Design and control of a space based two link manipulator with Lyapunov based control laws.

136 Pages·1.4 MB·en_US

by  Sorensen, Dennis R.;Agrawal, Brij N.

NAVAL POSTGRADUATESCHOOL
3NIA 93943-5002

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DESIGN AND CONTROPrLogrOamFEleAmentSNPumAbeCrE B| IAV.jSeclENDu T[ TWasOk NuLI|NWoKrk l:mi Accession No
1 Title(IncludeSecurity Classification)
MANIPULATOR WITH LYAPUNOV BASED CONTROLLAWS
1 Personal Author(s) Dennis R. Sorensen
13a Type ofReport 13b TimeCovered Il4 Date ofReport (year, month,day) I 15 Page Count
Engineer's Thesis From To September 1992 28
| 1
16 SupplementaryNotation The views expressed in this thesis are those ofthe author and do not reflect the official
policy or position ofthe Department ofDefense or the U.S. Government.
Cosati Codes 18 Subject Terms (continue on reverse ifnecessary and identify by block number)
Non-Linear Control System Design, Robotics, Satellite Attitude Control
19 Abstract (continue on reverse ifnecessary and identify by block number
The Flexible Spacecraft Simulator (FSS) at the Naval Postgraduate School was modified by replacing the
flexible appendage with a two link robotic manipulator. This experimental setup was designed to simulate motion
ofa spacecraft about the pitch axis. The spacecraft consists ofa main body, a two link manipulator, and
momentum wheel with actuator to control the pitch attitude ofthe spacecraft. Position information from the main
body and manipulators were obtained from Rotary Variable DisplacementTransducers (RVDT's). The equations
ofmotion were developed assuming that the main body and manipulator were rigid bodies. The resulting
coupled, nonlinear, time variant equations ofmotion were used to analyze the dynamics and kinematics ofthe
body, manipulator as well as the interaction between the two. Three different control strategies were developed
using Lyapunov's Second or Direct Method. With the firstcontroller, simple linearfeedback ofposition and
velocity information with constant gains was used to position the manipulator and stabilize the main body. A fifth
order polynomial was used to generate a reference trajectory for the second controller. This trajectory was used in
conjunction with a tracking Lyapunov controller to position and stabilize the system. In the third controller, a
near-minimum-time technique was used to generate a reference trajectory. This reference trajectory was employed
to design a tracking controller similar to that used in the polynomial reference controller.
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Brij N. Agrawal [phone] AA/Ag
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DESIGN AND CONTROL OF A SPACE BASED TWO LINK MANIPULATOR
WITH LYAPUNOV BASED CONTROL LAWS
by
Dennis R. Sorensen
Lieutenant Commander, United States Navy
B.S., Iowa State University, 1981
M.S. Astronautical Engineering, Naval Postgraduate School, 1991
Submitted in partial fulfillment
of the requirements for the degree of
ENGINEER OF AERONAUTICS AND ASTRONAUTICS
from the
NAVAL POSTGRADUATE SCHOOL
September 1992
ABSTRACT
The Flexible Spacecraft Simulator (FSS) at the Naval Postgraduate School
was modified by replacing the flexible appendage with a two link robotic
manipulator. This experimental setup was designed to simulate motion of a
spacecraft about the pitch axis. The spacecraft consists of a main body, a two
link manipulator, and momentum wheel actuator to control the pitch attitude of
the spacecraft. Position information from the main body and manipulators was
obtained from Rotary Variable Displacement Transducers (RVDT). The equations
of motion were developed assuming that the main body and manipulator were
rigid bodies. The resulting coupled, nonlinear, time invariant equations of motion
were used to analyze the dynamics and kinematics of the main body and
manipulator as well as the interaction between the main body and manipulator.
Three different control strategies were developed using Lyapunov's Second
or Direct Method. With the first controller, simple linear feedback of position and
velocity information with constant gains was used to position the manipulator
and stabilize the main body. A fifth order polynomial was used to generate a
reference trajectory for the second controller. This trajectory was used in
conjunction with a tracking controller to position and stabilize the system. In the
third controller, a near-minimum-time technique was used to generate a reference
trajectory. This reference trajectory was employed using a tracking controller
similar to that used in the polynomial reference controller.
111
u*
ACKNOWLEDGMENTS
Many people have contributed to the success of this project but the most
notable among these people was Mr. Rafford Bailey. Mr. Bailey was the
laboratory manager for the Spacecraft Robotics Simulator and was primarily
responsible for the design, manufacture, and assembly of the manipulator. Mr. Pat
Hickey and Mr. John Moulton of the Department Of Aeronautics were
instrumental in the manufacture of manipulator components in a timely and
expeditious manner. Air Force Captain Gary Yale and Dr. Hyochoong Bang
provided invaluable assistance with many of the theoretical and analytical
aspects for the design and analysis of the control system. Professor John L.
Junkins, the George J. Eppright Chair Professor at Texas A & M University and
visiting Co-Chair of the Space Systems Academic Group at the Naval
Postgraduate School presented a firm foundation for the non-linear control
theory and Lyapunov stability theory that formed the theoretical basis for the
control law design. Finally, to Professor Brij N. Agrawal, who provided the
funding, spacecraft attitude, dynamics and control expertise, and was responsible
for the overall coordination and success of this project.
IV
93943.5002
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TABLE OF CONTENTS
INTRODUCTION
I. 1
H. EXPERIMENTAL SETUP 4
A. SPACE ROBOTICS SIMULATOR DESCRIPTION 4
B. EXPERIMENT DESCRIPTION 4
1. Spacecraft Main Body 5
2. Two Link Manipulator 7
3. Granite Table 10
AC
4. - 100 10
VAX
5. 3100 Series Computer 11
SYSTEM INTEGRATION
C. 11
ANALYTICAL MODEL
HI. 14
A
COORDINATE SYSTEMS
14
EQUATIONS OFMOTION
B. 17
1. Lagrange's Equations OfMotion 17
2. Kinetic Energy 17
3. Equation OfMotion 18
4. Applied Torques 19
C. LYAPUNOV STABLE CONTROLLER DESIGN 20
1. Lyapunov Stable Controller With Linear Feedback 21
2. Lyapunov Stable Tracking Controller 24
D. REFERENCE TRAJECTORY GENERATION 25
Polynomial Reference Trajectory 25
1.
Minimum-Time-Maneuver 29
2.
3. Near-Minimum-Time Rigid Body Maneuver 30
E. ANALYTICAL MODEL SUMMARY 34
IV. RESULTS AND DISCUSSION 36
A. REFERENCE MANEUVER 36
B. LINEAR CONSTANT GAIN FEEDBACK CONTROLLER 37
POLYNOMIAL REFERENCE TRACKING CONTROLLER
C. 41
NEAR-MINIMUM-TIME REFERENCE TRACKING
D.
CONTROLLER 45
V. CONCLUSIONS 52
A. SUBJECTS FOR FUTURE RESEARCH 54
APPENDIX A 56
APPENDIX B 57
,
A. SYSTEM KINETIC ENERGY 57
1. Body 1 Kinetic Energy 57
2. Body 2 Kinetic Energy 57
3. Body 3 Kinetic Energy 57
4. Total Kinetic Energy 57
B. EQUATIONS OFMOTION 57
Mass Matrix 57
1.
2. Coriolis And Centrifugal Acceleration Terms: 58
C. POLYNOMIAL REFERENCE TRAJECTORY 59
1. Vector Polynomial Describing Tip Position: 59
2. Boundary Conditions And Polynomials 59
3. Vector Position 59
4. Vector Velocity 59
VI