The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is estab- lished, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange princi...The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is estab- lished, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal trans- formations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.展开更多
For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ∧ dξμ, in which the motion equations of the system can be written into the form of the ca...For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ∧ dξμ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates πμand quasi-momenta ξμ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates πμby a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton–Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton–Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton–Jacobi method.展开更多
In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities...In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive neuro-fuzzy control laws are developed using state scaling and backstepping. Semiglobal uniform ultimate bound-edness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neigh-borhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. By using fuzzy logic approximation, the proposed control is free of control singularity problem. An adaptive control-based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 (t 0 ) = 0.展开更多
The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter e...The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter estimation. The proposed control strategies guarantee the convergence of the closed-loop system. The simulation example demonstrates the efficiency of the proposed method.展开更多
Based on the weak Noether symmetry proposed by Mei F X, this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type, and presents expressions of three kinds of conserved quantities by we...Based on the weak Noether symmetry proposed by Mei F X, this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type, and presents expressions of three kinds of conserved quantities by weak Noether symmetry. Finally, the application of this new results is showed by a practical example.展开更多
This paper considers the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) by output feedback for a class of uncertain nonholonomic systems. By combining the nonsmooth change of coor...This paper considers the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) by output feedback for a class of uncertain nonholonomic systems. By combining the nonsmooth change of coordinates and output feedback domination design together, we construct a simple linear time-varying output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The simulation demonstrates the effectiveness of the proposed controller.展开更多
This paper investigates the robust stabilization of the nonholonomic control systems with strongly non- linear uncertainties. In order to make the state scaling effective and to prevent the finite time escape phenomen...This paper investigates the robust stabilization of the nonholonomic control systems with strongly non- linear uncertainties. In order to make the state scaling effective and to prevent the finite time escape phenomenon from happening, the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization. The recursive integrator backstepping technique is applied to the design of the robust controller. The simulation example demonstrates the efficiency and robust features of the proposed method.展开更多
This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances The objective is to design the almost global adaptive asymptotical controllers in probability Uo and u1 for th...This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances The objective is to design the almost global adaptive asymptotical controllers in probability Uo and u1 for the systems by using discontinuous control. A switching control law Uo is designed to almost globally asymptotically stabilize the state x0 in both the singular Xo(t0)=0 case and the non-singular Xo(to)≠O case. Then the state scaling technique is introduced for the discontinuous feedback into the (x1, x2,…, xn)-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law u1 has been presented for (x1, x2, …, xn) -subsystem for both different Uo in non-singular x0 (t0)≠0 case and the singular case X0 (t0)=0. The control algorithm validity is proved by simulation.展开更多
This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay.Applying a novel Lyapunov functional and backstepping recursive method,the de...This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay.Applying a novel Lyapunov functional and backstepping recursive method,the design of robust nonlinear state feedback controllers is proposed,which can guarantee the stability of the closed-loop systems.Finally,a numerical example is provided to show the effectiveness of the method.展开更多
This paper reports latest developments in event-triggered and self-triggered control of uncertain nonholonomic systems in the perturbed chained form.In order to tackle the effects of drift uncertain nonlinearities,non...This paper reports latest developments in event-triggered and self-triggered control of uncertain nonholonomic systems in the perturbed chained form.In order to tackle the effects of drift uncertain nonlinearities,nonholonomic constraints and nonsmooth aperiodic sampling in eventbased control,a novel systematic design scheme is proposed by integrating set-valued maps with stateseparation and state-scaling techniques.The stability analysis of the closed-loop event-triggered control system is based on the cyclic-small-gain techniques that overcome the limitation of Lyapunov theory in the construction of Lyapunov functions for nonsmooth dynamical systems and enjoy inherent robustness properties due to the use of gain-based characterization of robust stability.More specifically,the closed-loop event-triggered control system is transformed into an interconnection of multiple input-tostate stable systems,to which the cyclic-small-gain theorem is applied for robust stability analysis.New self-triggered mechanisms are also developed as natural extensions of the event-triggered control result.The proposed event-based control design approach is new and original even when the system model is reduced to the ideal unperturbed chained form.Interestingly,the proposed methodology is also applicable to a broader class of nonholonomic systems subject to state and input-dependent uncertainties.The efficacy of the obtained event-triggered controllers is validated by a benchmark example of mobile robots subject to parametric uncertainties and a measurement noise such as bias in the orientation.展开更多
The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide wit...The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide with the corresponding equations in the non-perturbational case, and that there are e2 -terms but no e-terms in the differential equations of the second-order moments. Two propositions are obtained. Finally, an example is given to illustrate the application of the results.展开更多
The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new...The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.展开更多
The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the ba...The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.展开更多
