In this paper,the entrapping control problem of discrete-time AUVs with local coordinate frames is studied.To achieve entrapment in arbitrarily shaped orbits and formations,we design a bearingbased leader-following fr...In this paper,the entrapping control problem of discrete-time AUVs with local coordinate frames is studied.To achieve entrapment in arbitrarily shaped orbits and formations,we design a bearingbased leader-following framework fully in the discrete-time domain with four parts:the orientation estimation unit,estimator unit,controller unit and parameters tuning unit.With bearing measurements and communication information,the orientation estimation unit can estimate orientations of local coordinate frames infinite time,and the estimator unit can achieve local localization.Based on estimation,the controller unit can drive each AUV to track the desired orbit or formation with an arbitrary shape.We present su±cient conditions under which stability of the overall system is proved using the theorem offinite-time stability and LaSalle's theorem for the discrete-time system.Moreover,the parameters tuning unit can calculate optimal parameters to improve overall performance.Additionally,we extend our schemes to nonholonomic AUVs with unicycle models.Finally,simulation results demonstrate the effectiveness of the proposed scheme.展开更多
In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend ...In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend the work to Kerr-Newman black hole in dragging coordinates frame.It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame,which supports and extends Robinson and Wilczek's opinion.展开更多
This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and position...This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.展开更多
Posture recognition plays an important role in many applications,such as security system and monitoring system.Joint quaternion combined with support vector machine(SVM) can solve the problem of moving human posture r...Posture recognition plays an important role in many applications,such as security system and monitoring system.Joint quaternion combined with support vector machine(SVM) can solve the problem of moving human posture recognition.It is a simple and effective algorithm that only three joints are used as the feature points in the whole human skeleton.Using the quaternion of the three joints,a feature vector with five parameters in gait cycle is extracted.The efficiency of the proposed method is demonstrated through an experimental study,and walking and running postures can be distinguished accurately.展开更多
An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors...An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors and coordinates.In order to provide a theoretical basis for coordinate and frame transformations,and to simplify the transformation process in specic problem studies,the geometric product of vectors is redened(the geometric product of vectors is the sum of the negative inner product and the outer product of the vectors),thus the one-to-one correspondence relationship between unit vectors and imaginary units is established.According to Hurwitz's theorem,the vector space of the outer product is gotten and dened,and its dimension cannot be chosen arbitrarily.Based on Arthur Cayley's(1845)multiplication rules of octonions,transformation formulas for a seven-dimensional vector space and rotation matrices for coordinate frame transformations are derived.It is pointed out that the three-dimensional rotation matrices commonly used in astrometry and geodesy are special cases thereof.According to the redefinition of the geometric product of vectors,the multiplication rules of quaternions can be directly obtained,as well as the multiplication table of imaginary units of octonions.It is further indicated that the multiplication tables of imaginary units for octonions and hypercomplex numbers of higher dimensions are not unique.展开更多
基金supported by the National Natural Science Foundation of China(61922058,62025305)the Fellowship of China National Postdoctoral Program for Innovative Talents(BX2021181).
文摘In this paper,the entrapping control problem of discrete-time AUVs with local coordinate frames is studied.To achieve entrapment in arbitrarily shaped orbits and formations,we design a bearingbased leader-following framework fully in the discrete-time domain with four parts:the orientation estimation unit,estimator unit,controller unit and parameters tuning unit.With bearing measurements and communication information,the orientation estimation unit can estimate orientations of local coordinate frames infinite time,and the estimator unit can achieve local localization.Based on estimation,the controller unit can drive each AUV to track the desired orbit or formation with an arbitrary shape.We present su±cient conditions under which stability of the overall system is proved using the theorem offinite-time stability and LaSalle's theorem for the discrete-time system.Moreover,the parameters tuning unit can calculate optimal parameters to improve overall performance.Additionally,we extend our schemes to nonholonomic AUVs with unicycle models.Finally,simulation results demonstrate the effectiveness of the proposed scheme.
基金supported by National Natural Science Foundation of China under Grant No.10773008
文摘In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend the work to Kerr-Newman black hole in dragging coordinates frame.It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame,which supports and extends Robinson and Wilczek's opinion.
基金supported by Nanyang Technological University,Singapore under the Wallenberg-NTU Presidential Postdoctoral Fellowship and the Natural Science Foundation in Heilongjiang Province,China(YQ2022F003).
文摘This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.
基金the Key Project of the National Natural Science Foundation of China(No.61134009)National Natural Science Foundations of China(Nos.61473077,61473078,61503075)+6 种基金Cooperative Research Funds of the National Natural Science Funds Overseas and Hong Kong and Macao Scholars,China(No.61428302)Program for Changjiang Scholars from the Ministry of Education,ChinaSpecialized Research Fund for Shanghai Leading Talents,ChinaProject of the Shanghai Committee of Science and Technology,China(No.13JC1407500)Innovation Program of Shanghai Municipal Education Commission,China(No.14ZZ067)Shanghai Pujiang Program,China(No.15PJ1400100)the Fundamental Research Funds for the Central Universities,China(Nos.15D110423,2232015D3-32)
文摘Posture recognition plays an important role in many applications,such as security system and monitoring system.Joint quaternion combined with support vector machine(SVM) can solve the problem of moving human posture recognition.It is a simple and effective algorithm that only three joints are used as the feature points in the whole human skeleton.Using the quaternion of the three joints,a feature vector with five parameters in gait cycle is extracted.The efficiency of the proposed method is demonstrated through an experimental study,and walking and running postures can be distinguished accurately.
基金supported by the National Natural Science Foundation of China(No.42574047,No.12473068,No.41774039,No.42074002).
文摘An afne space is a set consisting of points and vectors.A vector space(or linear space)is an afne space with a specied origin.For a given afne coordinate system,there exists a one-to-one correspondence between vectors and coordinates.In order to provide a theoretical basis for coordinate and frame transformations,and to simplify the transformation process in specic problem studies,the geometric product of vectors is redened(the geometric product of vectors is the sum of the negative inner product and the outer product of the vectors),thus the one-to-one correspondence relationship between unit vectors and imaginary units is established.According to Hurwitz's theorem,the vector space of the outer product is gotten and dened,and its dimension cannot be chosen arbitrarily.Based on Arthur Cayley's(1845)multiplication rules of octonions,transformation formulas for a seven-dimensional vector space and rotation matrices for coordinate frame transformations are derived.It is pointed out that the three-dimensional rotation matrices commonly used in astrometry and geodesy are special cases thereof.According to the redefinition of the geometric product of vectors,the multiplication rules of quaternions can be directly obtained,as well as the multiplication table of imaginary units of octonions.It is further indicated that the multiplication tables of imaginary units for octonions and hypercomplex numbers of higher dimensions are not unique.
