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Electromagnetic formation flight technology utilizes electromagnetic force and torque between satellites to control satellites' relative position and attitude without consuming propellant, thus having broad application prospects. However, the dynamics of electromagnetic formation flying are nonlinear and strongly coupled, posing challenges to the 6-DOF control of electromagnetic formation and the magnetic dipole allocation of satellites. The frequency division multiplexing method can approximate decoupling formation dynamics by loading multi-frequency AC carriers onto satellite magnetic dipoles and is likely to achieve more control functions. A design method for AC carriers based on frequency division multiplexing is proposed to decouple formation dynamics while controlling electromagnetic force and torque. This paper further provides an analytical solution for the magnetic dipoles of the electromagnetic force/torque equations. In addition, in response to external disturbances, model uncertainty, and the inability to obtain relative velocity and angular velocity information of the formation system, this paper establishes a 6-DOF coupling model based on dual quaternion and implements tracking control using the active disturbance rejection control method. Based on the internal force characteristics of the electromagnetic formation, an expression for the equilibrium distribution of reaction wheel torque is derived to avoid some reaction wheels' rapid accumulation of angular momentum. Numerical simulation results show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

• The finite-time velocity-free problem of 6-DOF spacecraft control is considered. • A novel finite-time velocities observer is presented in the dual-quaternion form. • A new observer-based non-singular terminal sliding mode control law is proposed. • The finite-time stability of observer-alone and the system is strictly proved. • The control law can be applied to various tasks by designing the reference frame. This paper addresses the problem of spacecraft's finite-time six-degree-of-freedom(6-DOF) tracking control without velocity measurements. To estimate the unavailable incorporating angular and translational velocities (called the dual angular velocity), a novel observer with a simple structure and finite-time stability is presented in the dual quaternion frame. Then, combining with the estimated dual angular velocity, a continuous velocity-free 6-DOF control law based on the terminal sliding mode theory is presented to achieve the relative pose tracking objective within finite time, where the specially designed parameter ensures its non-singularity. In addition, by designing the desired reference frame, the proposed control law can be employed to various missions. With consideration of the observation errors, a rigorous proof is provided to demonstrate the finite-time stability of the observer-alone and the observer-based control law. Two typical numerical simulations, hovering and circumnavigation, are carried out to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• An algebraic synthesis method is proposed to construct novel single-loop 6R spatial mechanisms. • The mechanisms can achieve constant velocity transmission between designated input/output axes. • All the floating joints of the single-loop 6R spatial mechanisms rotate around fixed axes. • The transmission quality of the mechanisms is optimized within a specified range of motion. • Transmission characteristics of the single-loop mechanisms are verified by kinematics analysis. This paper addresses the algebraic synthesis of novel single-loop 6R spatial mechanisms, enabling constant -1:1 or 1:1 velocity ratio transmission between two adjacent axes, whether parallel, intersecting, or skew. Based on the motion polynomial over dual quaternions, an algebraic synthesis method including four steps is presented to construct and optimize single-loop 6R spatial mechanisms with a constant transmission ratio of -1:1 or 1:1 between arbitrarily designated input and output axes. Using this method, several novel single-loop 6R spatial mechanisms for constant velocity transmission are constructed by designating different poses and rotation directions of the input and output axes. Kinematics analysis of single-loop 6R spatial mechanisms is implemented to verify their transmission characteristics. The results reveal that the generated 1-DOF single-loop 6R novel mechanisms can indeed transmit motion with a constant transmission ratio of -1:1 or 1:1 between two adjacent parallel, intersecting, or skew axes. This work provides a framework for further investigation on single-loop mechanisms with special transmission characteristics. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered integrated attitude and orbit control problem is studied for the distributed spacecraft formation system. First, the operation rules of dual numbers and dual quaternion are presented, and the attitude-orbit coupling error dynamics models for single spacecraft and spacecraft formation are established based on the dual quaternion. An event-triggered attitude-orbit coupled sliding mode tracking control law is proposed to stabilize the attitude-orbit control system, which can reduce the communication burden among spacecraft at the same time. Under the developed control scheme, the state trajectory of attitude-orbit control systems can arrive on the designed sliding surface in finite time, and the asymptotic stability of the overall formation control system can be ensured. Considering the fact that the inertia and mass parameters in practice may not be measured exactly, an adaptive sliding mode control law is further proposed. Finally, a simulation example is given to verify the validity and feasibility of the proposed spacecraft event-triggered control method. [ABSTRACT FROM AUTHOR]

