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One of the simplest and most popular methods to design a model-based controller for a nonlinear dynamic system is to apply linear control theories to the linearized model of the nonlinear system. For linearization, first-order Taylor series expansion is a straightforward and widely used method. Although the related linearization method is fairly simple, unfortunately, it causes an error in the linearized model, especially in highly nonlinear systems. Different strategies have been proposed to increase the robustness of linearization-based control methods against the linearization error. All of the methods somehow look at the linearization error as uncertainty or disturbance, which has to be rejected. Generally speaking, the lack of the linearization technique reduces the quality of control. One area in which quality and simplicity of control can be necessary is spacecraft attitude control. For the purpose of spacecraft attitude control, this paper improves a well-known trajectory linearization control (TLC) method as a simple and practical nonlinear trajectory tracking control method using an error-less, fine linearization technique. The modified TLC is then used to develop a control law for spacecraft attitude control with only three tunable control parameters and an approximation of the spacecraft inertia matrix. Finally, due to the elimination of uncertainty caused by the linearization error, in a simple way, the novel attitude controller leads to better performance in comparison with the traditional method. The superiority of the new approach is illustrated in numerical simulations.

Accurate estimation of the dynamic parameters comprising a robot's dynamics model is of paramount importance for simulation and real-time model-based control. The conventional approaches for obtaining the identification model are extremely cumbersome, and incapable of offering universal applicability, as well as physical feasibility of dynamic parameter identification. To this end, the work presented herein proposes a novel and generic identification methodology, for retrieving the dynamic parameters of serial manipulators with arbitrary degrees of freedom (DOFs), based on the Lie theory. In this approach, the robot dynamics model that includes frictional terms is analytically represented as a closed-form matrix equation, by rearranging the classical recursive Newton–Euler formulation. The link inertia matrix that comprises inertia tensors, masses, and Center of Mass (CoM) positions, together with the joint friction coefficients, are extracted from the regrouped linear dynamics model by means of the Kronecker product. Meanwhile, the introduced Kronecker–Sylvester identification equation is formulated as an optimization problem involving dynamic parameters with physical feasibility constraints, and is ultimately estimated via linear matrix inequality techniques and semidefinite programming using joint position, velocity, acceleration, and torque data. Identification results of dynamic parameters are accurately procured through a series of practical tests that entail providing a seven-DOF Rokae xMate robot, with optimized Fourier-series-based excitation trajectories. Experimental validation serves the purpose of demonstrating the proposed method's efficacy, in terms of accurately retrieving a serial manipulator's dynamic parameters.

Only partial system knowledge for the generalized robotic dynamics with input saturation, i.e., the regression matrix for the specific robot, is required to design the proposed adaptive finite-time saturated tracking control (AFTSTC). It contains a nonlinear auxiliary tracking error, which can shape the system frequency response. As the operating point is in the neighborhood of the zero auxiliary tracking error, nonlinear filtering gains can be increased to accelerate its tracking ability. Moreover, the traditional skew-symmetric matrix’s condition for the time derivative of inertia matrix and the Coriolis and centrifugal force matrix is not necessarily required such that the uncertainties and the finite-time convergence are reduced. The computational complexity as compared with the fuzzy neural network adaptive control is also addressed. The stability of the closed-loop system is verified by the Lyapunov stability theory. Finally, two practical robotic examples are given to validate the effectiveness and robustness of the proposed control.

This article presents a novel proportional-integral approximation-free control (PIAFC) for nonlinear robotic systems with unknown Coriolis and gravity dynamics. One key merit is to transform the original motion tracking problem into an alternative system stabilization problem by introducing prescribed performance functions (PPFs) and the associated error transformation. Another idea is to develop a proportional-integral error compensation mechanism and incorporate it into the approximation-free control synthesis, such that the tracking error converges to zero in the steady-state. In this framework, only the inertia matrix is required and the computationally demanding function approximators are avoided, while the unknown Coriolis and gravity dynamics can be effectively handled. Moreover, the transient tracking error can be retained within a preset boundary. Stability analysis of the closed-loop control system is carried out in terms of the Lyapunov theorem. Finally, extensive comparative simulations and experimental results on a realistic SCARA robotic test-rig illustrate the superiority of the suggested method over several other methods.

