Time-Optimal Control of the Bi-Steerable Robot: A Case Study in Optimal Control of Nonholonomic Systems
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
2012
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| Schlagwörter: | |
| Links: | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-75036 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025699989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 171 S. Ill., graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Time-Optimal Control of the Bi-Steerable Robot |b A Case Study in Optimal Control of Nonholonomic Systems |c von Markus Mauder |
| 246 | 1 | 3 | |a Zeitoptimale Steuerung des zweiachsgelenkten Roboters: Eine Fallstudie zur optimalen Steuerung nichtholonomer Systeme |
| 264 | 1 | |c 2012 | |
| 300 | |a XI, 171 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 502 | |a Würzburg, Univ., Diss., 2012 | ||
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| 650 | 0 | 7 | |a Zeitoptimale Regelung |0 (DE-588)4190614-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mobiler Roboter |0 (DE-588)4191911-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mobiler Roboter |0 (DE-588)4191911-7 |D s |
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 1908844 |
|---|---|
| _version_ | 1821935095093657600 |
| adam_text | IMAGE 1
CONTENTS
VORWORT I
ABSTRACT III
LIST O F FIGURES IX
LIST O F TABLES XI
1 INTRODUCTION 1
1.1 HISTORICAL PERSPECTIVE 2
1.2 PROBLEM FORMULATION AND MOTIVATION 5
1.3 MAIN RESULTS 8
1.4 OUTLINE OF WORK 9
1 PRELIMINARIES 1 1
2 TIME-OPTIMAL CONTROL 13
2.1 CONTROL SYSTEM 13
2.2 TIME-OPTIMAL CONTROL PROBLEMS 14
2.3 METHODS FOR TIME-OPTIMAL CONTROL 18
3 NONHOLONOMIC SYSTEMS 19
3.1 BASICS OF NONLINEAR CONTROL SYSTEMS 20
3.1.1 FUNDAMENTAL PROPERTIES OF NONLINEAR CONTROL SYSTEMS 20
3.1.2 CONTROL SYSTEMS ON LIE GROUPS 21
3.1.3 INTEGRABILITY OF DISTRIBUTIONS 22
3.1.4 CONTROLLABILITY 25
3.2 HOLONOMIC AND NONHOLONOMIC CONSTRAINTS 26
3.2.1 HOLONOMIC CONSTRAINTS 26
3.2.2 NONHOLONOMIC CONSTRAINTS 26
3.3 NONHOLONOMIC SYSTEMS 28
3.3.1 NONHOLONOMIC KINEMATIC SYSTEMS 29
3.3.2 NORMAL FORMS OF NONHOLONOMIC KINEMATIC SYSTEMS 30
3.4 EXAMPLES 31
3.4.1 UNICYCLE 31
3.4.2 CAR-LIKE ROBOT 33
3.4.3 SNAKEBOARD 35
3.5 OPEN-LOOP CONTROL OF NONHOLONOMIC SYSTEMS 37
4 OPTIMALITY CONDITIONS FOR TIME-OPTIMAL CONTROL PROBLEMS 39
4.1 EXISTENCE OF TIME-OPTIMAL SOLUTIONS 39
4.2 THE MAXIMUM PRINCIPLE FOR TIME-OPTIMAL CONTROL PROBLEMS 40
4.2.1 HAMILTONIAN FUNCTION 40
4.2.2 NECESSARY OPTIMALITY CONDITIONS 41
4.2.3 DISCUSSION OF THE MAXIMUM PRINCIPLE 42
4.3 EXTREMALS 43
V
HTTP://D-NB.INFO/1033551864
IMAGE 2
VI CONTENTS
4.4 BOUNDARY VALUE PROBLEMS 45
4.5 OVERVIEW OF FURTHER NECESSARY OPTIMALITY CONDITIONS 46
4.5.1 LEGENDRE-CLEBSCH CONDITIONS 46
4.5.2 BOUNDS ON THE NUMBER OF SWITCHINGS 47
4.5.3 THEORY OF ENVELOPES 48
