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 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
Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A...Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.展开更多
By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic system...By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.展开更多
This paper presents that a serpentine curve-based controller can solve locomotion control problems for articulated space robots with extensive flight phases,such as obstacle avoidance during free floating or attitude ...This paper presents that a serpentine curve-based controller can solve locomotion control problems for articulated space robots with extensive flight phases,such as obstacle avoidance during free floating or attitude adjustment before landing.The proposed algorithm achieves articulated robots to use closed paths in the joint space to accomplish the above tasks.Flying snakes,which can shuttle through gaps and adjust their landing posture by swinging their body during gliding in jungle environments,inspired the design of two maneuvers.The first maneuver generates a rotation of the system by varying the moment of inertia between the joints of the robot,with the magnitude of the net rotation depending on the controller parameters.This maneuver can be repeated to allow the robot to reach arbitrary reorientation.The second maneuver involves periodic undulations,allowing the robot to avoid collisions when the trajectory of the global Center of Mass(CM)passes through the obstacle.Both maneuvers are based on the improved serpenoid curve,which can adapt to redundant systems consisting of different numbers of modules.Finally,the simulation illustrates that combining the two maneuvers can help a free-floating chain-type robot traverse complex environments.Our proposed algorithm can be used with similar articulated robot models.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
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.
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 (Grant Nos. 10872084, 10472040)the Outstanding Young Talents Training Fund of Liaoning Province of China (Grant No. 3040005)the Research Program of Higher Educa-tion of Liaoning Province of China (Grant No. 2008S098)
文摘Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.
基金Supported by the National Natural Science Foundation of China (Grant No. 10272034)the Research Fund for the Doctoral Program of Higher Education of Chinathe Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020)
文摘By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
基金co-supported by the National Science Fund for Distinguished Young Scholars,China(No.52025054)the National Natural Science Foundation of China(No.61961015).
文摘This paper presents that a serpentine curve-based controller can solve locomotion control problems for articulated space robots with extensive flight phases,such as obstacle avoidance during free floating or attitude adjustment before landing.The proposed algorithm achieves articulated robots to use closed paths in the joint space to accomplish the above tasks.Flying snakes,which can shuttle through gaps and adjust their landing posture by swinging their body during gliding in jungle environments,inspired the design of two maneuvers.The first maneuver generates a rotation of the system by varying the moment of inertia between the joints of the robot,with the magnitude of the net rotation depending on the controller parameters.This maneuver can be repeated to allow the robot to reach arbitrary reorientation.The second maneuver involves periodic undulations,allowing the robot to avoid collisions when the trajectory of the global Center of Mass(CM)passes through the obstacle.Both maneuvers are based on the improved serpenoid curve,which can adapt to redundant systems consisting of different numbers of modules.Finally,the simulation illustrates that combining the two maneuvers can help a free-floating chain-type robot traverse complex environments.Our proposed algorithm can be used with similar articulated robot models.
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.
