The main purpose of the paper consists in illustrating a procedure for expressing the equations of motion for a general time-dependent constrained system. Constraints are both of geometrical and differential type. The...The main purpose of the paper consists in illustrating a procedure for expressing the equations of motion for a general time-dependent constrained system. Constraints are both of geometrical and differential type. The use of quasi-velocities as variables of the mathematical problem opens the possibility of incorporating some remarkable and classic cases of equations of motion. Afterwards, the scheme of equations is implemented for a pair of substantial examples, which are presented in a double version, acting either as a scleronomic system and as a rheonomic system.展开更多
Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
This paper addresses the time-varying formation-containment(FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired traje...This paper addresses the time-varying formation-containment(FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired trajectory. Input the fixed time-varying formation template to the leader and start executing, this process also needs to track the desired trajectory, and the follower needs to converge to the convex hull that the leader crosses. Firstly, the dynamic models of nonholonomic systems are linearized to second-order dynamics. Then, based on the desired trajectory and formation template, the FC control protocols are proposed. Sufficient conditions to achieve FC are introduced and an algorithm is proposed to resolve the control parameters by solving an algebraic Riccati equation. The system is demonstrated to achieve FC, with the average position and velocity of the leaders converging asymptotically to the desired trajectory. Finally, the theoretical achievements are verified in simulations by a multi-agent system composed of virtual human individuals.展开更多
This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are es...This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the applic...The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided.展开更多
Puts forward an algebraic structure of the Chaplygin's equations of nonholonomic systems, establish the Poisson's theory of the integration equations and gives an example for illustrating the application of th...Puts forward an algebraic structure of the Chaplygin's equations of nonholonomic systems, establish the Poisson's theory of the integration equations and gives an example for illustrating the application of the result.展开更多
Aimed at the stabilization of the nonholonomic chained system under fixed sample control, two control laws were proposed. The discrete model of the nonholonomic chained system under zero-hold was obtained through the ...Aimed at the stabilization of the nonholonomic chained system under fixed sample control, two control laws were proposed. The discrete model of the nonholonomic chained system under zero-hold was obtained through the integrate method to the continuous model. And the discrete model was transformed to the form with two linear subsystems through coordinate transformation. Two feedback control laws, time-invariant control law and time-varying control law, were proposed; and the local stabilization and global stabilization were realized respectively. The simulation results show the effectiveness of the proposed control laws. The discrete nonholonomic chained system can converge to zero from any initial state exponentially, and the convergence rate can be changed through changing the parameters of the control laws.展开更多
Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Suf...Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.展开更多
The existing research on dynamics and slip ratio of wheeled mobile robot （WMR） are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the...The existing research on dynamics and slip ratio of wheeled mobile robot （WMR） are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS- Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS- Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified, Moreover, the relative horizontal motion between fore/hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore/hind wheels become larger/smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.展开更多
A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quant...A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.展开更多
This paper investigates the visual servoing robust stabilization of nonholonomic mobile robots. The calibration of visual parameters is not only complicated, but also needs great consumption of calculated time so that...This paper investigates the visual servoing robust stabilization of nonholonomic mobile robots. The calibration of visual parameters is not only complicated, but also needs great consumption of calculated time so that the accurate calibration is impossible in some situations for high requirement of real timing. Hence, it is interesting and important to consider the design of stabilizing controllers for nonholonomic kinematic systems with uncalibrated visual parameters. A novel uncertain model of these nonholonomic kinematic systems is proposed. Based on this model, a stabilizing controller is discussed by using dynamic feedback and two-step techniques. The proposed robust controller makes the mobile robot image pose and the orientation converge to the desired configuration despite the lack of depth information and the lack of precise visual parameters. The stability of the closed loop system is rigorously proved. The simulation is given to show the effectiveness of the presented controllers.展开更多
As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately...As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. Considering the unknown parameters of two models, this paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then, in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed adopting reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control scheme can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot.展开更多
In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then th...In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.展开更多
