The Experts below are selected from a list of 1977 Experts worldwide ranked by ideXlab platform
Andrew R. Teel - One of the best experts on this subject based on the ideXlab platform.
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On Path-Lifting Mechanisms and Unwinding in Quaternion-Based Attitude Control
IEEE Transactions on Automatic Control, 2013Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Because the space of Unit Quaternions constitutes a double cover of the rigid-body-attitude space, Quaternion-based control laws are often—by design—inconsistent, i.e., they do not have a unique value for each rigid-body attitude. Inconsistent Quaternion-based control laws require an additional mechanism that uniquely converts an attitude estimate into its Quaternion representation; however, conversion mechanisms that are memoryless—e.g., selecting the Quaternion having positive scalar component—have a limited domain where they remain injective and, when used globally, introduce discontinuities into the closed-loop system. We show—through an explicit construction and Lyapunov analysis—that such discontinuities can be hijacked by arbitrarily small measurement disturbances to stabilize attitudes far from the desired attitude. To remedy this limitation, we propose a hybrid-dynamic algorithm for smoothly lifting an attitude path to the Unit-Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets. Finally, we employ the main results to show that certain hybrid feedbacks can globally asymptotically stabilize the attitude of a rigid body.
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ACC - On Quaternion-based attitude control and the unwinding phenomenon
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, Quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the Unit Quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the Unit Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.
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On Quaternion-based attitude control and the unwinding phenomenon
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, Quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the Unit Quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the Unit Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.
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On the non-robustness of inconsistent Quaternion-based attitude control systems using memoryless path-lifting schemes
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Quaternion-based feedback control laws that are inconsistent (i.e. do not have a unique value for a given attitude) require an additional mechanism that lifts a continuous attitude trajectory to the Unit Quaternion space. Lifting mechanisms that are memoryless, for example, selecting the Quaternion having positive scalar component, have a limited domain where they remain injective and, when used globally, introduce discontinuities into the closed-loop system. We show that such discontinuities can be exploited by an arbitrarily small measurement disturbance to stabilize attitudes far from the desired attitude and destroy "global" attractivity properties.
Hui Zhou - One of the best experts on this subject based on the ideXlab platform.
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Orientationability analyses of a special class of the Stewart–Gough parallel manipulators using the Unit Quaternion representation
Advanced Robotics, 2013Co-Authors: Clement Gosselin, Hui ZhouAbstract:This paper addresses the orientation-singularity and orientationability analyses of a special class of the Stewart–Gough parallel manipulators whose moving and base platforms are two similar semi-symmetrical hexagons. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical expression representing the singularity locus of this class of parallel manipulators in a six-dimensional Cartesian space is obtained. It shows that for a given orientation, the position-singularity locus is a cubic polynomial expression in the moving platform position parameters, and for a given position, the orientation-singularity locus is an analytical expression but not a polynomial directly with respect to the mobile platform orientation parameters. Further inspection shows that for the special class of parallel manipulators, there must exist a nonsingular orientation void in the orientation space around the orientation origin for each position in the position-workspace. Therefore, a new perf...
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orientationability analyses of a special class of the stewart gough parallel manipulators using the Unit Quaternion representation
Advanced Robotics, 2013Co-Authors: Clement Gosselin, Hui ZhouAbstract:This paper addresses the orientation-singularity and orientationability analyses of a special class of the Stewart–Gough parallel manipulators whose moving and base platforms are two similar semi-symmetrical hexagons. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical expression representing the singularity locus of this class of parallel manipulators in a six-dimensional Cartesian space is obtained. It shows that for a given orientation, the position-singularity locus is a cubic polynomial expression in the moving platform position parameters, and for a given position, the orientation-singularity locus is an analytical expression but not a polynomial directly with respect to the mobile platform orientation parameters. Further inspection shows that for the special class of parallel manipulators, there must exist a nonsingular orientation void in the orientation space around the orientation origin for each position in the position-workspace. Therefore, a new perf...
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Orientation-singularity and nonsingular orientation-workspace analyses of the Stewart-Gough Platform using Unit Quaternion representation
2010 Chinese Control and Decision Conference, 2010Co-Authors: Weixi Ji, Zhuo Li, Hui ZhouAbstract:This paper mainly addresses the orientation-singularity analysis and the nonsingular orientation-workspace computation of the Stewart-Gough Platform. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical symbolic expression that represents the orientation-singularity locus of the manipulator at a fixed position is derived. It is shown that for the Stewart-Gough Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace. Using the orientation representation and applying the inverse kinematics solution of the Stewart-Gough Platform, a discretization method is proposed for the computation of the nonsingular orientation-workspace of the Stewart-Gough Platform. Based on the research on the orientation-singularity and nonsingular orientation-workspace of the manipulator, a new concept of “practical orientation-capability” is introduced as a performance index for the orientation-capability analysis of the Stewart-Gough Platform at a certain position in the position-workspace. Examples of a 6/6-SPS Stewart-Gough Platform are given to demonstrate these theoretical results.