In this paper, we present a model for the inverse dynamics of underactuated manipulators that is free from inertial coupling singularities. The framework’s main idea is to include a small-amplitude wave on the trajectory of the rotating active joints. First, we derive the modified nonlinear dynamics for the multijoint manipulators with multiple degrees-of-freedom (DoF). Next, a 4-DoF mass-rotating underactuated manipulator with two passive and two active joints is chosen. Then, a condition assuming the positive definiteness of the inertia matrix is developed to have the singularity-free inverse dynamics. Finally, we analytically study how singularities can be avoided and show an example simulation with a feed-forward control at the singular configuration.

The problem of attitude takeover control of spacecraft by using cellular satellites with limited communication, actuator faults and input saturation is investigated. In order to lighten the communication burden of cellular satellites, an event-triggered control strategy is adopted. The filtered attitude information needs to be transmitted only when the defined measurement error reaches the event-triggered threshold in this strategy. Then, to deal with the unknown inertia matrix, actuator faults, external disturbances and the errors caused by event-triggered scheme, fuzzy logic systems is introduced to estimate the uncertainties directly. Combining fuzzy logic control strategy and the event-triggered method, the first event-triggered adaptive fuzzy control law is developed. Then, torque saturation of cellular satellites is further considered in the second control law, where the upper bound of the uncertainties is estimated by fuzzy logic systems. The resulting closed-loop systems under the two control laws are guaranteed to be bounded. Finally, the effectiveness of two proposed control laws is verified by the numerical simulations.

This paper presents a method for preliminary design of the control which is needed to achieve underwater vehicle trajectories. The proposed way allows one to evaluate dynamics of underwater vehicle using a trajectory tracking control algorithm. At the first stage, we propose the controller, and at the second, we test dynamics of the system based on the properties resulting from the transformed equations of motion and the selected indexes. The controller, which is applicable for fully actuated vehicles, contains the system dynamics in the control gains. It takes into account not only model of the vehicle but also model of disturbances. The way for the dynamics investigation uses the transformed equations obtaining from the inertia matrix decomposition. Consequently, thanks to the observed properties, it is possible to estimate dynamics using the criteria set. The method is useful before real experiment to test various models of the vehicle, disturbances, and the control task. The procedure is based on simulation tests and the proposed criteria. Effectiveness of the approach is shown on two examples of 6 DOF underwater vehicle model and its modifications.

This paper develops a novel regressor-free robust controller for rigid robots whose dynamics can be described using the Euler–Lagrange equations of motion. The function approximation technique (FAT) is used to represent the robot’s inertia matrix, the Coriolis matrix, and the gravity vector as finite linear combinations of orthonormal basis functions. The proposed controller establishes a robust FAT control framework that uses a fixed control structure. The control objectives are to track reference trajectories in worst case scenarios where the robot dynamics are too costly to develop or otherwise unavailable. Detailed stability analysis via Lyapunov functions, the passivity property, and continuous switching laws shows uniform ultimate boundedness of the closed-loop dynamics. The simulation results of a three-degree-of-freedom (DOF) robot when the robot parameters are perturbed from their nominal values show good robustness of the proposed controller when compared with some well-established control methods. We also demonstrate success in the real-time experimental implementation of the proposed controller, which validates practicality for real-world robotic applications.

In this paper, we propose an alternative, simple, yet efficient estimation method to handle unknown dynamics and external disturbances for motion control of robotic systems. An unknown system dynamics estimator (USDE) is first proposed by introducing filter operations and simple algebraic calculations, where the external disturbances and unknown Coriolis/gravity dynamics can be estimated simultaneously. In the specific case where only the external disturbance is unknown, a further modified unknown disturbance estimator (MUDE) is introduced. These proposed USDE and MUDE can be easily implemented and their parameter tuning is straightforward compared with the nonlinear disturbance observer that requires calculation of the inverse of the inertia matrix. The acceleration signal of robotic joints is not used in the design of estimators. Moreover, we also show that the proposed estimators can be incorporated into the design of composite controllers to achieve satisfactory motion tracking response. The closed-loop control system stability and convergence of both the tracking error and estimation error are all guaranteed. Finally, the effectiveness of the two proposed methods is validated by using simulations and experiments based on a SCARA robot test-rig.