In temporal knowledge graphs (TKGs), the status of facts is intricately tied to the dynamic and precise nature of temporal factors. Existing research merely treats time as supplementary information, without considering the latent semantic changes caused by the positional changes of entities within specific relations in a temporal context. Furthermore, due to the coarse granularity of timestamps in existing TKGs, the number of multiple relations pattern among entities significantly increases, limiting model performance. This paper proposes a T ime- E volving Information and L atent S emantics model (TELS), which represents facts as dual quaternion embeddings to provide a compact and elegant representation. Specifically, we use timestamp dual quaternions, transforming the entity and relation into temporal entity and temporal relation through dual quaternion multiplication. Besides, we introduce semantic-aware dual quaternion to capture the latent semantics arising from the positional changes of entities within specific relations. Next, TELS consists of two parts: (a) We use semantic-aware dual quaternions to perform transformations on head entity and tail entity respectively through dual quaternion multiplication. Next, we utilize temporal relation to transform head entity to tail entity through dual quaternion multiplication. (b) We adopt an evolutionary hierarchical factor to encapsulate the differences in modulus distribution between the temporal head entity and temporal tail entity. In this way, TELS not only uses dual quaternions to handle key patterns and multiple relations pattern, but also handles evolutionary hierarchical patterns by capturing the modulus distribution differences between temporal entities. Meanwhile, TELS learns semantic-aware dual quaternion embeddings to capture the latent semantics endowed by relations to entities. Empirically, TELS can boost the performance over seven temporal knowledge graph benchmarks. [ABSTRACT FROM AUTHOR]

We propose a practical method for computing the singular value decomposition of dual quaternion matrices. The dual quaternion Householder matrix is first proposed, and by combining the properties of dual quaternions, we can implement the transformation of a dual quaternion matrix to a bidiagonalized dual number matrix. We have proven that the singular values of a dual quaternion matrix are same to the singular values of its bidiagonalized dual number matrix. Numerical experiment demonstrates the effectiveness of our proposed method for computing the singular value decomposition of dual quaternion matrices. [ABSTRACT FROM AUTHOR]

In order to solve the problem of noise interference in camera calibration and robot forward kinematics solution, this study proposes a dual quaternion hand-eye calibration algorithm based on twice opposition-learning and random differential variation (ODHPO). The hand-eye calibration equation was innovatively rewritten in the form of dual quaternion, and the F-norm minimization model of the rotation and translation error function was constructed for optimization. At the same time, the penalty function method is introduced to effectively transform the constrained optimization problem in hand-eye calibration into an unconstrained problem, which is further solved by the ODHPO algorithm for global optimization. Compared with the singular value decomposition algorithm based on the traditional dual quaternion method, the ODHPO algorithm performs better in global optimization ability and convergence stability. Through numerical simulation and real robot hand-eye calibration experiments, it is proved that the proposed algorithm is superior to the traditional dual quaternion (CDQ) algorithm, the classical algorithms Tsai method and Navy method in terms of solution accuracy, sensitivity to the number of pose transformations and stability, demonstrating its potential for application and practical significance in robot vision system. ● An improved hunter-prey optimization algorithm with twice opposition-learning and random difference variation is proposed. ● A dual quaternion hand-eye calibration algorithm based on improved hunter-prey optimization is proposed. ● The effectiveness of the improved algorithm is verified by 12 benchmark test functions ● The proposed calibration algorithm is superior to other traditional calibration algorithms [ABSTRACT FROM AUTHOR]