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Orientation-singularity and orientation capability analysis of Stewart Platform based on Unit Quaternion representation
2010 IEEE International Conference on Mechatronics and Automation, 2010Co-Authors: Hui Zhou, Weixi JiAbstract:This paper mainly addresses the orientation-singularity and orientation capability analyses of the Stewart Platform. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical symbolic expression which represents the orientation-singularity locus of the mechanism at a given position, is derived. It is shown that for the Stewart Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace, and then a new performance index which describes the orientation capability of the mechanism at a given position is presented. Furthermore, effects of the geometric parameters and the position of the moving platform on the orientation capability of the mechanism are also presented in detail in this paper.
Abdelhamid Tayebi - One of the best experts on this subject based on the ideXlab platform.
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Unit Quaternion-Based Output Feedback for the Attitude Tracking Problem
IEEE Transactions on Automatic Control, 2008Co-Authors: Abdelhamid TayebiAbstract:In this note, we propose a Quaternion-based dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a Unit Quaternion) is used in the control law together with the Unit Quaternion representing the attitude tracking error. Roughly speaking, the necessary damping that would have been achieved by the direct use of the angular velocity can be achieved, in our approach, by the vector part \mathtilde q of the error signal between the output of the auxiliary system and the Unit Quaternion tracking error. The resulting velocity-free control scheme guarantees almost global asymptotic stability which is as strong as the topology of the motion space can permit. In the regulation case, our control law is a pure Quaternion feedback (i.e., consisting of two terms that are vector parts of Unit-Quaternion), and hence, the control torques are naturally bounded by the control gains. Simulation results are provided to show the effectiveness of the proposed control scheme.
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CDC - A velocity-free attitude tracking controller for rigid spacecraft
2007 46th IEEE Conference on Decision and Control, 2007Co-Authors: Abdelhamid TayebiAbstract:In this paper, we propose a Quaternion-based dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a Unit Quaternion) is used in the control law together with the Unit Quaternion representing the attitude tracking error. Roughly speaking, the necessary damping that would have been achieved by the direct use of the angular velocity can be achieved, in our approach, by the vector part q of the error signal between the output of the auxiliary system and the Unit Quaternion tracking error. The resulting velocity-free control scheme guarantees almost global 1 asymptotic stability which is as strong as the topology of the motion space can permit. Simulation results are provided to show the effectiveness of the proposed control scheme.
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A velocity-free attitude tracking controller for rigid spacecraft
2007 46th IEEE Conference on Decision and Control, 2007Co-Authors: Abdelhamid TayebiAbstract:In this paper, we propose a Quaternion-based dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a Unit Quaternion) is used in the control law together with the Unit Quaternion representing the attitude tracking error. Roughly speaking, the necessary damping that would have been achieved by the direct use of the angular velocity can be achieved, in our approach, by the vector part q of the error signal between the output of the auxiliary system and the Unit Quaternion tracking error. The resulting velocity-free control scheme guarantees almost global 1 asymptotic stability which is as strong as the topology of the motion space can permit. Simulation results are provided to show the effectiveness of the proposed control scheme.
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Unit Quaternion observer based attitude stabilization of a rigid spacecraft without velocity measurement
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Abdelhamid TayebiAbstract:In this paper, we propose an alternative solution to the attitude stabilization problem without velocity measurement. Our approach consists of using a Unit Quaternion observer and a linear feedback control law in terms of the vector parts of the actual Unit Quaternion and the estimation-error Quaternion. The closed loop system leads to a passive mapping between the observer input and the vector part of the estimation-error Quaternion, which in turns allows to choose the observer input as a simple feedback in terms of the vector part of the estimation-error Quaternion. The resulting control scheme, without velocity measurement and without the use of a lead filter, guarantees global asymptotic stability. Simulation results are provided to show the effectiveness of the proposed controller
Christopher G. Mayhew - One of the best experts on this subject based on the ideXlab platform.