This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient c...This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.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
A controller design is proposed for a class of high order nonholonomic systems with nonlinear drifts. The purpose is to ensure a solution for the closed-loop system regulated to zero. Adding a power integrator backste...A controller design is proposed for a class of high order nonholonomic systems with nonlinear drifts. The purpose is to ensure a solution for the closed-loop system regulated to zero. Adding a power integrator backstepping technique and the switching control strategy are employed to design the controller. The state scaling is applied to the recursive manipulation. The simulation example demonstrates the effectiveness and robust features of the proposed method.展开更多
A mobile robot is one of the well-known nonholonomic systems. In this paper, a new adaptive tracking controller for the kinematic model of a nonholonomic mobile robot with unknown parameters is proposed. Stability of ...A mobile robot is one of the well-known nonholonomic systems. In this paper, a new adaptive tracking controller for the kinematic model of a nonholonomic mobile robot with unknown parameters is proposed. Stability of the rule is proved through the use of a Liapunov function. The artificial electrostatic field cooperates with error posture in steering in the controller. At last, this method is implemented on the simulations and the wheeled mobile robot. Results show the effectiveness of the controllers.展开更多
The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integ...The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t →∞.As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.展开更多
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem,...The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie-Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie--Mei symmetry.展开更多
This paper focuses on autonomous motion control of a nonholonomic platform with a robotic arm, which is called mobile manipulator. It serves in transportation of loads in imperfectly known industrial environments with...This paper focuses on autonomous motion control of a nonholonomic platform with a robotic arm, which is called mobile manipulator. It serves in transportation of loads in imperfectly known industrial environments with unknown dynamic obstacles. A union of both procedures is used to solve the general problems of collision-free motion. The problem of collision-free motion for mobile manipulators has been approached from two directions, Planning and Reactive Control. The dynamic path planning can be used to solve the problem of locomotion of mobile platform, and reactive approaches can be employed to solve the motion planning of the arm. The execution can generate the commands for the servo-systems of the robot so as to follow a given nominal trajectory while reacting in real-time to unexpected events. The execution can be designed as an Adaptive Fuzzy Neural Controller. In real world systems, sensor-based motion control becomes essential to deal with model uncertainties and unexpected obstacles.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11272287 and 11472247)the Program for Changjiang Scholars and Innovative Research Team in University of China(Grant No.IRT13097)
文摘The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is estab- lished, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal trans- formations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.
基金National Natural Science Foundation of China(Grant Nos.11972177,11972122,11802103,11772144,11872030,and 11572034)the Scientific Research Starting Foundation for Scholars with Doctoral Degree of Guangdong Medical University(Grant Nos.B2019042 and B2019021).
文摘For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ∧ dξμ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates πμand quasi-momenta ξμ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates πμby a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton–Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton–Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton–Jacobi method.
文摘In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive neuro-fuzzy control laws are developed using state scaling and backstepping. Semiglobal uniform ultimate bound-edness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neigh-borhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. By using fuzzy logic approximation, the proposed control is free of control singularity problem. An adaptive control-based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 (t 0 ) = 0.
基金supported by the National Natural Science Foundation of China (No.60574007, 60674027)Doctoral Foundation of Education Ministry of China (No.20050446001)
文摘The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter estimation. The proposed control strategies guarantee the convergence of the closed-loop system. The simulation example demonstrates the efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No 20040007022)
文摘Based on the weak Noether symmetry proposed by Mei F X, this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type, and presents expressions of three kinds of conserved quantities by weak Noether symmetry. Finally, the application of this new results is showed by a practical example.
基金This work was supported by the National Natural Science Foundation of China(No.60304003,60574007,60574080) Scholastic Youth Foundation of Qufu Normal University.
文摘This paper considers the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) by output feedback for a class of uncertain nonholonomic systems. By combining the nonsmooth change of coordinates and output feedback domination design together, we construct a simple linear time-varying output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The simulation demonstrates the effectiveness of the proposed controller.
基金National Natural Science Foundation of China (No.60674027).
文摘This paper investigates the robust stabilization of the nonholonomic control systems with strongly non- linear uncertainties. In order to make the state scaling effective and to prevent the finite time escape phenomenon from happening, the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization. The recursive integrator backstepping technique is applied to the design of the robust controller. The simulation example demonstrates the efficiency and robust features of the proposed method.
文摘This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances The objective is to design the almost global adaptive asymptotical controllers in probability Uo and u1 for the systems by using discontinuous control. A switching control law Uo is designed to almost globally asymptotically stabilize the state x0 in both the singular Xo(t0)=0 case and the non-singular Xo(to)≠O case. Then the state scaling technique is introduced for the discontinuous feedback into the (x1, x2,…, xn)-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law u1 has been presented for (x1, x2, …, xn) -subsystem for both different Uo in non-singular x0 (t0)≠0 case and the singular case X0 (t0)=0. The control algorithm validity is proved by simulation.