The dual quaternion plays an advantageous role in the field of robotic kinematics and dynamics due to its compact expression. It is well known that quaternion can be easily implemented as algebraic operations on vectors through matrix operators. Similarly, the dual matrix operators can convert dual quaternion operations to matrix operations. However, it has not received adequate attention, and thus there are very few applications at present. With the dual matrix operators of dual quaternion, this paper re-verifies the equivalency between the conjugate formula of unit dual quaternion and dual Euler–Rodrigues formula. To combine this equivalence with the homomorphic mapping of Lie groups, a theoretical correlation of the current hand-eye calibration methods is established. Motivated by the attempt to establish a more complete scheme for hand-eye calibration, a new simultaneous method based on the conjugate formula of dual quaternion is proposed. The method verifies that the rotation problem can be extended to the rigid-body transformation problem via the dual algebra. Finally, the simulation and experimental validations for the hand–eye calibration method are given. • The conjugate formula of unit dual quaternion is re-verified via the dual operations. • A new simultaneous method is defined for hand-eye calibration. • The theoretical correlation with the existing methods is established. [ABSTRACT FROM AUTHOR]

This paper proposes an innovated approach to model an electromagnetic force which is an ideal control force without plume and light pollution for optical imaging system. The main scope is modeling the 3-axis coupled electromagnetic force using dual quaternion for its advantages in describing spiral motion with translation and rotation motion simultaneously. The derivation procedure relies on a far field model of the electromagnetic force, and also, the force is re-formulized. Final equations show the dual quaternion dynamics can express the relative motion caused by the electromagnetic force acting on the position and attitude integrally. A new mission concept of diffraction imaging system in GEO is discussed as application scenario of the new dynamics model. Two cases with different mass were simulated to verify the new model, and the results display the electromagnetic force is significant for a small mass spacecraft in GEO. • The electromagnetic force is expressed by dual quaternion. • A novel dynamics model is derived to describe GEO electromagnetic collocated satellite. • The motion of diffraction imaging system is modelled using dual quaternion. [ABSTRACT FROM AUTHOR]

• An algebraic synthesis method is proposed to form novel multi-loop linkages for rotation scaling. • Multi-loop planar, spherical, and spatial linkages can be constructed using the proposed method. • The generated linkages can exactly transmit angular motion with prescribed transmission ratios. • Exact angular motion transmission between parallel, intersecting, or skew axes is achieved. • Transmission characteristics of the multi-loop linkages are proved by kinematics analysis. This paper deals with the algebraic synthesis and input-output analysis of one degree-of-freedom (1-DOF) multi-loop planar, spherical, and spatial linkages for increasing or decreasing angular motion with a desired constant transmission ratio between two adjacent parallel, intersecting, and skew axes respectively. Based on the rotation scaling model and motion polynomials over dual quaternions, an algebraic synthesis method including three procedures is proposed to exactly construct novel multi-loop linkages owning arbitrarily prescribed constant transmission ratios and input/output axes. To illustrate this method, several 1-DOF multi-loop planar, spherical, and spatial linkages for rotation scaling are synthesized by designating various input and output axes as well as transmission ratios. Taking some multi-loop planar, spherical, and spatial linkages as examples, input-output analysis is carried out to verify their transmission characteristics. The results demonstrate that the generated 1-DOF multi-loop linkages can indeed transmit motion with prescribed constant transmission ratios and input/output axes. This work provides a framework for further investigation on mechanisms performing specified tasks for motion transmission. [ABSTRACT FROM AUTHOR]

Abstract We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of their relevance to kinematics and mechanism science, we put particular emphasis on factorization results for quaternion, dual quaternion and split quaternion polynomials. A general algorithm ensures existence of a factorization for generic polynomials over division rings but we also consider factorizations for non-division rings. We explain the current state of the art, present some new results and provide examples and counter examples. [ABSTRACT FROM AUTHOR]

Abstract To solve the shortcomings of the traditional monocular vision measurement algorithm, which needs to be solved iteratively, this paper proposes a method based on binocular vision for measuring the relative pose of moving rigid bodies. In this paper, the coordinates of the feature points of the follower rigid body coordinate system are obtained by using the method of least squares. At the same time, combined with the dual quaternion algorithm, the leader and follower rigid bodies' coordinate systems are uniformly described, and the model takes the minimum sum of squared errors as the objective function and solves the pose parameters by the dual quaternion method. The simulation results show that the dual quaternion algorithm not only overcomes the shortcomings of the traditional quaternion and translation vector split description coordinate system transformation but also has strong stability; the relative position error is less than 0.05 m, and the relative attitude error is less than 0.2°, which can meet the measurement accuracy requirements of the relative pose of the moving rigid body. [ABSTRACT FROM AUTHOR]

Highlights • Space manipulators can act as actuators for spacecraft due to the dynamic coupling. • Pose control forces provides equality constraints for trajectory planning problem. • Convex optimization method found the globally optimal solution efficiently. • Balance manipulator compensates for coupling and environmental disturbance. Abstract This paper presents a trajectory planning algorithm for a space robot with dual-manipulators. Here one manipulator of the space robot captures a target, and another manipulator is free. In this case, this study uses one manipulator as the mission manipulator to capture the target, and another as the balance manipulator aiming at the compensation of the pose disturbance. For this method, a novel trajectory planning algorithm applied to the balance manipulator is presented. The trajectory planning problem is transformed into series of problems of the optimal state solution, and then the iterative algorithms for the trajectory planning are designed. In the iterative algorithms, the bias force on the spacecraft base caused by the balance manipulator is used as the compensation force. Then, to calculate the expected compensation force and torque, a pose control law for the spacecraft base is introduced. The expected compensation force and torque provide equality constraints for optimization problems, which implies that the trajectory planning algorithm compensates for not only the disturbance generated by the manipulator's motion, but also environmental disturbances. This is because the expected compensation force and torque depend on the pose change of the spacecraft base rather than the type of the disturbance. Numerical simulation was carried out to analyze the proposed trajectory planning method. It was observed that the method greatly reduces the disturbance of Manipulator A on the spacecraft base. These results validated the effectiveness of the proposed method for the trajectory planning to make the spacecraft base disturbance up to minimum. [ABSTRACT FROM AUTHOR]

The avoidance of singularities is critical to design and control of parallel robots. This paper aims at efficient determination of the maximal singularity-free joint space and workspace of a class of six-DOF parallel robots with six kinematic chains of same type. We represent the singularity-free joint space by a 6-cube and determine it firstly. The singularity-free workspace is generated by continuous motion of all active joints in the singularity-free joint space. As a result, the boundary of the workspace can be obtained with simultaneous consideration of position and orientation of the mobile platform. The size relation between the maximal singularity-free joint space and workspace is discussed. To efficiently determine the singularity-free joint space and workspace, we propose dual quaternion-based Jacobian matrices and construct an efficient algorithm. The algorithm detects singularities in a given joint space and simultaneously calculates its corresponding workspace. The computational costs of the proposed algorithm and the traditional one are compared using a 6-U P S parallel robot, leading to 9 seconds and 458 seconds respectively. Finally, both the maximal singularity-free joint space and workspace of a 6- P US parallel robot are determined to further demonstrate the effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of spacecraft attitude and position synchronization in libration point orbits between a leader and a follower. Using dual quaternion, the dimensionless relative coupled dynamical model is derived considering computation efficiency and accuracy. Then a model-independent dimensionless cascade pose-feedback active disturbance rejection controller is designed to spacecraft attitude and position tracking control problems considering parameter uncertainties and external disturbances. Numerical simulations for the final approach phase in spacecraft rendezvous and docking and formation flying are done, and the results show high-precision tracking errors and satisfactory convergent rates under bounded control torque and force which validate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the collision-free distributed coordination control of six-DOF spacecraft formation flying. Dual quaternions are used to develop the kinematic and dynamic models of relative translational and rotational motion between spacecraft. By assuming that the reference relative orbit and attitude information is only available to a subset of members in formation, an observer is introduced to estimate the reference information in finite time. With the estimates provided by the observer, a sliding mode controller is then designed for the coordination of six-DOF formation flying. Meanwhile, the artificial potential function method is employed to design evasive maneuvers in case of any collisions during orbital maneuvering. The overall stability of the closed-loop system is guaranteed by a Lyapunov-based method. The feasibility of the proposed control scheme is then demonstrated by a typical formation reconfiguration mission in a low Earth orbit environment. [ABSTRACT FROM AUTHOR]

The forward kinematics is the basis of the design and control of the parallel robots. This paper aims to provide an efficient solution to the forward kinematics of a class of six-degrees-of-freedom parallel robots for real-time applications. With a unit dual quaternion used as the generalized coordinates of the robot system, the forward kinematic equations are derived to be a set of quadratic ones. An efficient algorithm is proposed to get the actual solution to them. The convergence and singularity problems of the new algorithm have been discussed. We have provided a convergence strategy and revealed the internal relation of the singularity with that of the parallel robot, proving the feasibility of the algorithm and giving the working condition in the practical applications. The new algorithm have been compared to the Newton's method for an 8-U P S parallel robot, resulting in the time consumptions of 0.2187 milliseconds and 14.25 milliseconds respectively. And then we perform a simulation of the state-feedback control for an 8- P US parallel robot. The two examples present the applications of the new algorithm and demonstrate its validity and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a motion control approach with a focus on robotic manipulators based on screw theory and dual quaternions. The stability analysis of a general dual quaternion based controller has been capitalized to design an additional bounded twist controller. This controller is proposed to limit the maximum twist of the end-effector within a desired value, while preserving the accuracy achievable with high-gain feedback controllers. The proposed controllers could be useful for robotic tasks where curved motion is preferred over straight line motion. In that regard, the trajectories taken by the proposed controllers were analyzed for pose-to-pose control and some strategies have been provided for the proposed coupled controller to modify the natural trajectory. These behaviors were verified on a real robot as well as in simulation, comparing the experimental results with conventional decoupled controllers. The proposed controllers achieved smooth coupled motions which can be useful for tasks such as pick and place and assembly operations. Moreover, our coupled controllers based on screw theory need less actuator motion than the conventional decoupled approach for certain situations. • Screw motion controllers are introduced, based on dual quaternions and screw theory. • A generalized dual quaternion controller for meeting different behaviors is proposed. • A general stability proof is introduced for designing dual quaternion controllers. • A comparison is provided between coupled and decoupled controllers for curved motion. • Controllers based on screw theory tend to drive manipulators in screw paths. [ABSTRACT FROM AUTHOR]

This paper exploits screw theory expressed via unit dual quaternion representation and its algebra to formulate both the forward (position+velocity) kinematics and pose control of an n -dof robot arm in an efficient way. Efficiency is in less computer memory usage, in fast computation of the equations, in singularity-free representation of task space, in robustness to numerical errors, and in compactness of the representations. The formulation is simple, intuitive and straightforward to implement. We validated this formulation experimentally on a 7 dof robot arm. [ABSTRACT FROM AUTHOR]

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability. [ABSTRACT FROM AUTHOR]

We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametric curve as trajectory. The minimal motion degree equals the trajectory's degree minus its circularity. Hence, it is lower than the degree of a trivial curvilinear translation for circular curves. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of the high performance adaptive control algorithm for 6-DOF systems described by dual quaternions. The fast adaptation is achieved from the introduced stable adaptation dynamics in the closed-loop system which cannot be expected in the conventional adaptive controller designed upon the certainty equivalence framework. The development of the proposed adaptive control algorithm relies on the two newly introduced algebraic operations. The one is a dual filter for a dual relative error signal. The dual filter essentially has a linear low-pass filter structure and enables us to recast the system dynamics into a linear parameter-affine system dynamics in dual quaternions combined with dual control inputs. The other is an isomorphism between a dual quaternion and a vector for the error measurement. Using this isomorphism, the stability proof of the closed-loop dual quaternion system based on the proposed Lyapunov-like function is rewritten in the form of familiar matrix/vector algebra. In order to demonstrate the performance improvement, numerical simulation results are given, which compare the proposed adaptive control method with the conventional one from the certainty-equivalence principle. [ABSTRACT FROM AUTHOR]

