In this paper,the formation control problem of secondorder nonholonomic mobile robot systems is investigated in a dynamic event-triggered scheme.Event-triggered control protocols combined with persistent excitation(PE...In this paper,the formation control problem of secondorder nonholonomic mobile robot systems is investigated in a dynamic event-triggered scheme.Event-triggered control protocols combined with persistent excitation(PE)conditions are presented.In event-detecting processes,an inactive time is introduced after each sampling instant,which can ensure a positive minimum sampling interval.To increase the flexibility of the event-triggered scheme,internal dynamic variables are included in event-triggering conditions.Moreover,the dynamic event-triggered scheme plays an important role in increasing the lengths of time intervals between any two consecutive events.In addition,event-triggered control protocols without forward and angular velocities are also presented based on approximate-differentiation(low-pass)filters.The asymptotic convergence results are given based on a nested Matrosov theorem and artificial sampling methods.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
In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrat...In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.展开更多
This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, ba...This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.展开更多
For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are stu...For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.展开更多
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
The form invariance and the conserved quantity for a weakly nonholonomic system (WNS) are studied. The WNS is a nonholonomic system (NS) whose constraint equations contain a small parameter. The differential equat...The form invariance and the conserved quantity for a weakly nonholonomic system (WNS) are studied. The WNS is a nonholonomic system (NS) whose constraint equations contain a small parameter. The differential equations of motion of the system are established. The definition and the criterion of form invariance of the system are given. The conserved quantity deduced from the form invariance is obtained. Finally, an illustrative example is shown.展开更多
To study the Noether's theorem of nonholonomic systems of non_Chetaev's type with unilateral constraints in event space, firstly, the principle of D'Alembert_Lagrange for the systems with unilateral constr...To study the Noether's theorem of nonholonomic systems of non_Chetaev's type with unilateral constraints in event space, firstly, the principle of D'Alembert_Lagrange for the systems with unilateral constraints in event space is presented, secondly, the Noether's theorem and the Noether's inverse theorem for the nonholonomic systems of non_Chetaev's type with unilateral constraints in event space are studied and obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group, finally, an example is given to illustrate the application of the result.展开更多
This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the ...This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results.展开更多
A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic ...A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsform...It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the 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
Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetacv type in the event space are investigated. The dif...Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetacv type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetacv type in the event space. An example is given to illustrate the application of the results.展开更多
Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservativ...Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.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
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
The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the inva...The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.展开更多
The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's prin...The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.展开更多
The problem of adaptive regulation of a class of high-order parametric nonholonomic systems in chained-form was discussed. Using adding a power integrator technique and state scaling with discontinuous projection tech...The problem of adaptive regulation of a class of high-order parametric nonholonomic systems in chained-form was discussed. Using adding a power integrator technique and state scaling with discontinuous projection technique, a discontinuous adaptive dynamic controller was constructed. The controller guarantees the estimated value of unknown parameter is in the prescribed extent.展开更多
Conformal invariance and conserved quantities for a nonholonomic system of Chetaev's type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obta...Conformal invariance and conserved quantities for a nonholonomic system of Chetaev's type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system's con- formal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.展开更多
基金supported by the Beijing Natural Science Foundation(4222053).
文摘In this paper,the formation control problem of secondorder nonholonomic mobile robot systems is investigated in a dynamic event-triggered scheme.Event-triggered control protocols combined with persistent excitation(PE)conditions are presented.In event-detecting processes,an inactive time is introduced after each sampling instant,which can ensure a positive minimum sampling interval.To increase the flexibility of the event-triggered scheme,internal dynamic variables are included in event-triggering conditions.Moreover,the dynamic event-triggered scheme plays an important role in increasing the lengths of time intervals between any two consecutive events.In addition,event-triggered control protocols without forward and angular velocities are also presented based on approximate-differentiation(low-pass)filters.The asymptotic convergence results are given based on a nested Matrosov theorem and artificial sampling methods.
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.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143)
文摘This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.
基金supported by the National Natural Science Foundation of China(No.11272227)
文摘For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.
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supported by the National Natural Science Foundation of China(Nos.10932002,10972031,and 11272050)
文摘The form invariance and the conserved quantity for a weakly nonholonomic system (WNS) are studied. The WNS is a nonholonomic system (NS) whose constraint equations contain a small parameter. The differential equations of motion of the system are established. The definition and the criterion of form invariance of the system are given. The conserved quantity deduced from the form invariance is obtained. Finally, an illustrative example is shown.
文摘To study the Noether's theorem of nonholonomic systems of non_Chetaev's type with unilateral constraints in event space, firstly, the principle of D'Alembert_Lagrange for the systems with unilateral constraints in event space is presented, secondly, the Noether's theorem and the Noether's inverse theorem for the nonholonomic systems of non_Chetaev's type with unilateral constraints in event space are studied and obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group, finally, an example is given to illustrate the application of the result.
文摘This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032)
文摘A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.
文摘It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the 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.
基金Project supported by the National Natural Science Foundation of China (Grant No 10572021).
文摘Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetacv type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetacv type in the event space. An example is given to illustrate the application of the results.
基金Project supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos. 144019, 20152, and 114052)
文摘Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.
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 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The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.
文摘The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.
基金Project supported by the Scientific Research Foundation of Education Bureau of Henan Province (No.2003110002).
文摘The problem of adaptive regulation of a class of high-order parametric nonholonomic systems in chained-form was discussed. Using adding a power integrator technique and state scaling with discontinuous projection technique, a discontinuous adaptive dynamic controller was constructed. The controller guarantees the estimated value of unknown parameter is in the prescribed extent.
基金Project supported by the National Natural Science Foundation of China (No. 10932002)the Natural Science Foundation of Zhejiang Province of China (No. LY12A02008)
文摘Conformal invariance and conserved quantities for a nonholonomic system of Chetaev's type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system's con- formal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.