This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorit...This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorithm for a measured point with additional rotational rigid body motion constraints is proposed.The motion constraints of the rotational rigid body were analyzed,and a mathematical model of the measured point algorithm in the swiveling axes was established.The Levenberg-Marquard method was used to solve the nonlinear superstatically determined equations.The spatial coordinate error was used to separate the spatial deviation of the measured point.An identification model of the position-independent and position-dependent geometric errors was established.The three-dimensional coordinate-solving algorithm of the measured point in the swiveling axis and geometric error identification method based on the Monte Carlo method were analyzed numerically.Geometric error measurement and cutting experiments were performed on a VMC25100U five-axis machining center,which integrated two swiveling axes.Geometric errors of the A-and B-axes were identified and measured experimentally.The angular positioning errors before and after compensation were measured using a laser interferometer,which verified the effectiveness of the proposed algorithm.A cutting experiment of a round table part was performed.The shape and position accuracy of the processed part before and after compensation were detected using a coordinate measuring machine.It verified that the geometric error of the swiveling axis was effectively compensated by the algorithm proposed herein.展开更多
This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory....This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory.The unmodeled dynamics of the system are considered,and an adaptive neural network controller is designed using the backstepping method and radial basis function neural network.The stability of the closed-loop system and the boundedness of the tracking error are verified using Lyapunov theory.The simulation results show that our approach is a good solution to the motion constraint problem of the line-driven soft robotic arm.展开更多
Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of...Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.展开更多
In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of th...In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.展开更多
The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Ni...The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degr...Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.展开更多
The aim of this paper is to present a finite element modeling of the dynamic motion of a turbine rotor and its controller design with the mass unbalance under a crack on a rotating shaft. This process is an advanced m...The aim of this paper is to present a finite element modeling of the dynamic motion of a turbine rotor and its controller design with the mass unbalance under a crack on a rotating shaft. This process is an advanced method to the mathematical description of a system including an influence of a mass unbalance and a crack on the rotor shaft. As the first step, the shaft is physically modeled with a finite element method and the dynamic mathematical model is derived by using the Hamilton principle;thus, the system is represented by various subsystems. The equation of motion of a shaft with a mass unbalance and a crack is established by adapting the local mass unbalance and stiffness change through breathing and gaping from the existence of a crack. This is a reference system for the given system. Based on a fictitious model for transient behavior induced from vibration phenomena measured at the bearings, an elementary estimator is designed for the safety control and detection of a mass unbalance on the shaft. Using the state estimator, a bank of an estimator is established to get the diagnosis and the system data for a controller.展开更多
This paper presents a novel hybrid task priority-based motion planning algorithm of a space robot. The satellite attitude control task is defined as the primary task, while the leastsquares-based non-strict task prior...This paper presents a novel hybrid task priority-based motion planning algorithm of a space robot. The satellite attitude control task is defined as the primary task, while the leastsquares-based non-strict task priority solution of the end-effector plus the multi-constraint task is viewed as the secondary task. Furthermore, a null-space task compensation strategy in the joint space is proposed to derive the combination of non-strict and strict task-priority motion planning,and this novel combination is termed hybrid task priority control. Thus, the secondary task is implemented in the primary task＇s null-space. Besides, the transition of the state of multiple constraints between activeness and inactiveness will only influence the end-effector task without any effect on the primary task. A set of numerical experiments made in a real-time simulation system under Linux/RTAI shows the validity and feasibility of the proposed methodology.展开更多
Constrained modeling and state estimation have attracted much attention in recent years. This paper focuses on target motion modeling and tracking in road coordinates. An improved initialization method,which uses the ...Constrained modeling and state estimation have attracted much attention in recent years. This paper focuses on target motion modeling and tracking in road coordinates. An improved initialization method,which uses the optimal fusion of the position measurements in different directions,is presented for the constraint coordinate Kalman filter(CCKF). The CCKF is evaluated with a comprehensive comparison to the state-of-art linear equality constraint estimation methods. Numerical simulation results demonstrate the better performance of the CCKF. Then the interacting multiple model CCKF(IMM-CCKF) is proposed to manifest the advantages of the CCKF in complex motion modeling and state estimations. The effectiveness of the IMM-CCKF in maneuvering target tracking with spatial equality constraints is demonstrated by numerical experiments.展开更多
The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of ap...The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.展开更多
The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the tot...The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.展开更多
An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors...An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.展开更多
With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical s...With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed展开更多
基金Supported by Shanxi Provincial Natural Science Foundation(Grant No.2021JM010)The Youth Innovation Team of Shaanxi Universities.
