A near-optimal control approach to 3D ball-in-socket joint space robot models with initial angular momenta |
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| Authors: | Tatsuya Kai Kazuho Tamaki |
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| Institution: | 1. Kyushu University, Japan;2. Nippon Steel Corporation, Japan;1. Department of Spine Center, Aichi Medical University Hospital, Karimata Yazako, Nagakute, Aichi 480-1195, Japan;2. Department of Neurological Surgery, Aichi Medical University Hospital, Karimata Yazako, Nagakute, Aichi 480-1195, Japan;1. Max Planck Institute for Informatics, Saarbrücken, Germany;2. CISUC, Department of Informatics Engineering, University of Coimbra, Portugal;3. Department of Mathematics and Natural Sciences, University of Wuppertal, Germany;1. Bloorview Research Institute, Holland Bloorview Kids Rehabilitation Hospital, 150 Kilgour Rd, Toronto, M4K 1E1, Canada;2. Rehabilitation Sciences Institute, University of Toronto, 500 University Ave, Toronto, M5G 1V7, Canada;3. Diagnostic Imaging, Hospital for Sick Children, 555 University Avenue, Toronto, M5G 1X8, Canada;4. Department of Medical Imaging, University of Toronto, 263 McCaul Street, Toronto, M5T 1W7, Canada;5. Department of Psychology, University of Toronto, 100 St. George Street, Toronto, M5S 3G3, Canada;6. Department of Developmental Paediatrics, University of Toronto, 1 King’s College Circle, Toronto, M5S 1A8, Canada;7. Hurvitz Brain Sciences Program, Canadian Partnership for Stroke Recovery, Sunnybrook Research Institute, 2075 Bayview Ave, Toronto, M4N 3M5, Canada;8. Department of Physical Therapy, University of Toronto, 500 University Ave, Toronto, M5G 1V7, Canada |
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| Abstract: | Control of space robots in the 3D space is known as one of the difficult problems in nonlinear control theory, and if there exist initial angular momenta for space robots, the control problem becomes an increasing challenge. However, it is quite important to take into account the existence of initial angular momenta from the aspect of realistic situations. This paper deals with a control problem for a 3D space robot of two rigid bodies with an initial angular momentum. First, we give a model of a space robot with an initial angular momentum, called the ball-in-socket joint model. We next propose a near-optimal control method for general nonlinear affine control systems based on the finite dimensional orthonormal basis and give some theoretical analysis for the method. Moreover, a near-optimal control algorithm is also shown. Then, we apply the near-optimal control algorithm to a 3D attitude control problem of the ball-in-socket joint model with an initial angular momentum, and illustrate numerical simulations in order to show the effectiveness of our method. |
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