The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite traj...The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.展开更多
Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion function...Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.展开更多
This paper proposes a new type of control laws for free rigid bodies. The start point is the dual quaternion and its characteristics. The logarithm of a dual quaternion is defined, based on which kinematic control law...This paper proposes a new type of control laws for free rigid bodies. The start point is the dual quaternion and its characteristics. The logarithm of a dual quaternion is defined, based on which kinematic control laws can be developed. Global exponential convergence is achieved using logarithmic feedback via a generalized proportional control law, and an appropriate Lyapunov function is constructed to prove the stability. Both the regulation and tracking problems are tackled. Omnidirectional control is discussed as a case study. As the control laws can handle the interconnection between the rotation and translation of a rigid body, they are shown to be more applicable than the conventional method.展开更多
We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of rea...We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real numbers.We define the magnitude of a dual quaternion,as a dual number.Based upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.展开更多
An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H...An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.展开更多
To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This pape...To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.展开更多
A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constrai...A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constraint relationship of image itself and sequence images is constructed to compensate the systematic errors.The feasibility of this method used in bundle adjustment is theoretically tested by the analysis of the structural characteristics of error equation and normal equation based on dual quaternion.Different distributions of control points and stepwise regression analysis are introduced into the experiment for RC30 image.The results show that the adjustment accuracy can achieve 0.2min plane and 1min elevation.As a result,this method provides a new technique for geometric location problem of remote sensing images.展开更多
This paper addresses a cooperative relative navigation problem for multiple aerial agents,relying on visual tracking information between vehicles.The research aims to investigate a sensor fusion architecture and algor...This paper addresses a cooperative relative navigation problem for multiple aerial agents,relying on visual tracking information between vehicles.The research aims to investigate a sensor fusion architecture and algorithm that leverages partially available absolute navigation knowledge while exploiting collaborative visual interaction between vehicles in mission flight areas,where satellite navigation-denied regions are irregularly located.To achieve this,the paper introduces a new approach to defining the relative poses of cameras and develops a corresponding process to secure the relative pose information.This contrasts with previous research,which simply linearized the relative pose information of aircraft cameras into navigation states defined in an absolute coordinate system.Specifically,the target pose in relative navigation is defined,and the pose of the camera and feature points are directly derived using dual quaternion representation,which compactly represents both translation and rotation.Furthermore,a mathematical model for the relative pose of the camera is derived through the dual quaternion framework,enabling an explicit pose formulation of relative navigation.The study investigates navigation performance in typical mission flight scenarios using an in-house high-fidelity simulator and quantitatively highlights the contributions of the proposed scheme by comparing the navigation error performance.Consequently,the proposed method demonstrates to have navigation accuracy in decimeter level even in GNSS-denied environments and an improved 3D Root Mean Square(RMS)error by30%smaller than the conventional absolute navigation framework.展开更多
For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over th...For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.展开更多
This paper investigates the problem of controlling a chasing spacecraft(chaser)to track and rendezvous with an uncontrolled target.Based on the actual situation,the torque-free motion of an axisymmetric prolate rigid ...This paper investigates the problem of controlling a chasing spacecraft(chaser)to track and rendezvous with an uncontrolled target.Based on the actual situation,the torque-free motion of an axisymmetric prolate rigid body is employed to represent the short-term attitude motion of the tumbling target.By taking advantage of the dual quaternion’s compact and efficient description of the general rigid motion,the coupled and integrated model of the 6-degree-of-freedom(6-DOF)relative motion between the chaser and the tumbling target is derived in the chaser’s body fixed frame after taking full consideration of coordinate transformation.Based on the logarithm of dual quaternion,a sliding mode control(SMC)law based on the exponential reaching law and the continuous relay function is brought forward to address the problem of synchronization control of the 6-DOF relative motion.Simulation results illustrate the effectiveness of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(60974107)the Research Foundation of Nanjing University of Aeronautics and Astronautics(2010219)~~
文摘The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.
基金Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA).
文摘Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.