A time-delayed control (TDC) method is known as a simple, robust and non model-based control scheme that requires the fast sampling time, the accurate measurement of joint acceleration signals, and the accuracy of the inertia model of a robot manipulator. Among them, sampling time and acceleration signals are hardware dependent and can be solved. Then a user specified inertia model becomes a key role for the performance of TDC. When the selection of the diagonal element of the inertia matrix of a robot manipulator is used, the ill selection of the constant inertia matrix may lead to the poor tracking performance as well as instability. In addition, an appropriate selection of an inertia matrix for different tasks of the robot is not easy. Therefore, in this paper, an intelligent way of using a neural network is proposed to compensate for the deviation of the constant inertia matrix of a robot manipulator. The role of the neural network is to improve the tracking performance of a robot manipulator by compensating for the deviated error of the inertia matrix while satisfying the stability bound. Simulation studies of a three link robot are presented to confirm the proposal.

This paper studies the pose tracking control problem for satellite proximity operations between a target and a chaser satellite, by which we mean that the chaser is required to track a desired time-varying trajectory given in advance with respect to the target. Firstly, by consulting an adaptive sliding-mode control method in literature developed for a class of nonlinear uncertain systems, an effective pose tracking controller is obtained. This controller requires no information about the mass and inertia matrix of the chaser, and takes into account the gravitational acceleration, the gravity-gradient torque, the J2 perturbing acceleration, and unknown bounded disturbance forces and torques. Then, an updated controller is proposed by combining the aforementioned controller and the unscented Kalman filter (UKF). This updated controller estimates the inertial parameters of the chaser through UKF, so it is of better adaptive ability to the initial estimation of the inertial parameters. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed controllers. The simulation results show that the updated controller is more accurate.

To analyze the rigid–flexible coupling effects on the dynamic performance of a robot system, a dynamic model of a parallel robot with flexible spatial links is derived in detail using a floating frame of reference (FFR) formulation. Compared to the previous rigid–flexible coupling model where the kinematic chains are all flexible links or where the joints are all flexible components, the inertia matrix and the stiffness matrix are not constant matrix which leading to the differences in respect of dynamic performance in model. To verify the correctness of the derived dynamics equations, the dynamics solutions of the spatial parallel robot from an ideal rigid–body model and the FFR model containing rigid and flexible coordinates were established by an FFR formulation. Furthermore, a finite element analysis (FEA) model, which included rigid links and flexible spatial links, was constructed for comparison. The comparison of the three models showed that the trajectory trends were the same, but the motion trajectories of the end-effector obtained by the FFR and FEA models varied within a certain range, and the maximum variations occurred at the peaks of the trajectories. However, since the FFR model considered the coupling effects of rigid and flexible links and the micro-displacement of the end-effector, the amount of deformation was the largest.

This paper presents a reduced-order extended state observer (ESO) based sliding mode control scheme for friction compensation of a three-wheeled omnidirectional mobile robot. Compared with previous works, the proposed control approach is attractive from an implementation point of view. It does not require any explicit friction model, with quite low computation cost. First, a dynamic model with unknown friction forces is given. Then, the controller is designed, consisting of two parts. One part of the control effort is to compensate the friction effects, which are estimated by a reduced-order ESO without using any explicit friction model. The inverse of inertia matrix is also avoided in the proposed reduced-order ESO. The other part of the control effort is designed based on a second-order sliding mode technique known as super-twisting algorithm, in presence of parameter uncertainties. In addition, stability analysis of the designed control system is presented. Extensive experiments are conducted to verify the effectiveness and robustness of the proposed control design in compensating different friction effects.

In this paper, an observer-based adaptive backstepping attitude maneuver controller (briefly, OBABC) for flexible spacecraft is presented. First, an observer is constructed to estimate the flexible modal variables. Based on the proposed observer, a backstepping control law is presented for the case where the inertia matrix is known. Further, an adaptive law is developed to estimate the unknown parameters of the inertia matrix of the flexible spacecraft. By utilizing Lyapunov theory, the proposed OBABC law can guarantee the asymptotical convergence of the closed-loop system in the presence of the external disturbance, incorporating with the L2-gain performance criterion constraint. Simulation results show that the attitude maneuver can be achieved by the proposed observer-based adaptive backstepping attitude control law.

Unmanned surface vessels (USVs) are supposed to be able to adapt unstructured environments by means of multi-sensor active perception without any human interference, and high-accuracy path following is achieved for USVs by effective control strategies and intelligent devices of e-navigation. This paper proposes a finite-time predictor line-of-sight (LOS)-based integral sliding-mode adaptive neural (FPISAN) scheme for the path following of USVs in the presence of unknown dynamics and external disturbances, which copies with the problem of merging with the kinematic level and the kinetic level of USVs. From the point of view of USVs’ practical engineering, the inertia matrix of USVs maintains nonzero off-diagonal. In order to ensure that USVs can converge to and follow a defined path, a novel LOS-based guidance law that can acquire sideslip angles by error predictors within a finite time is presented, called finite-time predictor-based LOS (FPLOS). Then, the path-following control laws are designed by combining the neural network (NN) technique with the integral sliding-mode method, where radial basis function NN (RBFNN) is applied to approximate lumped unknown dynamics induced by nonparametric uncertainties and external disturbances. The theoretical analysis verifies that the path-following guidance-control system of USVs is semiglobally uniformly ultimately bounded (SGUUB) with the aid of Lyapunov stability theory. The effectiveness and performance of this presented scheme are illustrated by simulation experiments with the comparison. Note to Practitioners —The design of heading guidance laws and path-following control laws for path following of USVs subject to unknown dynamics and external disturbances is a critical problem, which affects the development of USVs. This problem associated with practical engineering of USVs due to the actual navigation environment that is complex, diversified, and highly unstructured. This paper presents a wholly tight strategy to compensate for unknown sideslip angles and approximate lumped unknown dynamics. Hence, an effective scheme being denoted FPISAN mentioned above is developed for path following of USVs.

For the free-floating space manipulator with free-swinging joint failure, motions among its active joints, passive joints, free-floating base, and end-effector are coupled. It is significant to make clear all motion coupling relationships, which are defined as “kinematic coupling relationships” and “dynamic coupling relationships,” inside the system. With the help of conservation of system momentum, the kinematic model is established, and velocity mapping relation between active joints and passive joints, velocity mapping relation between active joints and base, velocity mapping relation between active joints and end-effector. We establish the dynamic model based on the Lagrange equation, and the system inertia matrix is partitioned according to the distribution of active joints, passive joints, and the base. Then, kinematic and dynamic coupling relationships are explicitly derived, and coupling indexes are defined to depict coupling degree. Motions of a space manipulator with free-swinging joint failure simultaneously satisfy the first-order nonholonomic constraint (kinematic coupling relationships) and the second-order nonholonomic constraint (dynamic coupling relationships), and the manipulator can perform tasks through motion planning and control. Finally, simulation experiments are carried out to verify the existence and correctness of the first-order and second-order nonholonomic constraints and display task execution effects of the space manipulator. This research analyzes the kinematic and dynamic characteristics of the free-floating space manipulator with free-swinging joint failure for the first time. It is the theoretical basis of free-swinging joint failure treatment for a space manipulator.

In this work, the H ∞ control for mechanical systems and its application in Robotics is discussed. The controller is designed in discrete time and it is synthesized for mechanical systems that are modeled by means of the Euler–Lagrange formulation. Making use of the discrete Hamilton–Jacobi–Isaacs equation the control law is derived. The discrete control law is then applied to a continuous-time 6-DoF bipedal robot model in order to track the walking pattern references for each link. The system along with the control law is simulated, with the system subjected to an external disturbance that emulates the action of a group of unknown bounded forces over the links of the bipedal robot. Furthermore, an algorithm to diminish the effect of the disturbance is proposed such that the full knowledge of the plant is not needed but only the linear part of the mass and inertia matrix; this algorithm is combined with the H ∞ controller and applied to a robotic arm. Finally, this work is compared to a similar approach that uses H ∞ technique in continuous time.

Knowing the dynamic properties of a non-cooperative spacecraft is critical for robotic capture and service in orbit. However, using visual observation alone is not sufficient to identify all the inertial parameters (the mass, mass center location, and inertia matrix) of an unknown target object. This paper presents a method to fully identify all the inertial parameters of a non-cooperative object in orbit with data from visual and force-moment sensors. We propose to use a flexible rod to change a target's movement, which is a prerequisite to identify the true values of the target's dynamic properties. A novel algorithm for processing the collected force and torque data is introduced, which reduces the effect of noise on the identification accuracy. Simulation results have shown that for a large target, we only need to apply a very small force to completely identify all the inertial parameters with an acceptable error in the presence of sensor measurement errors as well as a rough initial guess.

This brief is devoted to the fixed-time six-DOF tracking control problem for noncooperative spacecraft fly-around mission in the presence of the parameters uncertainties and disturbances. First, a new and coupled six-DOF relative motion dynamic model without using any target orbital information is established. Subsequently, a novel nonsingular fixed-time terminal sliding mode (NFTSM) with bounded convergence time in regardless of the initial states is designed, which not only can circumvent the singularity problem, but also has faster convergence performance than fast terminal sliding mode. By employing the designed NFTSM and the adaptive technique, a continuous adaptive nonsingular fixed-time fast terminal sliding mode control strategy with no information of the mass, inertia matrix, and disturbances is proposed, which can eliminate the chattering phenomenon and guarantee the fixed-time reachability of the relative position and attitude tracking errors into the small regions containing the origin. Finally, the performance of the proposed control schemes is demonstrated by numerical simulations.

The recently developed Vector Inertia Tensor Attitude Estimation, VITAE, method is enhanced by the addition of two different preprocessing algorithms that modify the observation vectors prior to attitude estimation. The first preprocessing algorithm is for use in cases that have one observation vector that is much more accurate than the other observation vectors. Such cases suffer numerical error caused by the large relative weight of the very accurate observation vector. Use of the preprocessing algorithm eliminates large variation in vector weights and resulting numerical error. The second preprocessing algorithm enables VITAE to generate results equivalent to a very accurate suboptimal attitude determination algorithm that produces results extremely close to the optimum solution. Preprocessing algorithms eliminate the need to select observation vector weights to remove eigenvalue degeneracy and allows the weights to be based solely on optimality, thereby improving estimation accuracy. When optimum weights are used, the inertia matrix is recognized as the information matrix, which links VITAE to other attitude estimation algorithms. The preprocessing algorithms used with VITAE were able to uncover erroneous results in a few published test cases. The VITAE solutions were validated analytically, through the inertia matrix’s inverse relationship to the error covariance matrix. A loss function comparison is also included to further validate the preprocessing algorithms and related VITAE solution.

In this paper application of a nonlinear tracking control algorithm for dynamics testing of underwater vehicles is presented. The controller, suitable for fully actuated vehicles, is based on a velocity transformation which results from the inertia matrix decomposition. After use of the transformation some properties of the system dynamics are observable. The matrices containing the dynamical parameters set are included next into the control gain matrices. Consequently it is possible, introducing a set of indexes, to propose a procedure for dynamics investigation. The approach can serve as a useful tool before experiment because it gives an insight into the vehicle dynamic model. The simulation studies demonstrated on a 6-DOF underwater vehicle model show effectiveness of the given strategy.

This paper presents a unifying dynamics formulation for nonsmooth multibody systems (MBSs) subject to changing topology and multiple impacts based on a linear projection operator. An oblique projection matrix ubiquitously yields all characteristic variables of such systems as follows: (i) the constrained acceleration before jump discontinuity from the projection of unconstrained acceleration, (ii) post-impact velocity from the projection of pre-impact velocity, (iii) impulse during impact from the projection of pre-impact momentum, (iv) generalized constraint force from the projection of generalized input force, and (v) post-impact kinetic energy from pre-impact kinetic energy based on projected inertia matrix. All solutions are presented in closed-form with elegant geometrical interpretations. The formulation is general enough to be applicable to MBSs subject to simultaneous multiple impacts with nonidentical restitution coefficients, changing topology, i.e., unilateral constraints becoming inactive or vice versa, or even when the overall constraint Jacobian becomes singular. Not only do the solutions always exist regardless of the constraint condition, but also the condition number for a generalized constraint inertia matrix is minimized in order to reduce numerical sensitivity in computation of the projection matrix to roundoff errors. The model is proven to be energetically consistent if a global restitution coefficient is assumed. In the case of nonidentical restitution coefficients, the set of energetically consistent restitution matrices is characterized by using a linear matrix inequality (LMI).

This study investigates the vibration mode structure of general cyclically symmetric systems with central components vibrating as three-dimensional rigid bodies. This work does not rely on the assumptions of the system matrix symmetries; asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of a general cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem, all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure.

In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains. The results reported here follow the same research line as (Donaire et al., 2016a) and (Romero et al., 2016a) bridging the gap between the Hamiltonian and the Lagrangian formulations used, correspondingly, in these papers. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

We consider new polynomially solvable cases of the well-known Quadratic Assignment Problem involving coefficient matrices with a special diagonal structure. By combining the new special cases with polynomially solvable special cases known in the literature we obtain a new and larger class of polynomially solvable special cases of the QAP where one of the two coefficient matrices involved is a Robinson matrix with an additional structural property: this matrix can be represented as a conic combination of cut matrices in a certain normal form. The other matrix is a conic combination of a monotone anti-Monge matrix and a down-benevolent Toeplitz matrix. We consider the recognition problem for the special class of Robinson matrices mentioned above and show that it can be solved in polynomial time.

This paper investigates a quasi-model free control (QMFC) approach for the post-capture control of a non-cooperative space object. The innovation of this paper lies in the following three aspects, which correspond to the three challenges presented in the mission scenario. First, an excitation-response mapping search strategy is developed based on the linearization of the system in terms of a set of parameters, which is efficient in handling the combined spacecraft with a high coupling effect on the inertia matrix. Second, a virtual coordinate system is proposed to efficiently compute the center of mass (COM) of the combined system, which improves the COM tracking efficiency for time-varying COM positions. Third, a linear online corrector is built to reduce the control error to further improve the control accuracy, which helps control the tracking mode within the combined system's time-varying inertia matrix. Finally, simulation analyses show that the proposed control framework is able to realize combined spacecraft post-capture control in extremely unfavorable conditions with high control accuracy.

The inertial pointing problem of a rigid satellite by solely magnetic torqueing is considered in this paper. To ensure globally uniformly ultimately bounded motion about the reference in inertial space, a sliding mode attitude control law, which consists of equivalent and reaching control terms, based on a novel time-varying sliding manifold is designed. The originality of the sliding manifold relies on the inclusion of two time-integral terms. The usage of the proposed sliding manifold makes the application of the equivalent control method to the considered problem possible, and it is proven that the state trajectories reach the newly designed sliding manifold in finite time even under the effect of four realistically modeled disturbance components and parametric uncertainty of all inertia matrix entries. For the constructed purely magnetic attitude control system, stability and existence of the sliding mode as well as state trajectories' finite time convergence to the sliding manifold are demonstrated via Lyapunov function techniques. The results of a simulation example verify the robust stability of the designed attitude control system. The steady state performance of the attitude control system is evaluated in the altitude range of low-Earth-orbits. Robust and global attitude stabilization of magnetically actuated spacecraft... | Request PDF. Available from: https://www.researchgate.net/publication/322964566_Robust_and_global_attitude_stabilization_of_magnetically_actuated_spacecraft_through_sliding_mode [accessed Mar 22 2018].

Using nanosatellites to reclaim a failed satellite needs nanosatellites to attach to its surface to take over its attitude control function. This is challenging, since parameters including the inertia matrix of the combined spacecraft and the relative attitude information of attached nanosatellites with respect to the given body-fixed frame of the failed satellite are all unknown after the attachment. Besides, if the total control capacity needs to be increased during the reclaiming process by new nanosatellites, real-time parameters updating will be necessary. For these reasons, an integrated identification and control method is proposed in this paper, which enables the real-time parameters identification and attitude takeover control to be conducted concurrently. Identification of the inertia matrix of the combined spacecraft and the relative attitude information of attached nanosatellites are both considered. To guarantee sufficient excitation for the identification of the inertia matrix, a modified identification equation is established by filtering out sample points leading to ill-conditioned identification, and the identification performance of the inertia matrix is improved. Based on the real-time estimated inertia matrix, an attitude takeover controller is designed, the stability of the controller is analysed using Lyapunov method. The commanded control torques are allocated to each nanosatellite while the control saturation constraint being satisfied using the Quadratic Programming (QP) method. Numerical simulations are carried out to demonstrate the feasibility and effectiveness of the proposed integrated identification and control method.

In order to improve the convergence rate of standard sliding mode controller, time efficient controllers based on Bang–Bang logic for satellite attitude stabilization and tracking control are developed in this paper. The time efficient open-loop control algorithm Bang–Bang control is combined with closed-loop sliding mode control to improve system robustness. A two-stage structure sliding mode with a fixed angular velocity stage and a fixed deceleration stage is proposed in this paper. The sliding mode parameter is real-time updating hence the modified sliding mode could have Bang–Bang character. The system inertia matrix uncertainty and disturbance torque is discussed and the controller proposed in this paper is robust to the perturbation. The control torque constraint is also discussed and the constraint on control parameters is given. The performance of the controller is demonstrated by numerical simulation.