基金supported by the National Natural Science Foundation of China (No.60974127)
文摘This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay.Applying a novel Lyapunov functional and backstepping recursive method,the design of robust nonlinear state feedback controllers is proposed,which can guarantee the stability of the closed-loop systems.Finally,a numerical example is provided to show the effectiveness of the method.
基金the National Natural Science Foundation of China Grant Nos.61633007and U1911401the National Natural Science Foundation of China under Grant No.EPCN1903781。
文摘This paper reports latest developments in event-triggered and self-triggered control of uncertain nonholonomic systems in the perturbed chained form.In order to tackle the effects of drift uncertain nonlinearities,nonholonomic constraints and nonsmooth aperiodic sampling in eventbased control,a novel systematic design scheme is proposed by integrating set-valued maps with stateseparation and state-scaling techniques.The stability analysis of the closed-loop event-triggered control system is based on the cyclic-small-gain techniques that overcome the limitation of Lyapunov theory in the construction of Lyapunov functions for nonsmooth dynamical systems and enjoy inherent robustness properties due to the use of gain-based characterization of robust stability.More specifically,the closed-loop event-triggered control system is transformed into an interconnection of multiple input-tostate stable systems,to which the cyclic-small-gain theorem is applied for robust stability analysis.New self-triggered mechanisms are also developed as natural extensions of the event-triggered control result.The proposed event-based control design approach is new and original even when the system model is reduced to the ideal unperturbed chained form.Interestingly,the proposed methodology is also applicable to a broader class of nonholonomic systems subject to state and input-dependent uncertainties.The efficacy of the obtained event-triggered controllers is validated by a benchmark example of mobile robots subject to parametric uncertainties and a measurement noise such as bias in the orientation.
文摘The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide with the corresponding equations in the non-perturbational case, and that there are e2 -terms but no e-terms in the differential equations of the second-order moments. Two propositions are obtained. Finally, an example is given to illustrate the application of the results.
文摘The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.
基金Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209)the National Natural Science Foundation of China (Grant Nos. 90816001 and 11102060)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20093108110005)the Shanghai Subject Chief Scientist Project, China (Grant No. 09XD1401700)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.
文摘This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.
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 National Natural Science Foundation of China (No. 60674027)
文摘A controller design is proposed for a class of high order nonholonomic systems with nonlinear drifts. The purpose is to ensure a solution for the closed-loop system regulated to zero. Adding a power integrator backstepping technique and the switching control strategy are employed to design the controller. The state scaling is applied to the recursive manipulation. The simulation example demonstrates the effectiveness and robust features of the proposed method.
文摘A mobile robot is one of the well-known nonholonomic systems. In this paper, a new adaptive tracking controller for the kinematic model of a nonholonomic mobile robot with unknown parameters is proposed. Stability of the rule is proved through the use of a Liapunov function. The artificial electrostatic field cooperates with error posture in steering in the controller. At last, this method is implemented on the simulations and the wheeled mobile robot. Results show the effectiveness of the controllers.
基金supported by National Natural Science Foundation of China(Nos.61273091,61004013 and 61304059)Ph.D.Programs Foundation of Ministry of Education of China,and Fundamental Research Funds for the Central Universities(No.CXLX12 0096)
文摘The trajectory tracking control is considered for nonholonomic mechanical systems with affine constraints and dynamic friction. A new state transformation is proposed to deal with affine constraints, and then an integral feedback compensation strategy is used to identify the dynamic friction. The proposed controller ensures that the output tracking errors converge to zero as t →∞.As an application, a detailed example is presented to illustrate the effectiveness of the control scheme.
文摘The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie-Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie-Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie--Mei symmetry.
文摘This paper focuses on autonomous motion control of a nonholonomic platform with a robotic arm, which is called mobile manipulator. It serves in transportation of loads in imperfectly known industrial environments with unknown dynamic obstacles. A union of both procedures is used to solve the general problems of collision-free motion. The problem of collision-free motion for mobile manipulators has been approached from two directions, Planning and Reactive Control. The dynamic path planning can be used to solve the problem of locomotion of mobile platform, and reactive approaches can be employed to solve the motion planning of the arm. The execution can generate the commands for the servo-systems of the robot so as to follow a given nominal trajectory while reacting in real-time to unexpected events. The execution can be designed as an Adaptive Fuzzy Neural Controller. In real world systems, sensor-based motion control becomes essential to deal with model uncertainties and unexpected obstacles.