The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlle...The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlled vehicle.In this context,a novel form of the prescribed performance guiding vector field is introduced,accompanied by a prescribed-time sliding mode con-trol approach.Furthermore,the interdependence among the pre-scribed parameters is discussed.To validate the effectiveness of the proposed method,numerical simulations are presented to demonstrate the efficacy of the approach.展开更多
In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman co...In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, an example is presented to illustrate the application of the results.展开更多
This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized L...This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.展开更多
The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system,...The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
A mathematical model expressing the motion of a pair of multi-DOF robot fingers with hemi-spherical ends, grasping a 3-D rigid object with parallel fiat surfaces, is derived, together with non-holonomic constraints. B...A mathematical model expressing the motion of a pair of multi-DOF robot fingers with hemi-spherical ends, grasping a 3-D rigid object with parallel fiat surfaces, is derived, together with non-holonomic constraints. By referring to the fact that humans grasp an object in the form of precision prehension, dynamically and stably by opposable forces, between the thumb and another finger （index or middle finger）, a simple control signal constructed from finger-thumb opposition is proposed, and shown to realize stable grasping in a dynamic sense without using object information or external sensing （this is called ＂blind grasp＂ in this paper）. The stability of grasping with force/torque balance under non-holonomic constraints is analyzed on the basis of a new concept named ＂stability on a manifold＂. Preliminary simulation results are shown to verify the validity of the theoretical results.展开更多
Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateralconstraints in the Nielsen style are studied.The differential equations of motion for the system above are es...Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateralconstraints in the Nielsen style are studied.The differential equations of motion for the system above are established.The definition and the criteria of Mei symmetry,conditions,and expressions of Mei conserved quantity deduced directlyfrom the Mei symmetry are given.An example is given to illustrate the application of the results.展开更多
The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of ...The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.展开更多
In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems...In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invarianc...In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
This paper proves that Hanlilton's prmciple of both using the Appell-Chetaevcondition and not using the Appell-CHETAEV conditiion is the variational principle of stationary action.The relevant problems are discussed
For the non-holonomic constraint robot,determining the pose of its end-effector will rely on its joints' displacement and the velocity of its non-holonomic constraint joints as well.Therefore,it becomes increasing...For the non-holonomic constraint robot,determining the pose of its end-effector will rely on its joints' displacement and the velocity of its non-holonomic constraint joints as well.Therefore,it becomes increasingly difficult to obtain the analytic solution of its self-motion manifold in the traditional way for solving matrix equation.In this paper,we take the pose of end manipulator as the result of the joint sequential motion based on the mentality of motion equivalence,the structure and the reference velocity which correspond precisely to the points in self-motion manifold as self-motion variable.Thus an analytical solution for the self-motion manifold of the 8 degree of freedom wheeled mobile manipulator is presented by taking vector algebra as a tool,which facilitates deriving the closed solution of its self-motion manifold.In the closing part of this paper,calculating examples of self-motion manifold and mechanism self-motion simulation are proposed,which proves the validity of solution algorithm for self-motion manifold.展开更多
The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of...The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.展开更多
The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral variational principles of second kind are set up. From the latter, the general relation of ...The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral variational principles of second kind are set up. From the latter, the general relation of δq’-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only all previous relations of δq-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds are pointed out.展开更多
The real-time control of the non-holonomic wheel robot has put forward higher requirements for the accuracy and speed of dynamical simulation,so it is necessary to study the new dynamic modeling and calculation method...The real-time control of the non-holonomic wheel robot has put forward higher requirements for the accuracy and speed of dynamical simulation,so it is necessary to study the new dynamic modeling and calculation methods adapting to modern information processingtechnology.Different from the traditional method solving differential-algebraic equation,the objective is to establish optimization model and effective calculating scheme for dynamics of non-holonomic system based on basic dynamical principle.The optimization model cannot be obtained directly from the traditional Gauss'principle.By using Gauss'principle of variational form,this paper deduces the minimum principle in the form of generalized coordinates and quasi-coordinates,respectively,thus allowing dynamical problems of non-holonomic systems to be incorporated into the framework of solving constrained or unconstrained optimization problems.Furthermore,we study a numerical calculation scheme that uses an optimization algorithm for the second form of the above optimization models.As an example,the dynamical problem of a differential-driven wheeled mobile-robot system is discussed.The optimization dynamic model of a non-holonomic robot system and the calculation model of the optimization algorithm are established.Comparing theresults of the optimization calculation with the differential-algebraic equations commonly used in dynamical problem for non-holonomic system reveals that the method in this paper is superior in terms of calculation speed and can more effectively handle constraint violations without extra constraint revision needed.展开更多
