Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 ...Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.展开更多
A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and ...A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.展开更多
The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially ...The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.展开更多
A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space.Sixteen extreme poses are obtained in a Stewart platform.The singular points of the extreme p...A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space.Sixteen extreme poses are obtained in a Stewart platform.The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points,and thereby the maximum link lengths are achieved.The rotation angles of joints and the distances between two neighboring links are analyzed in a calculation example in which that the mechanism moves among the extreme poses is assumed.Then an algorithm to test the safety mechanism is presented taking the constraint conditions into account.A safety mechanism having optimal properties of global movement is worked out by optimizing all structural parameters through minimizing the average condition number of extreme poses.展开更多
A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbi...A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbit spacecraft. Principle and structure of the six-degree-of-freedom simulation system are introduced. The docking process dynamic of the vehicles is modeled. Experiment results and mathematical simulation data are compared to validating the simulation system. The comparisons of the results prove that the simulation system proposed can effectively simulate the on-orbit docking process of the spacecraft.展开更多
Vibrations inherently generated by on-board disturbance sources degrade the performance of the instruments in an on-orbit spacecraft,which have stringent accuracy requirements.The Stewart platform enables both track-p...Vibrations inherently generated by on-board disturbance sources degrade the performance of the instruments in an on-orbit spacecraft,which have stringent accuracy requirements.The Stewart platform enables both track-positioning and vibration control.The strut of the Stewart platform is designed as a piezoelectric(PZT) element in series with a voice coil motor(VCM) element and a viscoelastic element.The track-positioning system uses a VCM as the main positioning control driver and a PZT as the positioning compensator.The vibration control system uses the characteristics of struts including active and passive control elements to attenuate the vibration.Simulation results indicate that the Stewart platform with the designed struts has good performance in tracking and vibration attenuation with different interference waves.展开更多
Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore cont...Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore controller research is either low in tracking performance and movement smoothness when it ignores the nonlinearity and dynamics coupling,or complex in algorithm and has the need of acceleration feedback or observer when the dynamics coupling and nonlinearity is included.To solve the dilemma,a new controller,backstepping adaptive control of hydraulic Stewart platform using dynamic surface is put forward based on the complete dynamics including the upper platform dynamics and hydraulic nonlinearity in driving system.Asymptotic stability of the whole system is proved by Lyapunov method.The proposed algorithm is simple by avoiding the use of acceleration.The simulation results indicate that the control algorithm performs better than the normal PID controller in control precision,dynamic response and depression of the cross coupling.展开更多
In order to solve the problem of difficult modeling and identification caused by time-variable parameters,multiple inputs and outputs and unstable open loop,a subsystem model-based close-loop grey-box identification m...In order to solve the problem of difficult modeling and identification caused by time-variable parameters,multiple inputs and outputs and unstable open loop,a subsystem model-based close-loop grey-box identification method was put forward when consider the main coupling effects of hydraulic Stewart platform.Firstly,the whole system is divided into three TITO(Two Input Two Output) subsystems according to the characteristics of the pseudo-mass matrix,hence transfer function matrix model of the subsystem can also be found.Secondly,since the Stewart platform is unstable,the close-loop transfer model of the subsystem is derived under the proportional controllers.The inverse M serial is adopted as the identification signal to get the experimental data.All parameters of the subsystem are determined in close-loop indirect identification by PEM(Prediction Error Method).Finally,a case study validates the correctness and effectiveness of the subsystem model-based close-loop grey-box identification method for hydraulic Stewart platform.展开更多
The windy environment is the main cause affecting the efficiency of offshore wind turbine installation.In order to improve the stability and efficiency of single-blade installation of offshore wind turbines under high...The windy environment is the main cause affecting the efficiency of offshore wind turbine installation.In order to improve the stability and efficiency of single-blade installation of offshore wind turbines under high wind speed conditions,the Stewart platform is used as an auxiliary tool to help dock the wind turbine blade in this paper.In order to verify the effectiveness of the Stewart platform for blade docking,a blade docking simulation system consisting of the Stewart platform,wind turbine blade,and wind load calculation module was built based on Simulink/SimscapeMultibody.At the same time,the PID algorithm is used to control the Stewart platform so that the blade can effectively track the desired trajectory during the docking process to ensure the successful docking of the blade.Through the simulation of the docking process for blades with a length of 61.5 meters,this paper successfully demonstrates a docking system that might facilitate future docking processes.It also shows that the Stewart platform can effectively reduce the vibration and the movement range of the blade root and improve the stability and efficiency of blade docking.展开更多
The control stability of the end manipulator of a cable-suspended Stewart platform in disturbance was studied by combination of the multi-body system dynamics and control theory and the eigensystem realization algorit...The control stability of the end manipulator of a cable-suspended Stewart platform in disturbance was studied by combination of the multi-body system dynamics and control theory and the eigensystem realization algorithm （ERA）. The corresponding closodloop vibration control strategies were suggested based on position prediction with PD （proportional plus derivative ） control. Numerical simulation was made on a scale model to study the vibration control effects of the stewart platform with flexible suspension, including system response to step load, system response to cyclic load, and instability. Then, experiments for Stewart platform with cable suspension were designed to study the actual control effects and validate the validity of numerical simulation. The results show that the experimental results agree with the simulation results well, and the the system has a fairly good control effect to the end manipulator. Therefore, a preliminary conclusion can be made that it is feasible using the Stewart platform as the vibration control platform of the flexible support system, by position prediction of the base platform and PD feedback control law.展开更多
Most of the spatially moving vehicles and game controllers use a 2-3 DOF （degrees of freedom） joystick to manipulate objects position. However, most of the spatially moving vehicles have more than 3 degrees of freed...Most of the spatially moving vehicles and game controllers use a 2-3 DOF （degrees of freedom） joystick to manipulate objects position. However, most of the spatially moving vehicles have more than 3 degrees of freedom, such as helicopters, quadrotors, and planes. Therefore, additional equipment like pedals or buttons is required during the manipulation. In this study, a passive Stewart platform based 6 degrees of freedom joystick was developed to control spatially moving objects. The Stewart platform mechanism is a 6-degrees of freedom parallel mechanism, which has been used for simulators. The main challenge of using a parallel mechanism to manipulate objects is the computational burden of its forward kinematics. Therefore, an artificial neural network was used for the forward kinematic solution of the Stewart platform mechanism to obtain the fastest response. Linear potentiometers were used for the Stewart platform legs. A mathematical model of a quadrotor was used to test the capability of the joystick. The developed spatial joystick successfully manipulated the virtual quadrotor model.展开更多
A procedure of computing the position of the planar Stewart platfrom with coplanar ground points is presented avoiding the computation of Groebner basis by standard algorithm. The polynomial system resulted is triangu...A procedure of computing the position of the planar Stewart platfrom with coplanar ground points is presented avoiding the computation of Groebner basis by standard algorithm. The polynomial system resulted is triangularized. The number of arithmetic operations needed can be predisely counted.展开更多
For an electrical six-degree-of-freedom Stewart platform,it is difficult to compute the equivalent inertia of each motor in real time,as the inertia is time-varying.In this study,an analysis using Kane's equation ...For an electrical six-degree-of-freedom Stewart platform,it is difficult to compute the equivalent inertia of each motor in real time,as the inertia is time-varying.In this study,an analysis using Kane's equation is undertaken of the driven torque of the movements of motor systems(including motor friction,movements of motor systems along with the actuators,rotation around axis of rotors and snails),as well as driven torque of the platform and actuators.The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor(PMSM) dynamics.By equalizing the driven torque and electromagnetic torque,a model was established.This method,taking into consideration the influence of counter electromotive force(EMF) and motor friction,could be applied to the real-time dynamic control of the platform,through which the calculation of the time-varying equivalent inertia is avoided.Finally,simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined.With this approach,the multi-body dynamics of the electrical Stewart platform is better understood.展开更多
The present work aims to develop an object tracking controller for the Stewart platform using a computer vision-assisted machine learning-based approach.This research is divided into two modules.The first module focus...The present work aims to develop an object tracking controller for the Stewart platform using a computer vision-assisted machine learning-based approach.This research is divided into two modules.The first module focuses on the design of a motion controller for the Physik Instrumente(PI)-based Stewart platform.In contrast,the second module deals with the development of a machine-learning-based spatial object tracking algorithm by collecting information from the Zed 2 stereo vision system.Presently,simple feed-forward neural networks(NN)are used to predict the orientation of the top table of the platform.While training,the x,y,and z coordinates of the three-dimensional(3D)object,extracted from images,are used as the input to the NN.In contrast,the orientation information of the platform(that is,rotation about the x,y,and z-axes)is considered as the output from the network.The orientation information obtained from the network is fed to the inverse kinematics-based motion controller(module 1)to move the platform while tracking the object.After training,the optimised NN is used to track the continuously moving 3D object.The experimental results show that the developed NN-based controller has successfully tracked the moving spatial object with reasonably good accuracy.展开更多
The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given...The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given orientation capability is defined for the synthesis of a well behaved workspace. Two performance measures are presented, i.e. the local dexterity and workspace radius ratio. The dimensions of the platform are determined with a prior knowledge of how the design parameters affect the dexterity and workspace radius ratio, resulting in an optimal design in terms of these performance indices. An example of application to the kinematic design of a hexapod machine tool is given to illustrate the effectiveness of this approach.展开更多
文摘Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.
基金supported by National Natural Science Foundation of China (Grant Nos. 10973023,11103046,11203048)
文摘A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.
基金supported by Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No.NCET-04-0325)
文摘The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.
文摘A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space.Sixteen extreme poses are obtained in a Stewart platform.The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points,and thereby the maximum link lengths are achieved.The rotation angles of joints and the distances between two neighboring links are analyzed in a calculation example in which that the mechanism moves among the extreme poses is assumed.Then an algorithm to test the safety mechanism is presented taking the constraint conditions into account.A safety mechanism having optimal properties of global movement is worked out by optimizing all structural parameters through minimizing the average condition number of extreme poses.
文摘A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbit spacecraft. Principle and structure of the six-degree-of-freedom simulation system are introduced. The docking process dynamic of the vehicles is modeled. Experiment results and mathematical simulation data are compared to validating the simulation system. The comparisons of the results prove that the simulation system proposed can effectively simulate the on-orbit docking process of the spacecraft.
基金Project supported by the NSAF of China(No.11176008)the Jiangsu Provincial 333 High Talent Program,and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China
文摘Vibrations inherently generated by on-board disturbance sources degrade the performance of the instruments in an on-orbit spacecraft,which have stringent accuracy requirements.The Stewart platform enables both track-positioning and vibration control.The strut of the Stewart platform is designed as a piezoelectric(PZT) element in series with a voice coil motor(VCM) element and a viscoelastic element.The track-positioning system uses a VCM as the main positioning control driver and a PZT as the positioning compensator.The vibration control system uses the characteristics of struts including active and passive control elements to attenuate the vibration.Simulation results indicate that the Stewart platform with the designed struts has good performance in tracking and vibration attenuation with different interference waves.
文摘Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore controller research is either low in tracking performance and movement smoothness when it ignores the nonlinearity and dynamics coupling,or complex in algorithm and has the need of acceleration feedback or observer when the dynamics coupling and nonlinearity is included.To solve the dilemma,a new controller,backstepping adaptive control of hydraulic Stewart platform using dynamic surface is put forward based on the complete dynamics including the upper platform dynamics and hydraulic nonlinearity in driving system.Asymptotic stability of the whole system is proved by Lyapunov method.The proposed algorithm is simple by avoiding the use of acceleration.The simulation results indicate that the control algorithm performs better than the normal PID controller in control precision,dynamic response and depression of the cross coupling.
文摘In order to solve the problem of difficult modeling and identification caused by time-variable parameters,multiple inputs and outputs and unstable open loop,a subsystem model-based close-loop grey-box identification method was put forward when consider the main coupling effects of hydraulic Stewart platform.Firstly,the whole system is divided into three TITO(Two Input Two Output) subsystems according to the characteristics of the pseudo-mass matrix,hence transfer function matrix model of the subsystem can also be found.Secondly,since the Stewart platform is unstable,the close-loop transfer model of the subsystem is derived under the proportional controllers.The inverse M serial is adopted as the identification signal to get the experimental data.All parameters of the subsystem are determined in close-loop indirect identification by PEM(Prediction Error Method).Finally,a case study validates the correctness and effectiveness of the subsystem model-based close-loop grey-box identification method for hydraulic Stewart platform.
文摘The windy environment is the main cause affecting the efficiency of offshore wind turbine installation.In order to improve the stability and efficiency of single-blade installation of offshore wind turbines under high wind speed conditions,the Stewart platform is used as an auxiliary tool to help dock the wind turbine blade in this paper.In order to verify the effectiveness of the Stewart platform for blade docking,a blade docking simulation system consisting of the Stewart platform,wind turbine blade,and wind load calculation module was built based on Simulink/SimscapeMultibody.At the same time,the PID algorithm is used to control the Stewart platform so that the blade can effectively track the desired trajectory during the docking process to ensure the successful docking of the blade.Through the simulation of the docking process for blades with a length of 61.5 meters,this paper successfully demonstrates a docking system that might facilitate future docking processes.It also shows that the Stewart platform can effectively reduce the vibration and the movement range of the blade root and improve the stability and efficiency of blade docking.