4.6 OVERVIEW OF SUFFICIENT OPTIMALITY CONDITIONS 48
4.6.1 ARROW AND MANGASARIAN SUFFICIENT CONDITIONS 48
4.6.2 LOCAL SECOND-ORDER SUFFICIENT CONDITIONS WITH RICCATI EQUATION 49
4.6.3 LOCAL SECOND-ORDER SUFFICIENT CONDITIONS FOR BANG-BANG EXTREMALS
50 4.6.4 BOLTYANSKII S SUFFICIENT CONDITION 50
4.7 EXAMPLE: TIME-OPTIMAL CONTROL OF THE UNICYCLE 51
II MODELING AND EXTREMALS 5 3
5 THE BI-STEERABLE ROBOT 55
5.1 LITERATURE REVIEW 58
5.2 MODELING 60
5.2.1 BICYCLE MODEL AND CONFIGURATION SPACE 60
5.2.2 KINEMATICS OF THE BICYCLE MODEL 62
5.2.3 VELOCITY CONSTRAINT AND CONSTRAINT DISTRIBUTION 64
5.3 MODEL ANALYSIS 65
5.3.1 CONTROLLABILITY 65
5.3.2 INTEGRABILITY OF THE CONSTRAINT DISTRIBUTION 67
5.3.3 SYSTEM PROPERTIES OF THE REDUCED KINEMATIC MODEL 68
5.4 DISCUSSION OF THE MODELS OF THE BI-STEERABLE ROBOT 73
6 EXTREMALS FOR TIME-OPTIMAL CONTROL O F THE BI-STEERABLE ROBOT 75
6.1 NECESSARY OPTIMALITY CONDITIONS 75
6.1.1 APPLICATION OF THE MAXIMUM PRINCIPLE . 75
6.1.2 MAXIMIZATION OF THE HAMILTONIAN FUNCTION 77
6.2 EXISTENCE OF TIME-OPTIMAL SOLUTIONS 80
6.3 CLASSIFICATION OF THE EXTREMALS 82
6.4 ANALYSIS OF NORMAL REGULAR EXTREMALS 85
6.4.1 PROPERTIES 86
6.4.2 SIMULATION RESULTS 88
6.4.3 DISCUSSION 89
6.5 ANALYSIS OF NORMAL SINGULAR EXTREMALS 90
6.6 DISCUSSION OF THE EXTREMALS 91
III PATH PLANNING AND OPTIMALITY 9 3
7 APPROACH FOR TIME-OPTIMAL CONTROL 95
7.1 SIMPLIFICATION OF THE PATH PLANNING PROBLEM 96
7.2 PATH PLANNING USING NORMAL REGULAR EXTREMALS 98
7.2.1 PATH PLANNING AS OPTIMIZATION PROBLEM 98
7.2.2 SOLUTION T O THE OPTIMIZATION PROBLEM 102
7.2.3 ALGORITHM FOR PATH PLANNING 105
7.2.4 DISCUSSION OF THE PATH PLANNING 107
7.3 TIME-OPTIMAL CONTROL BY ITERATED PATH PLANNING 108
7.3.1 ITERATED PATH PLANNING OVER A DECREASING TIME HORIZON 108
7.3.2 ALGORITHM FOR TIME-OPTIMAL CONTROL I L L
7.3.3 DISCUSSION OF THE TIME-OPTIMAL CONTROL 112
IMAGE 3
CONTENTS VII
7.4 MODIFICATIONS FOR PRACTICAL APPLICATION 113
8 TIME-OPTIMAL CONTROL O F THE BI-STEERABLE ROBOT 115
8.1 SIMPLIFICATION OF THE PATH PLANNING PROBLEM 116
8.2 IMPLEMENTATION OF THE APPROACH FOR TIME-OPTIMAL CONTROL 118
8.2.1 PARAMETERIZATION OF THE SEARCH SPACE 118
8.2.2 DISCRETIZATION INTERVAL 120
8.2.3 FINAL TIME OF THE INITIAL TIME HORIZON 121
8.3 ANALYSIS OF THE CONVERGENCE 122
8.4 SIMULATION RESULTS 125
8.4.1 SETUP OF THE SIMULATION 125
8.4.2 PROBABILITY OF CONVERGENCE OF THE LOCAL OPTIMIZATION 125
8.4.3 SIMULATION RESULTS OF THE TIME-OPTIMAL CONTROL 127
8.5 OPTIMAL SOLUTIONS OF THE BI-STEERABLE ROBOT AND THE CAR-LIKE ROBOT
129
8.6 DISCUSSION OF THE TIME-OPTIMAL CONTROL 130
9 OPTIMALITY O F NORMAL REGULAR EXTREMALS O F THE BI-STEERABLE ROBOT 135
9.1 APPLICATION OF NECESSARY OPTIMALITY CONDITIONS 135
9.2 TRANSFORMED TIME-OPTIMAL CONTROL PROBLEM WITH FIXED END TIME 137
9.3 APPLICATION OF SUFFICIENT OPTIMALITY CONDITIONS 139