This paper presents the controller design for the path following of a spherical mobile robot, BHQ-1. Firstly, a desired velocity for the reference path is deduced from the kinematic model, which cannot be transformed ...This paper presents the controller design for the path following of a spherical mobile robot, BHQ-1. Firstly, a desired velocity for the reference path is deduced from the kinematic model, which cannot be transformed into the classic chained form. Secondly, a necessary torque for the desired velocity is obtained based on the dynamic model. As to the kinematics, a one-dimensional function is selected to measure the two-directional tracking error, and the velocity of rolling forward is reasonably assumed to be constant; therefore the multiple-input multiple-output （MIMO） system is transformed into a single-input single-output （SISO） system. As to the dynamics, both exact dynamics and inexact dynamics with modeling error as well as bounded unknown disturbance are taken into account, based on which a proportional-derivative （PD） controller and a sliding mode controller with adaptive parameters are proposed respectively. Finally, convergence analysis and simulation results are provided to validate these controllers.展开更多
This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The defini...This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.展开更多
Spherical mobile robot has compact structure, remarkable stability, and flexible motion,which make it have many advantages over traditional mobile robots when applied in those unmanned environments, such as outer plan...Spherical mobile robot has compact structure, remarkable stability, and flexible motion,which make it have many advantages over traditional mobile robots when applied in those unmanned environments, such as outer planets. However, spherical mobile robot is a special highly under-actuated nonholonomic system, which cannot be transformed to the classic chained form. At present, there has not been a kinematics-based trajectory tracking controller which could track both the position states and the attitude states of a spherical mobile robot. In this paper, the four-state(two position states and two attitude states) trajectory tracking control of a type of spherical mobile robot driven by a 2-DOF pendulum was studied. A controller based on the shunting model of neurodynamics and the kinematic model was deduced, and its stability was demonstrated with Lyapunov’s direct method. The control priorities of the four states were allocated according to the magnification of each state tracking error in order to firstly ensure the correct tracking of the position states. The outputs(motor speeds) of the controller were regulated according to the maximum speeds and the maximum accelerations of the actuation motors in order to solve the speed jump problem caused by initial state errors, and continuous and bounded outputs were obtained. The effectiveness including the anti-interference ability of the proposed trajectory tracking controller was verified through MATLAB simulations.展开更多
This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under ...This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.展开更多
Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new con...Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.展开更多
The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th...The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.展开更多
A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided b...A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.展开更多
文摘The main purpose of the paper consists in illustrating a procedure for expressing the equations of motion for a general time-dependent constrained system. Constraints are both of geometrical and differential type. The use of quasi-velocities as variables of the mathematical problem opens the possibility of incorporating some remarkable and classic cases of equations of motion. Afterwards, the scheme of equations is implemented for a pair of substantial examples, which are presented in a double version, acting either as a scleronomic system and as a rheonomic system.
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
文摘This paper addresses the time-varying formation-containment(FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired trajectory. Input the fixed time-varying formation template to the leader and start executing, this process also needs to track the desired trajectory, and the follower needs to converge to the convex hull that the leader crosses. Firstly, the dynamic models of nonholonomic systems are linearized to second-order dynamics. Then, based on the desired trajectory and formation template, the FC control protocols are proposed. Sufficient conditions to achieve FC are introduced and an algorithm is proposed to resolve the control parameters by solving an algebraic Riccati equation. The system is demonstrated to achieve FC, with the average position and velocity of the leaders converging asymptotically to the desired trajectory. Finally, the theoretical achievements are verified in simulations by a multi-agent system composed of virtual human individuals.
文摘This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
文摘The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided.
文摘Puts forward an algebraic structure of the Chaplygin's equations of nonholonomic systems, establish the Poisson's theory of the integration equations and gives an example for illustrating the application of the result.
文摘Aimed at the stabilization of the nonholonomic chained system under fixed sample control, two control laws were proposed. The discrete model of the nonholonomic chained system under zero-hold was obtained through the integrate method to the continuous model. And the discrete model was transformed to the form with two linear subsystems through coordinate transformation. Two feedback control laws, time-invariant control law and time-varying control law, were proposed; and the local stabilization and global stabilization were realized respectively. The simulation results show the effectiveness of the proposed control laws. The discrete nonholonomic chained system can converge to zero from any initial state exponentially, and the convergence rate can be changed through changing the parameters of the control laws.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10672143 and 10572021
文摘Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.
基金supported by National Outstanding Youth Science Foundation of China (Grant No. 51125020)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2006AA04Z207)Program for New Century Excellent Talents in University, China
文摘The existing research on dynamics and slip ratio of wheeled mobile robot （WMR） are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS- Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS- Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified, Moreover, the relative horizontal motion between fore/hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore/hind wheels become larger/smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10672143 and 10572021.
文摘A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.
基金supported by the National Natural Science Foundation of China (No.60874002)the Key Program of Scientific Innovation of Shanghai Education Committee (No.09zz158)the Shanghai Key Discipline (No.S30501)
文摘This paper investigates the visual servoing robust stabilization of nonholonomic mobile robots. The calibration of visual parameters is not only complicated, but also needs great consumption of calculated time so that the accurate calibration is impossible in some situations for high requirement of real timing. Hence, it is interesting and important to consider the design of stabilizing controllers for nonholonomic kinematic systems with uncalibrated visual parameters. A novel uncertain model of these nonholonomic kinematic systems is proposed. Based on this model, a stabilizing controller is discussed by using dynamic feedback and two-step techniques. The proposed robust controller makes the mobile robot image pose and the orientation converge to the desired configuration despite the lack of depth information and the lack of precise visual parameters. The stability of the closed loop system is rigorously proved. The simulation is given to show the effectiveness of the presented controllers.
基金supported by State Key Laboratory of Robotics and System of China (Grant No. SKLR-2010 -MS - 14)State Key Lab of Embedded System and Service Computing of China(Grant No. 2010-11)
文摘As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. Considering the unknown parameters of two models, this paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then, in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed adopting reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control scheme can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot.
基金The Project is supported by the National Natural Science Foundation of China
文摘In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.
基金National Natural Science Foundation of China(50705003)National High-tech Research and Development Program of China(2007AA04Z252)"Blue Star Program"of Beihang University
文摘This paper presents the controller design for the path following of a spherical mobile robot, BHQ-1. Firstly, a desired velocity for the reference path is deduced from the kinematic model, which cannot be transformed into the classic chained form. Secondly, a necessary torque for the desired velocity is obtained based on the dynamic model. As to the kinematics, a one-dimensional function is selected to measure the two-directional tracking error, and the velocity of rolling forward is reasonably assumed to be constant; therefore the multiple-input multiple-output （MIMO） system is transformed into a single-input single-output （SISO） system. As to the dynamics, both exact dynamics and inexact dynamics with modeling error as well as bounded unknown disturbance are taken into account, based on which a proportional-derivative （PD） controller and a sliding mode controller with adaptive parameters are proposed respectively. Finally, convergence analysis and simulation results are provided to validate these controllers.
基金supported by the National Natural Science Foundation of China (Grant No 10572021)
文摘This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.
文摘Spherical mobile robot has compact structure, remarkable stability, and flexible motion,which make it have many advantages over traditional mobile robots when applied in those unmanned environments, such as outer planets. However, spherical mobile robot is a special highly under-actuated nonholonomic system, which cannot be transformed to the classic chained form. At present, there has not been a kinematics-based trajectory tracking controller which could track both the position states and the attitude states of a spherical mobile robot. In this paper, the four-state(two position states and two attitude states) trajectory tracking control of a type of spherical mobile robot driven by a 2-DOF pendulum was studied. A controller based on the shunting model of neurodynamics and the kinematic model was deduced, and its stability was demonstrated with Lyapunov’s direct method. The control priorities of the four states were allocated according to the magnification of each state tracking error in order to firstly ensure the correct tracking of the position states. The outputs(motor speeds) of the controller were regulated according to the maximum speeds and the maximum accelerations of the actuation motors in order to solve the speed jump problem caused by initial state errors, and continuous and bounded outputs were obtained. The effectiveness including the anti-interference ability of the proposed trajectory tracking controller was verified through MATLAB simulations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10772025)the Fund for Fundamental Research of Beijing Institute of Technology
文摘This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.
文摘Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.
文摘The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.
基金partly supported by the National Natural Science Foundation of China (No.50625516)the 863 program of China(No.2006AA09Z203,2006AA04A110)
文摘A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.