文摘This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorithm for a measured point with additional rotational rigid body motion constraints is proposed.The motion constraints of the rotational rigid body were analyzed,and a mathematical model of the measured point algorithm in the swiveling axes was established.The Levenberg-Marquard method was used to solve the nonlinear superstatically determined equations.The spatial coordinate error was used to separate the spatial deviation of the measured point.An identification model of the position-independent and position-dependent geometric errors was established.The three-dimensional coordinate-solving algorithm of the measured point in the swiveling axis and geometric error identification method based on the Monte Carlo method were analyzed numerically.Geometric error measurement and cutting experiments were performed on a VMC25100U five-axis machining center,which integrated two swiveling axes.Geometric errors of the A-and B-axes were identified and measured experimentally.The angular positioning errors before and after compensation were measured using a laser interferometer,which verified the effectiveness of the proposed algorithm.A cutting experiment of a round table part was performed.The shape and position accuracy of the processed part before and after compensation were detected using a coordinate measuring machine.It verified that the geometric error of the swiveling axis was effectively compensated by the algorithm proposed herein.
基金supported by the National Natural Science Foundation of China(62103039,62073030)the Scientific and Technological Innovation Foundation of Shunde Graduate School+8 种基金University of Science and Technology Beijing(USTB)(BK21BF003)the Korea Institute of Energy Technology Evaluation and Planning through the Auspices of the Ministry of TradeIndustry and EnergyRepublic of Korea(20213030020160)the Science and Technology Planning Project of Guangzhou City(202102010398,202201010758)the Guangzhou University-Hong Kong University of Science and Technology Joint Research Collaboration Fund(YH202205)Beijing Top Discipline for Artificial Intelligent Science and EngineeringUniversity of Science and Technology Beijing。
文摘This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory.The unmodeled dynamics of the system are considered,and an adaptive neural network controller is designed using the backstepping method and radial basis function neural network.The stability of the closed-loop system and the boundedness of the tracking error are verified using Lyapunov theory.The simulation results show that our approach is a good solution to the motion constraint problem of the line-driven soft robotic arm.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014)the Scientific Research and Innovation Plan for College Graduates of Jiangsu Province,China (Grant No. CXLX12_0720)
文摘Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
文摘In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.
文摘The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.
基金supported by China Scholarship Council (201504980073) for Zeguo Wang to visit Umea University
文摘Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.
文摘The aim of this paper is to present a finite element modeling of the dynamic motion of a turbine rotor and its controller design with the mass unbalance under a crack on a rotating shaft. This process is an advanced method to the mathematical description of a system including an influence of a mass unbalance and a crack on the rotor shaft. As the first step, the shaft is physically modeled with a finite element method and the dynamic mathematical model is derived by using the Hamilton principle;thus, the system is represented by various subsystems. The equation of motion of a shaft with a mass unbalance and a crack is established by adapting the local mass unbalance and stiffness change through breathing and gaping from the existence of a crack. This is a reference system for the given system. Based on a fictitious model for transient behavior induced from vibration phenomena measured at the bearings, an elementary estimator is designed for the safety control and detection of a mass unbalance on the shaft. Using the state estimator, a bank of an estimator is established to get the diagnosis and the system data for a controller.
基金supported in part by the National Program on Key Basic Research Project (No. 2013CB733103)the Program for New Century Excellent Talents in University (No. NCET-10-0058)
文摘This paper presents a novel hybrid task priority-based motion planning algorithm of a space robot. The satellite attitude control task is defined as the primary task, while the leastsquares-based non-strict task priority solution of the end-effector plus the multi-constraint task is viewed as the secondary task. Furthermore, a null-space task compensation strategy in the joint space is proposed to derive the combination of non-strict and strict task-priority motion planning,and this novel combination is termed hybrid task priority control. Thus, the secondary task is implemented in the primary task＇s null-space. Besides, the transition of the state of multiple constraints between activeness and inactiveness will only influence the end-effector task without any effect on the primary task. A set of numerical experiments made in a real-time simulation system under Linux/RTAI shows the validity and feasibility of the proposed methodology.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61201311)
文摘Constrained modeling and state estimation have attracted much attention in recent years. This paper focuses on target motion modeling and tracking in road coordinates. An improved initialization method,which uses the optimal fusion of the position measurements in different directions,is presented for the constraint coordinate Kalman filter(CCKF). The CCKF is evaluated with a comprehensive comparison to the state-of-art linear equality constraint estimation methods. Numerical simulation results demonstrate the better performance of the CCKF. Then the interacting multiple model CCKF(IMM-CCKF) is proposed to manifest the advantages of the CCKF in complex motion modeling and state estimations. The effectiveness of the IMM-CCKF in maneuvering target tracking with spatial equality constraints is demonstrated by numerical experiments.
基金Supported by National Natural Science Foundation of China(Grant No.51005195)Natural Science Research Fund for Youth in Higher Education Institutions of Hebei Province,China(Grant No.QN2014175)
文摘The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.
基金Project supported by the National Natural Science Foundation of China (No.10372014)the Natural Science Foundation of Beijing (No.1072008)
文摘The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.
基金Project supported by the National Natural Science Foundation of China (No. 10372014).
文摘An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.
文摘With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed