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On Path-Lifting Mechanisms and Unwinding in Quaternion-Based Attitude Control
IEEE Transactions on Automatic Control, 2013Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Because the space of Unit Quaternions constitutes a double cover of the rigid-body-attitude space, Quaternion-based control laws are often—by design—inconsistent, i.e., they do not have a unique value for each rigid-body attitude. Inconsistent Quaternion-based control laws require an additional mechanism that uniquely converts an attitude estimate into its Quaternion representation; however, conversion mechanisms that are memoryless—e.g., selecting the Quaternion having positive scalar component—have a limited domain where they remain injective and, when used globally, introduce discontinuities into the closed-loop system. We show—through an explicit construction and Lyapunov analysis—that such discontinuities can be hijacked by arbitrarily small measurement disturbances to stabilize attitudes far from the desired attitude. To remedy this limitation, we propose a hybrid-dynamic algorithm for smoothly lifting an attitude path to the Unit-Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets. Finally, we employ the main results to show that certain hybrid feedbacks can globally asymptotically stabilize the attitude of a rigid body.
-
ACC - On Quaternion-based attitude control and the unwinding phenomenon
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, Quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the Unit Quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the Unit Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.
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On Quaternion-based attitude control and the unwinding phenomenon
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Often, Quaternion-based feedbacks require an additional mechanism that lifts a continuous attitude path to the Unit Quaternion space. When this mechanism is memoryless, it has a limited domain where it remains injective and leads to discontinuities when used globally. To remedy this limitation, we propose a hybrid-dynamic algorithm for lifting a continuous attitude path to the Unit Quaternion space. We show that this hybrid-dynamic mechanism allows us to directly translate Quaternion-based controllers and their asymptotic stability properties (obtained in the Unit-Quaternion space) to the actual rigid-body-attitude space. We also show that when Quaternion-based controllers are not designed to account for the double covering of the rigid-body-attitude space by a Unit-Quaternion parameterization, they can give rise to the unwinding phenomenon, which we characterize in terms of the projection of asymptotically stable sets.
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On the non-robustness of inconsistent Quaternion-based attitude control systems using memoryless path-lifting schemes
Proceedings of the 2011 American Control Conference, 2011Co-Authors: Christopher G. Mayhew, Ricardo G. Sanfelice, Andrew R. TeelAbstract:The Unit Quaternion is a pervasive representation of rigid-body attitude used for the design and analysis of feedback control laws. Quaternion-based feedback control laws that are inconsistent (i.e. do not have a unique value for a given attitude) require an additional mechanism that lifts a continuous attitude trajectory to the Unit Quaternion space. Lifting mechanisms that are memoryless, for example, selecting the Quaternion having positive scalar component, have a limited domain where they remain injective and, when used globally, introduce discontinuities into the closed-loop system. We show that such discontinuities can be exploited by an arbitrarily small measurement disturbance to stabilize attitudes far from the desired attitude and destroy "global" attractivity properties.
Weixi Ji - One of the best experts on this subject based on the ideXlab platform.
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Orientation-singularity and nonsingular orientation-workspace analyses of the Stewart-Gough Platform using Unit Quaternion representation
2010 Chinese Control and Decision Conference, 2010Co-Authors: Weixi Ji, Zhuo Li, Hui ZhouAbstract:This paper mainly addresses the orientation-singularity analysis and the nonsingular orientation-workspace computation of the Stewart-Gough Platform. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical symbolic expression that represents the orientation-singularity locus of the manipulator at a fixed position is derived. It is shown that for the Stewart-Gough Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace. Using the orientation representation and applying the inverse kinematics solution of the Stewart-Gough Platform, a discretization method is proposed for the computation of the nonsingular orientation-workspace of the Stewart-Gough Platform. Based on the research on the orientation-singularity and nonsingular orientation-workspace of the manipulator, a new concept of “practical orientation-capability” is introduced as a performance index for the orientation-capability analysis of the Stewart-Gough Platform at a certain position in the position-workspace. Examples of a 6/6-SPS Stewart-Gough Platform are given to demonstrate these theoretical results.
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Orientation-singularity and orientation capability analysis of Stewart Platform based on Unit Quaternion representation
2010 IEEE International Conference on Mechatronics and Automation, 2010Co-Authors: Hui Zhou, Weixi JiAbstract:This paper mainly addresses the orientation-singularity and orientation capability analyses of the Stewart Platform. Employing a Unit Quaternion to represent the orientation of the moving platform, an analytical symbolic expression which represents the orientation-singularity locus of the mechanism at a given position, is derived. It is shown that for the Stewart Platform, it must exist a singularity free orientation void in the orientation space around the orientation origin for each position in the position-workspace, and then a new performance index which describes the orientation capability of the mechanism at a given position is presented. Furthermore, effects of the geometric parameters and the position of the moving platform on the orientation capability of the mechanism are also presented in detail in this paper.