文摘This paper proposes a new type of control laws for free rigid bodies. The start point is the dual quaternion and its characteristics. The logarithm of a dual quaternion is defined, based on which kinematic control laws can be developed. Global exponential convergence is achieved using logarithmic feedback via a generalized proportional control law, and an appropriate Lyapunov function is constructed to prove the stability. Both the regulation and tracking problems are tackled. Omnidirectional control is discussed as a case study. As the control laws can handle the interconnection between the rotation and translation of a rigid body, they are shown to be more applicable than the conventional method.
基金supported by Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA)supported by the National Natural Science Foundation of China(No.11971138)+3 种基金the Natural Science Foundation of Zhejiang Province of China(Nos.LY19A010019,LD19A010002)supported by Hong Kong Research Grants Council(Project 11204821)Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA)City University of Hong Kong(Project 9610034).
文摘We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real numbers.We define the magnitude of a dual quaternion,as a dual number.Based upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.
基金Project(2013CB035504)supported by the National Basic Research Program of China
文摘An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.
基金supported by the National Natural Science Foundation of China(6107412761427809)
文摘To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.
基金supported by the National Natural Science Foundations of China (Nos.41101441,60974107, 41471381)the Foundation of Graduate Innovation Center in NUAA(No.kfjj130133)
文摘A bundle adjustment method of remote sensing images based on dual quaternion is presented,which conducted the uniform disposal corresponding location and attitude of sequence images by the dual quaternion.The constraint relationship of image itself and sequence images is constructed to compensate the systematic errors.The feasibility of this method used in bundle adjustment is theoretically tested by the analysis of the structural characteristics of error equation and normal equation based on dual quaternion.Different distributions of control points and stepwise regression analysis are introduced into the experiment for RC30 image.The results show that the adjustment accuracy can achieve 0.2min plane and 1min elevation.As a result,this method provides a new technique for geometric location problem of remote sensing images.
基金supported by the Sejong Fellowship Program,South Korea(No.NRF-2022R1C1C2009014)the Basic Research Program(No.NRF-2022R1A2C1005237)from Korean National Research Fund。
文摘This paper addresses a cooperative relative navigation problem for multiple aerial agents,relying on visual tracking information between vehicles.The research aims to investigate a sensor fusion architecture and algorithm that leverages partially available absolute navigation knowledge while exploiting collaborative visual interaction between vehicles in mission flight areas,where satellite navigation-denied regions are irregularly located.To achieve this,the paper introduces a new approach to defining the relative poses of cameras and develops a corresponding process to secure the relative pose information.This contrasts with previous research,which simply linearized the relative pose information of aircraft cameras into navigation states defined in an absolute coordinate system.Specifically,the target pose in relative navigation is defined,and the pose of the camera and feature points are directly derived using dual quaternion representation,which compactly represents both translation and rotation.Furthermore,a mathematical model for the relative pose of the camera is derived through the dual quaternion framework,enabling an explicit pose formulation of relative navigation.The study investigates navigation performance in typical mission flight scenarios using an in-house high-fidelity simulator and quantitatively highlights the contributions of the proposed scheme by comparing the navigation error performance.Consequently,the proposed method demonstrates to have navigation accuracy in decimeter level even in GNSS-denied environments and an improved 3D Root Mean Square(RMS)error by30%smaller than the conventional absolute navigation framework.
基金supported by the National Natural Science Foundation of China (No. 61174126)
文摘For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.
基金supported by the National Science Foundation of China(61427809)
文摘This paper investigates the problem of controlling a chasing spacecraft(chaser)to track and rendezvous with an uncontrolled target.Based on the actual situation,the torque-free motion of an axisymmetric prolate rigid body is employed to represent the short-term attitude motion of the tumbling target.By taking advantage of the dual quaternion’s compact and efficient description of the general rigid motion,the coupled and integrated model of the 6-degree-of-freedom(6-DOF)relative motion between the chaser and the tumbling target is derived in the chaser’s body fixed frame after taking full consideration of coordinate transformation.Based on the logarithm of dual quaternion,a sliding mode control(SMC)law based on the exponential reaching law and the continuous relay function is brought forward to address the problem of synchronization control of the 6-DOF relative motion.Simulation results illustrate the effectiveness of the proposed method.