In this paper, finite time consensus problem is discussed for multiple non-holonomic mobile agents with constant communication delay. The objective is to design non-smooth distributed control laws such that multiple n...In this paper, finite time consensus problem is discussed for multiple non-holonomic mobile agents with constant communication delay. The objective is to design non-smooth distributed control laws such that multiple non-holonomic mobile agents can be all in agreement within any given finite time larger than communication delay. The authors propose a novel switching control strategy with the help of Lyapunov-based method and graph theory.展开更多
A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variatio...A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.展开更多
In this paper,by studying the domain of selection of the variables participating in variation operations,we prove that Suslov's point of view that the processes of variation and differentiation are not permutable ...In this paper,by studying the domain of selection of the variables participating in variation operations,we prove that Suslov's point of view that the processes of variation and differentiation are not permutable in non-holonomic systems is a misconception.We also prove that Hlde's point of view that the processes of variation and differentiation are permutable in non-holonomie systems has an imperfection.The work presented in this paper has solved the problem of the d-δ permutable property in non-holonomic systems.展开更多
In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same...In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.展开更多
The dot product of bases vectors on the super-surface of constraints of the nonlinear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable...The dot product of bases vectors on the super-surface of constraints of the nonlinear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable mass.These are very simple and convenient for computation.From these known equations,the equations of Chaplygin,Nielson,Appell,Mac-Millan et al.are deriv d;it is unnecessary to introduce the definition if Appell-Chetaev or Niu Qinping for the virtual displacement.These are compatible with the D'Alembert-Lagrange's principle.展开更多
The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displace...The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.展开更多
基金supported by the National Natural Science Foundation of China(62073019)。
文摘The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlled vehicle.In this context,a novel form of the prescribed performance guiding vector field is introduced,accompanied by a prescribed-time sliding mode con-trol approach.Furthermore,the interdependence among the pre-scribed parameters is discussed.To validate the effectiveness of the proposed method,numerical simulations are presented to demonstrate the efficacy of the approach.
文摘In this paper the Lie-form invariance of the non-holonomic systems with unilateral constraints is studied. The definition and the criterion of the Lie-form invariance of the system are given. The generalized Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, an example is presented to illustrate the application of the results.
基金The project supported by the Ministry of Science,Technologies and Development,Republic of Serbia(1874)
文摘This paper deals with the generalization of the fieldmethod to non-holonomic systems whose motion is subject toeither non-linear constraints or those of a higher order,whiletheir motion is modeled by the generalized Lagrange equa-tions of the second kind.Two examples are given to illustratethe theory.
基金supported by the National Natural Science Foundation of China(Grant No 10572021)the Preparatory Research Foundation of Jiangnan University,China(Grant No 2008LYY011)
文摘The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.
基金This work was supported in part by the Grant-in-Aid for Exploratory Research of the JSPS (No. 16656085).
文摘A mathematical model expressing the motion of a pair of multi-DOF robot fingers with hemi-spherical ends, grasping a 3-D rigid object with parallel fiat surfaces, is derived, together with non-holonomic constraints. By referring to the fact that humans grasp an object in the form of precision prehension, dynamically and stably by opposable forces, between the thumb and another finger （index or middle finger）, a simple control signal constructed from finger-thumb opposition is proposed, and shown to realize stable grasping in a dynamic sense without using object information or external sensing （this is called ＂blind grasp＂ in this paper）. The stability of grasping with force/torque balance under non-holonomic constraints is analyzed on the basis of a new concept named ＂stability on a manifold＂. Preliminary simulation results are shown to verify the validity of the theoretical results.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021Preparatory Research Foundation of Jiangnan under Grant No.2008LYY011
文摘Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateralconstraints in the Nielsen style are studied.The differential equations of motion for the system above are established.The definition and the criteria of Mei symmetry,conditions,and expressions of Mei conserved quantity deduced directlyfrom the Mei symmetry are given.An example is given to illustrate the application of the results.
文摘The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.