9.3.1 LOCAL SECOND-ORDER SUFFICIENT CONDITIONS WITH RICCATI EQUATION 140
9.4 SIMULATION RESULTS ON TIME-OPTIMAL NORMAL REGULAR EXTREMALS 143
9.5 TIME-OPTIMALITY AND NUMBER OF CUSPS OF NORMAL REGULAR EXTREMALS 145
9.5.1 NUMBER OF CUSPS AND END TIME 146
9.5.2 NECESSARY OPTIMALITY CONDITION ON THE NUMBER OF CUSPS 148
9.5.3 SIMULATION RESULTS AND CONDITION FOR NEAR TIME-OPTIMALITY 148
9.6 COMPARISON OF TIME-OPTIMAL NORMAL REGULAR AND NORMAL SINGULAR
EXTREMALS . . . 150 9.7 DISCUSSION OF THE OPTIMALITY RESULTS 153
10 CONCLUSION 155
10.1 SUMMARY 155
10.2 FUTURE WORK 156
A LISTINGS 157
A.L ALGORITHM FOR PATH PLANNING 157
A.2 ALGORITHM FOR TIME-OPTIMAL CONTROL 159
BIBLIOGRAPHY 161
INDEX 169
|
| any_adam_object | 1 |
| author | Mauder, Markus |
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| ctrlnum | (OCoLC)828791120 (DE-599)BVBBV040719737 |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| indexdate | 2024-12-20T16:24:09Z |
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| language | English |
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| physical | XI, 171 S. Ill., graph. Darst. |
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| spellingShingle | Mauder, Markus Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems Optimale Kontrolle (DE-588)4121428-6 gnd Zeitoptimale Regelung (DE-588)4190614-7 gnd Mobiler Roboter (DE-588)4191911-7 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4190614-7 (DE-588)4191911-7 (DE-588)4113937-9 |
| title | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems |
| title_alt | Zeitoptimale Steuerung des zweiachsgelenkten Roboters: Eine Fallstudie zur optimalen Steuerung nichtholonomer Systeme |
| title_auth | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems |
| title_exact_search | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems |
| title_full | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems von Markus Mauder |
| title_fullStr | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems von Markus Mauder |
| title_full_unstemmed | Time-Optimal Control of the Bi-Steerable Robot A Case Study in Optimal Control of Nonholonomic Systems von Markus Mauder |
| title_short | Time-Optimal Control of the Bi-Steerable Robot |
| title_sort | time optimal control of the bi steerable robot a case study in optimal control of nonholonomic systems |
| title_sub | A Case Study in Optimal Control of Nonholonomic Systems |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Zeitoptimale Regelung (DE-588)4190614-7 gnd Mobiler Roboter (DE-588)4191911-7 gnd |
| topic_facet | Optimale Kontrolle Zeitoptimale Regelung Mobiler Roboter Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-75036 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025699989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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