In this paper, a new forward kinematic algorithm based on dual quaternion for a six-degree-of-freedom (DOF) general Stewart Platform is proposed. The algorithm is established after taking into account the pose parameters of joints and the D–H parameters of each branch chain, which yields a precise mathematic model with a total of 174 geometric parameters. The validity of the algorithm is tested using an inverse kinematic algorithm of a general serial manipulator. The forward kinematic algorithms for the 6-6R and 6-2RP3R mechanisms can be expressed by a unified mathematic model. The proposed algorithm can solve the difficult problem of forward kinematics for the unsolved 6-6R parallel manipulator and can also be applied to error analysis, error synthesis, kinematic calibration, stiffness analysis and the accurate kinematic simulation by analysing the effect of geometric parameters on the platform. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce the application of dual quaternions in one interesting problem in structural biology, i.e., the description of protein structure. The secondary protein structure is a specific geometric shape and the description uses Chasles theorem which states that any rigid body displacement can be described by a screw motion. We will briefly introduce the theory of dual quaternions in connection with the screw motion. Consequently, it is shown that modeling based on dual quaternions is an elegant mathematical method and a compact formula for the description of secondary protein structure is derived using the dual quaternion calculus. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a special kind of overconstrained 6R closed linkage which we call angle-symmetric 6R linkage. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite joints. We give a classification of these linkages. It turns out that there are three types. First, we have the linkages with line symmetry. The second type is new. The third type is related to cubic motion polynomials. [Copyright &y& Elsevier]

Abstract: This paper addresses the synchronized control problem of relative position and attitude for spacecraft with input constraint. First, using dual quaternion, the kinematic and dynamic models of the six-degree-of-freedom relative motion of spacecraft are introduced. Second, a new adaptive sliding mode control scheme is proposed to guarantee the globally asymptotic convergence of relative motion despite the presence of control input constraint, parametric uncertainties and external disturbances. A detailed stability analysis of the resulting closed-loop system is included. Finally, simulation results are presented to illustrate the validity and effectiveness of the proposed controller, which has the following properties: (1) explicit accounting for the problem of input constraint, (2) fast convergent rate and accurate results can be obtained, (3) no chattering phenomenon is present in the control torque and control force, (4) self-adaptive regulation law is dynamically adjusted to ensure the tracking errors tend to zero asymptotically, (5) the upper bounds of unknown variables are estimated dynamically. [Copyright &y& Elsevier]

Abstract: Coordinated control problem of translation and rotation between two spacecraft is investigated in this paper. Using dual quaternion, we establish the relative coupled dynamic model in which the coupling effect between translational and rotational motion is indicated. Based on the logarithm of dual quaternion, a model-independent PD-like controller is proposed for spacecraft tracking control problem. The convergence of the closed loop system in the presence of external disturbances is proven theoretically. The validity of the proposed approach is demonstrated by numerical simulations. The advantages of the proposed controller are displayed by comparing with others. [Copyright &y& Elsevier]

Abstract: A line symmetric motion is the motion obtained by reflecting a rigid body in the successive generator lines of a ruled surface. In this work we review the dual quaternion approach to rigid body displacements, in particular the representation of the group SE(3) by the Study quadric. Then some classical work on reflections in lines or half-turns is reviewed. Next two new characterisations of line symmetric motions are presented. These are used to study a number of examples one of which is a novel line symmetric motion given by a rational degree five curve in the Study quadric. The rest of the paper investigates the connection between sets of half-turns and linear subspaces of the Study quadric. Line symmetric motions produced by some degenerate ruled surfaces are shown to be restricted to certain 2-planes in the Study quadric. Reflections in the lines of a linear line complex lie in the intersection of the Study quadric with a 4-plane. [ABSTRACT FROM AUTHOR]

The goal pursued by this article, is to evaluate the potential of sliding-mode control and estimation techniques, to address fault tolerance against a large class of actuator faults, including loss of controllability of the faulty actuator, for autonomous rendezvous between a chaser spacecraft and a passive spacecraft on a circular orbit. The proposed solution is based on the dual quaternion formalism, to describe in a single equation, rotational and translational spacecraft dynamics, solar array flexible modes, propellant sloshing, the most dimensioning space disturbances, and their coupling. Such a modelling formalism enables to propose a six degree-of-freedom fault tolerant control architecture, which relies on the generalized super-twisting control algorithm nested with a nonlinear fault estimator. An anti-windup strategy based on polytope algebra is applied to the control algorithm, to prevent instability due to actuator saturation when faults occur. Asymptotic stability of the proposed fault-tolerant control scheme is formally proved with respect to a wide variety of faults, providing that the first derivatives of the fault estimation error versus time and the sliding surface, are bounded. Intensive simulations from a functional engineering simulator that accurately simulates the rendezvous mission, are presented in the paper, as well as capture-oriented criteria. The presented results demonstrate that the proposed fault-tolerant solution is able to cover any kind of thruster faults, including total loss of controllability of the faulty thruster, as well as solar array flexible modes, propellant sloshing, gravity gradient, the second zonal harmonic, atmospheric drag and magnetic disturbances. [ABSTRACT FROM AUTHOR]

