularities in the Control of Free-Floating Space Manipulators
,”
ASME J. Dyn. Syst., Meas. Control
,
115
(
1
), pp.
44
52
.
6.
Papadopoulos
,
E.
, and
Dubowsky
,
S.
, 1991, “
On the Nature of Control Algorithms for Free-Floating Space Manipulators
,”
IEEE Trans. Rob. Autom.
,
7
(
6
), pp.
750
758
.
7.
Papadopoulos
,
E.
, 1992, “
Path Planning for Space Manipulators Exhibiting Nonholonomic Behavior
,”
Proceedings of the International Conference on Intelligent Robots and Systems, IROS 92
, pp.
669
675
.
8.
Papadopoulos
,
E.
,
Tortopidis
,
I.
, and
Nanos
,
K.
, 2005, “
Smooth Planning for Free-Floating Space Robots Using Polynomials
,”
Proceedings of IEEE International Conference on Robotics and Automation (ICRA ‘05)
, pp.
4272
4277
.
9.
Ukai
,
H.
,
Asano
,
T.
, and
Morita
,
Y.
, 1999, “
Modeling and Trajectory Control of Free-Flying Robot With Flexible Arms
,”
Proceedings of 14th IFAC World Congress, IFAC 1999
,
Beijing, China
, pp.
77
82
.
10.
Lim
,
S.
, 1992, “
Position and Vibration Control of Flexible Space Robots
,” Ph.D. thesis, Virginia Polytechnic Inst. and State Univ., Blacksburg, VA.
11.
Meirovitch
,
L.
, and
Lim
,
S.
, 1994, “
Maneuvering and Control of Flexible Space Robots
,”
J. Guid. Control Dyn.
,
17
(
3
), pp.
520
528
.
12.
Kane
,
T. R.
, and
Levinson
,
D. A.
, 1985,
Dynamics: Theory and Applications
,
McGraw-Hill
,
New York, NY
.
13.
Meirovitch
,
L.
, 1997,
Principles and Techniques of Vibrations
,
Prentice-Hall International Editions, Inc.
,
Englewood Cliffs, NJ
.
14.
Masoudi
,
R.
, 2002, “
A Comparison Between Trajectory and Vibration Control of Flexible Free-Flying and Free-Floating Space Robots
,” M.S. thesis, Shiraz University, Shiraz, Iran.
15.
Gear
,
C. W.
, 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
,
Prentice-Hall International Editions, Inc.
,
Englewood Cliffs, NJ
.
16.
Nakamura
,
Y.
, 1991,
Advanced Robotics: Redundancy and Optimization
,
Addison-Wesley Publishing Company, Inc.
,
Massachusetts
.
17.
Patel
,
R. V.
,
Laub
,
A. J.
, and
Dooren
,
P. M. V.
, 1994,
Numerical Linear Algebra Techniques for Systems and Control
,
The Institute of Electrical and Electronics Engineers, Inc.
,
New York, NY
.
18.
Kuo
,
B. C.
, 1980,
Digital Control Systems
,
Holt, Rinehart and Winston, Inc.
,
Illinois
.
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