文摘The control stability of the end manipulator of a cable-suspended Stewart platform in disturbance was studied by combination of the multi-body system dynamics and control theory and the eigensystem realization algorithm （ERA）. The corresponding closodloop vibration control strategies were suggested based on position prediction with PD （proportional plus derivative ） control. Numerical simulation was made on a scale model to study the vibration control effects of the stewart platform with flexible suspension, including system response to step load, system response to cyclic load, and instability. Then, experiments for Stewart platform with cable suspension were designed to study the actual control effects and validate the validity of numerical simulation. The results show that the experimental results agree with the simulation results well, and the the system has a fairly good control effect to the end manipulator. Therefore, a preliminary conclusion can be made that it is feasible using the Stewart platform as the vibration control platform of the flexible support system, by position prediction of the base platform and PD feedback control law.
文摘Most of the spatially moving vehicles and game controllers use a 2-3 DOF （degrees of freedom） joystick to manipulate objects position. However, most of the spatially moving vehicles have more than 3 degrees of freedom, such as helicopters, quadrotors, and planes. Therefore, additional equipment like pedals or buttons is required during the manipulation. In this study, a passive Stewart platform based 6 degrees of freedom joystick was developed to control spatially moving objects. The Stewart platform mechanism is a 6-degrees of freedom parallel mechanism, which has been used for simulators. The main challenge of using a parallel mechanism to manipulate objects is the computational burden of its forward kinematics. Therefore, an artificial neural network was used for the forward kinematic solution of the Stewart platform mechanism to obtain the fastest response. Linear potentiometers were used for the Stewart platform legs. A mathematical model of a quadrotor was used to test the capability of the joystick. The developed spatial joystick successfully manipulated the virtual quadrotor model.
文摘A procedure of computing the position of the planar Stewart platfrom with coplanar ground points is presented avoiding the computation of Groebner basis by standard algorithm. The polynomial system resulted is triangularized. The number of arithmetic operations needed can be predisely counted.
文摘For an electrical six-degree-of-freedom Stewart platform,it is difficult to compute the equivalent inertia of each motor in real time,as the inertia is time-varying.In this study,an analysis using Kane's equation is undertaken of the driven torque of the movements of motor systems(including motor friction,movements of motor systems along with the actuators,rotation around axis of rotors and snails),as well as driven torque of the platform and actuators.The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor(PMSM) dynamics.By equalizing the driven torque and electromagnetic torque,a model was established.This method,taking into consideration the influence of counter electromotive force(EMF) and motor friction,could be applied to the real-time dynamic control of the platform,through which the calculation of the time-varying equivalent inertia is avoided.Finally,simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined.With this approach,the multi-body dynamics of the electrical Stewart platform is better understood.
文摘The present work aims to develop an object tracking controller for the Stewart platform using a computer vision-assisted machine learning-based approach.This research is divided into two modules.The first module focuses on the design of a motion controller for the Physik Instrumente(PI)-based Stewart platform.In contrast,the second module deals with the development of a machine-learning-based spatial object tracking algorithm by collecting information from the Zed 2 stereo vision system.Presently,simple feed-forward neural networks(NN)are used to predict the orientation of the top table of the platform.While training,the x,y,and z coordinates of the three-dimensional(3D)object,extracted from images,are used as the input to the NN.In contrast,the orientation information of the platform(that is,rotation about the x,y,and z-axes)is considered as the output from the network.The orientation information obtained from the network is fed to the inverse kinematics-based motion controller(module 1)to move the platform while tracking the object.After training,the optimised NN is used to track the continuously moving 3D object.The experimental results show that the developed NN-based controller has successfully tracked the moving spatial object with reasonably good accuracy.
基金Project supported by the National Natural Science Foundation of China (Grant No. 59775006) other financial sources.
文摘The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given orientation capability is defined for the synthesis of a well behaved workspace. Two performance measures are presented, i.e. the local dexterity and workspace radius ratio. The dimensions of the platform are determined with a prior knowledge of how the design parameters affect the dexterity and workspace radius ratio, resulting in an optimal design in terms of these performance indices. An example of application to the kinematic design of a hexapod machine tool is given to illustrate the effectiveness of this approach.