• An algebraic method is proposed to synthesize multi-mode Bennett-based mechanisms. • Several mechanisms with different number of joints are constructed. • Explicit poses of joint axes of the generated mechanisms are obtained. • Multimode characteristics of the generated mechanisms are demonstrated. • 7R Bennett-based mechanisms could have four motion modes comparing to two modes in general. This paper systematically deals with the synthesis of multi-mode single-loop 6R, 7R and 8R Bennett-based mechanisms from an algebraic viewpoint. Based on the factorization of motion polynomials over dual quaternions, an algebraic method is proposed to synthesize multi-mode single-loop 6R, 7R and 8R Bennett-based mechanisms. Using this method, several multi-mode single-loop Bennett-based mechanisms with different number of joints are constructed depending on explicit poses of joint axes. Then motion mode analysis of the 7R mechanism is carried out by formulating and solving a set of kinematic loop equations using tools from algebraic geometry. The analysis demonstrates that this multi-mode 7R mechanism has four motion modes, including a two degree-of-freedom (DOF) double Bennett mode, a 2-DOF hybrid mode, a 1-DOF rotation mode and a 1-DOF spatial 7R mode. Meanwhile, multimode characteristics of the single-loop 6R and 8R mechanisms also are concisely demonstrated in light of reconfiguration analysis. This work provides an algebraic representation framework for further investigation on multi-mode mechanisms that composed of two or more single-loop overconstraint mechanisms. [ABSTRACT FROM AUTHOR]

This paper aims to provide an efficient way for analyzing operation modes and revealing corresponding motion characteristics of lower-mobility parallel mechanisms (LMPMs) using unit dual quaternions. Unit dual quaternions are first classified into 132 cases corresponding to 132 elementary operation modes based on the number of constant zero components. Meanwhile, the kinematic interpretation of these cases is presented in detail. Then a general method for analyzing operation modes and revealing motion characteristics of LMPMs is proposed according to unit dual quaternions and geometrical constraints. By this means, operation modes of LMPMs with complicated constraint conditions can also be analyzed, where a prime decomposition of the ideal corresponding to constraint equations in this condition is infeasible. Taken a 3-RSR LMPM and a 3-RPS LMPM as examples, the operation modes and motion characteristics can be obtained by the proposed approach. It is shown that the former LMPM has seven operation modes including two elementary operation modes and five extra operation modes. Under certain operation modes, the zero-torsion motion of the 3-RSR LMPM can not even be achieved. On the other hand, the latter has two operation modes in which the parasitic motion exists. To gain a deeper insight into the physical meaning of the operation modes, axodes are analyzed and drawn by mean of the velocity operator. It is demonstrated that the 3-RSR LMPM can realize an equal-diameter spherical pure rolling movement with variable diameters and the 3-RPS LMPM can achieve a rolling movement accompanied by sliding. [ABSTRACT FROM AUTHOR]

In traditional pose measurement algorithms, there are many visual measurement solutions for feature points and lines but few for feature circles. In this paper, the feature circle is described by the rotation characteristic of a point around a rotating axis in dual quaternion algebra. Dual vectors are used to describe the feature points, and Plücker lines are used to describe the rotation axis; that is, the dynamic characteristic of the feature point rotating around the Plücker line is used to describe the feature circle, and then the relative position and attitude information between the leader and follower rigid bodies are calculated by the principle of binocular vision measurement. The simulation results show that the algorithm can meet the requirements of the relative pose measurement accuracy of rigid bodies. [ABSTRACT FROM AUTHOR]