文摘In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘This paper proves that Hanlilton's prmciple of both using the Appell-Chetaevcondition and not using the Appell-CHETAEV conditiion is the variational principle of stationary action.The relevant problems are discussed
文摘For the non-holonomic constraint robot,determining the pose of its end-effector will rely on its joints' displacement and the velocity of its non-holonomic constraint joints as well.Therefore,it becomes increasingly difficult to obtain the analytic solution of its self-motion manifold in the traditional way for solving matrix equation.In this paper,we take the pose of end manipulator as the result of the joint sequential motion based on the mentality of motion equivalence,the structure and the reference velocity which correspond precisely to the points in self-motion manifold as self-motion variable.Thus an analytical solution for the self-motion manifold of the 8 degree of freedom wheeled mobile manipulator is presented by taking vector algebra as a tool,which facilitates deriving the closed solution of its self-motion manifold.In the closing part of this paper,calculating examples of self-motion manifold and mechanism self-motion simulation are proposed,which proves the validity of solution algorithm for self-motion manifold.
文摘The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19272064)
文摘The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral variational principles of second kind are set up. From the latter, the general relation of δq’-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only all previous relations of δq-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds are pointed out.
基金National Natural Science Foundation of China(Grant 11272167).
文摘The real-time control of the non-holonomic wheel robot has put forward higher requirements for the accuracy and speed of dynamical simulation,so it is necessary to study the new dynamic modeling and calculation methods adapting to modern information processingtechnology.Different from the traditional method solving differential-algebraic equation,the objective is to establish optimization model and effective calculating scheme for dynamics of non-holonomic system based on basic dynamical principle.The optimization model cannot be obtained directly from the traditional Gauss'principle.By using Gauss'principle of variational form,this paper deduces the minimum principle in the form of generalized coordinates and quasi-coordinates,respectively,thus allowing dynamical problems of non-holonomic systems to be incorporated into the framework of solving constrained or unconstrained optimization problems.Furthermore,we study a numerical calculation scheme that uses an optimization algorithm for the second form of the above optimization models.As an example,the dynamical problem of a differential-driven wheeled mobile-robot system is discussed.The optimization dynamic model of a non-holonomic robot system and the calculation model of the optimization algorithm are established.Comparing theresults of the optimization calculation with the differential-algebraic equations commonly used in dynamical problem for non-holonomic system reveals that the method in this paper is superior in terms of calculation speed and can more effectively handle constraint violations without extra constraint revision needed.
基金supported by the Young Faculty Foundation of Tianjin University under Grant No.TJUYFF-08B73
文摘In this paper, finite time consensus problem is discussed for multiple non-holonomic mobile agents with constant communication delay. The objective is to design non-smooth distributed control laws such that multiple non-holonomic mobile agents can be all in agreement within any given finite time larger than communication delay. The authors propose a novel switching control strategy with the help of Lyapunov-based method and graph theory.
基金The project supported by the National Natural Science Foundation of China （10272002） and the Doctoral Program from the Ministry of Education of China （20020001032） The English text was polished by Yunming Chen.
文摘A nonlinear dynamic model of a simple nonholonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton＇s Variational Principle. The critical values, at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs, and the equilibria are investigated by approximately analytical and numerical methods. The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not. The unidirectional snap-through phenomenon （i.e. catastrophe phenomenon） is destined to occur in the system no matter whether the constraint is lockable or not. The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is nonzero. The results obtained by two methods are consistent.
文摘In this paper,by studying the domain of selection of the variables participating in variation operations,we prove that Suslov's point of view that the processes of variation and differentiation are not permutable in non-holonomic systems is a misconception.We also prove that Hlde's point of view that the processes of variation and differentiation are permutable in non-holonomie systems has an imperfection.The work presented in this paper has solved the problem of the d-δ permutable property in non-holonomic systems.
文摘In this paper by means of typical engineering examples and deep theoretical analysis, we prove that under the effect of conservative force, the Hamilton principles in holonomic and non-holonomic systems have the same formula δ∫Ldt=0. The formula ∫δdt=0 is an evolved form of the formula δ∫Ldt=0. Therefore, the two formulas are unified.
文摘The dot product of bases vectors on the super-surface of constraints of the nonlinear non-holonomic space and Mesherskii equations may act as the equations of fundamental dynamics of mechanical system for the variable mass.These are very simple and convenient for computation.From these known equations,the equations of Chaplygin,Nielson,Appell,Mac-Millan et al.are deriv d;it is unnecessary to introduce the definition if Appell-Chetaev or Niu Qinping for the virtual displacement.These are compatible with the D'Alembert-Lagrange's principle.
文摘The Mac-Millan's equation for the non-linear non-holongmic system in one order is derived by using only principle of differential variation of Jourdain. Therefore definition of Niu Qinping for the virtual displacentent is unnecessary. This is the natural deduetion of the method in this paper and so with the non-linear and non holonomic system in high order.
