University of Central Florida STARS
Electronic Theses and Dissertations, 2004-2019
2009
Control Of Nonh=holonomic Systems
Hongliang Yuan University of Central Florida
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STARS Citation Yuan, Hongliang, "Control Of Nonh=holonomic Systems" (2009). Electronic Theses and Dissertations, 2004-2019. 4017. https://stars.library.ucf.edu/etd/4017 Control of Nonholonomic Systems
by
Hongliang Yuan B.E. University of Science & Technology of China, 2002 M.S. University of Central Florida, 2007
A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy from the School of Electrical Engineering and Computer Science in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida
Summer Term 2009
Major Professor: Zhihua Qu c 2009 by Hongliang Yuan Abstract
Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic sys- tems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization prob- lem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic au- tonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles’ kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveil- lance and formation control of a group of nonholonomic robots is investigated. A designing
iii scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs.
iv To My Family.
v Acknowledgments
I am thankful to Dr. Zhihua Qu, my supervisor, for his supports on this research. I am also thankful to Dr. Jing Wang and Jian Yang for their suggestions and assistance. I also give thanks to all the graduate students in the robotics/control lab for helpful discussions.
I thank my family for their patience and love.
vi TABLE OF CONTENTS
LIST OF FIGURES ...... xii
LIST OF TABLES ...... xv
CHAPTER 1 INTRODUCTION TO NONHOLONOMIC SYSTEMS .. 1
1.1DefinitionOfNonholonomicSystems...... 1
1.2SomeExamplesOfNonholonomicSystems...... 3
1.2.1 TheUnicycleorUAVKinematicModel ...... 3
1.2.2 Car-likeRobots ...... 4
1.2.3 HoppingRobots ...... 6
1.2.4 TheOriginofNonholonomy...... 7
1.3CanonicalFormsOfNonholonomicSystems...... 8
CHAPTER 2 CONTROLLABILITY OF NONHOLONOMIC SYSTEMS 11
2.1 Nonlinear Controllability Analysis Based On Lie Bracket ...... 12
2.2InterpretationOfLieBracketsFromControlViewpoint...... 14
2.3 Controllability Of Chained Systems ...... 16
vii 2.4DifficultiesInNonholonomicControls...... 17
CHAPTER 3 REVIEW OF NONHOLONOMIC CONTROLS ...... 19
3.1OpenLoopControls...... 21
3.2DiscontinuousFeedbackControls...... 24
3.3Time-VaryingContinuousControls...... 26
CHAPTER 4 SMOOTH PURE FEEDBACK STABILIZATION OF CHAINED
NONHOLONOMIC SYSTEMS ...... 28
4.1ProblemFormulation ...... 28
4.2GlobalStateScalingTransformationAndControlDesignScheme...... 31
4.2.1 Design of Control Component u1 ...... 31
4.2.2 AGlobalStateTransformation...... 33
4.2.3 Design of Control Component u2 ...... 35
4.3OptimalPerformance ...... 39
4.4DesignExamples...... 42
4.5SimulationsAndComparisonsWithOtherExistingControls ...... 43
4.6Conclusion...... 47
CHAPTER 5 SATURATED CONTROL OF CHAINED NONHOLONOMIC
SYSTEMS ...... 51
viii 5.1ProblemFormulation...... 53
5.2TheSaturatedControlDesign ...... 54
5.2.1 The Control Design u1 and u2 ...... 57
5.2.2 Choice of k and d ...... 62
5.3Simulations...... 64
5.4Conclusion ...... 67
CHAPTER 6 OPTIMAL REAL-TIME COLLISION-FREE MOTION PLAN-
NING FOR NONHOLONOMIC AUVS IN A 3D UNDERWATER SPACE
...... 68
6.1ProblemFormulation...... 73
6.1.1 TheKinematicModel...... 73
6.1.2 TheTrajectoryPlanningProblem...... 74
6.2Real-TimeTrajectoryPlanningForAUVs...... 77
6.2.1 TrajectoryPlanningwithoutObstacles...... 78
6.2.2 TrajectoryPlanningwithObstacles ...... 81
6.2.3 OptimalSolutionofCandidateTrajectories...... 83
6.2.4 Solution and Solvability ...... 86
6.3SimulationResults...... 90
ix 6.3.1 SingleObstacle...... 90
6.3.2 MultipleObstacles...... 92
6.4TorqueLevelTrackingControlOf3Dtrajectories...... 95
6.4.1 TheKinematicTrackingController...... 96
6.4.2 TheDynamicTrackingControlDesign...... 100
6.4.3 SimulationResults...... 105
6.5Conclusion ...... 106
CHAPTER 7 COORDINATED EXPLORATION AND FORMATION CON-
TROL FOR MULTIPLE UNMANNED AERIAL VEHICLES (UAVS) ... 109
7.1ProblemFormulation...... 110
7.2MotionPlanning...... 112
7.2.1 ParametricFeasibleTrajectories ...... 112
7.2.2 MotionPlanningforAvoidingStatic/DynamicObstacles...... 115
7.3CooperativeFormationControls ...... 118
7.3.1 FormationControlofMultipleUAVs...... 119
7.3.2 AdaptiveCooperativeFormationControls...... 121
7.3.3 CircularTrajectoriesandArbitraryTrajectories...... 122
7.3.4 Internal and External Collision Avoidance ...... 124
x 7.4Simulations...... 125
7.4.1 SimulationSettings...... 127
7.4.2 SimulationResults...... 128
7.5Conclusion...... 131
CHAPTER 8 CONCLUSION AND FUTURE WORK ...... 133
LIST OF REFERENCES ...... 138
xi LIST OF FIGURES
1.1TheUnicycleModel...... 3
1.2TheCar-likeRobotModel...... 5
1.3TheHoppingRobotModel...... 6
2.1LieBracketMotionEffects...... 14
4.1 Simulation Results of The Proposed Controls. (a),(c) State and Control with