Topology and performance are the two main topics dealt in the development of robotic mechanisms.However,it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified...Topology and performance are the two main topics dealt in the development of robotic mechanisms.However,it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame.As the properties associated with topology and performance,finite motion and instantaneous motion of the robot play key roles in the procedure.On the purpose of providing a fundamental preparation for integrated modeling and design,this paper carries out a review on the existing unified mathematic frameworks for motion description and computation,involving matrix Lie group and Lie algebra,dual quaternion and pure dual quaternion,finite screw and instantaneous screw.Besides the application in robotics,the review of the work from these mathematicians concentrates on the description,composition and intersection operations of the finite and instantaneous motions,especially on the exponential-differential maps which connect the two sides.Furthermore,an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development.The presented review offers insightful investigation to the motion description and computation,and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.展开更多
This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rig...This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.展开更多
For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all...For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.展开更多
This paper proposes an Equivariant Filtering(EqF)framework for the inertial-integrated state estimation.As the kin-ematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group S...This paper proposes an Equivariant Filtering(EqF)framework for the inertial-integrated state estimation.As the kin-ematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE_(2)(3),the sym-metry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter.We firstly formulate the inertial-integrated dynamics as the group-affine systems.Then,we prove the left equivariant properties of the inertial-integrated dynamics.Finally,we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame.The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation(GNSS)/Inertial Navigation System(INS)loosely integrated navigation experiments.展开更多
基金National Key R&D Program of China(Grant No.2018YFB1307800)National Natural Science Foundation of China(Grant Nos.51875391,51675366)Tianjin Science and Technology Planning Project(Grant Nos.18YFS DZC00010,18YFZCSF00590).
文摘Topology and performance are the two main topics dealt in the development of robotic mechanisms.However,it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame.As the properties associated with topology and performance,finite motion and instantaneous motion of the robot play key roles in the procedure.On the purpose of providing a fundamental preparation for integrated modeling and design,this paper carries out a review on the existing unified mathematic frameworks for motion description and computation,involving matrix Lie group and Lie algebra,dual quaternion and pure dual quaternion,finite screw and instantaneous screw.Besides the application in robotics,the review of the work from these mathematicians concentrates on the description,composition and intersection operations of the finite and instantaneous motions,especially on the exponential-differential maps which connect the two sides.Furthermore,an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development.The presented review offers insightful investigation to the motion description and computation,and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.
基金supported by the National Natural Science Foundation of China(61773024,62073002)the Eindhoven Artificial Intelligence Systems Institute(EAISI),and the ELLIIT Excellence Center and the Swedish Foundation for Strategic Research,Sweden(RIT150038)。
文摘This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.
文摘For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.
基金a grant from the National Key Research and Development Program of China(2018YFB1305001).
文摘This paper proposes an Equivariant Filtering(EqF)framework for the inertial-integrated state estimation.As the kin-ematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE_(2)(3),the sym-metry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter.We firstly formulate the inertial-integrated dynamics as the group-affine systems.Then,we prove the left equivariant properties of the inertial-integrated dynamics.Finally,we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame.The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation(GNSS)/Inertial Navigation System(INS)loosely integrated navigation experiments.