This paper discusses the range of the eigenvalues of a class of matrices. By using the eigenvalues range of a class of matrices, an extension of the inner product type Cauchy–Schwarz inequality is obtained, the convergence proof of the least squares based iterative algorithm for solving the coupled Sylvester matrix equations is given and the best convergence factor is determined. Moreover, by using the eigenvalues range of this class of matrices, an iterative algorithm for solving linear matrix equation is established. Three numerical examples are offered to illustrate the effectiveness of the results suggested in this paper.

This paper addresses robust attitude tracking by considering bounded external disturbances and uncertain inertia matrix. Rotation vector is adopted for attitude representation. On this basis, controller design is addressed for robust unwinding-free attitude tracking using a backstepping procedure based on similar skew-symmetric structure. A variable gain is included in the disturbance compensation term to enhance tracking precision with limited control strength. Compared with the related research works, the derived controller has a simple structure and a high computation effectiveness. Furthermore, the attitude tracking precision is prominently improved with limited control amplitude by introducing a variable gain in the proposed controller.

Perpetual points in mathematics defined recently, their significance, in systems dynamics is ongoing research. In linear unforced mechanical systems, the perpetual points are associated with rigid body motion, and they are not just a few points, but they form the perpetual manifolds. The mechanical systems with perpetual manifolds the rigid body motion are called perpetual mechanical systems. The concept of perpetual manifolds has been extended to the augmented perpetual manifolds of multidegree of freedom system, that the accelerations are equal but not necessarily zero. This is the case of externally forced perpetual mechanical systems that are moving in rigid body motion. A theorem defines the conditions that an externally forced mechanical system moves as a rigid body with state–space the exact augmented perpetual manifolds. Herein following this theorem, a corollary is written and proved. The corollary is about the perpetual mechanical system with nonlinear forces, and the perpetual one with linear internal forces. More precisely for the same time and state-dependent inertia matrix, and the same external forcing they have the same solution or otherwise stated their exact augmented perpetual manifolds that define their state space are the same. Therefore for the same initial conditions, they have the same motion. The theory, analytically and numerically, with two examples, is verified with excellent agreement. The significance of this work is that there is no need for complicated modeling and model update of nonlinear internal forces of mechanical systems when rigid body motions are the target.

The failure configuration which consists of four single-gimbal control moment gyroscopes (SGCMGs) of the widely-used regular pentagonal pyramid SGCMG system, i.e. failure 4-SGCMG configuration, is investigated in this paper. On account of the symmetry of regular pentagonal pyramid configuration, a conversion method which could transform any failure 4-SGCMG configuration to the chosen failure system is introduced. Then, the zero-momentum gimbal angle of the chosen failure system is derived and its distribution in gimbal angle space is analyzed. In order to avoid internal singularity, preferred initial gimbal angles are calculated basing on derivation of zero-momentum gimbal angles and the corresponding terminal singular surfaces are obtained through numerical simulations. Furthermore, a constraint about maneuver direction is introduced and a robust gimbal reorientation steering strategy is proposed. Finally, simulations on a non-chosen failure configuration with inertia matrix uncertainty demonstrate the effectiveness of the conversion method and robustness of the proposed steering law.

The problem of solving periodic Sylvester matrix equations is discussed in this paper. A new kind of iterative algorithm is proposed for constructing the least square solution for the equations. The basic idea is to develop the solution matrices in the least square sense. Two numerical examples are presented to illustrate the convergence and performance of the iterative method.

This paper introduces another version of biconjugate residual method (BCR) for solving the generalized coupled Sylvester matrix equations over centrosymmetric or anti-centrosymmetric matrix. We prove this version of BCR algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round-off errors. Furthermore, a method is provided for choosing the initial matrices to obtain the least norm solution of the problem. At last, some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed.

A hierarchical control architecture is presented for energy-efficient control of robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation limits, and yet minimizing the power losses in the joint actuators. The control formulation can incorporate the nonlinear friction cone constraints into the control without recourse to the common linear approximation of the constraints or introduction of slack variables. A performance metric is introduced that allows trading-off the multiple constraints when otherwise finding an optimal solution is not feasible. Moreover, the projection-based controller does not require the minimal-order dynamics model and hence allows switching contacts that are particularly appealing for legged or walking robots. The fundamental properties of constrained inertia matrix derived are similar to those of general inertia matrix of the system, and subsequently these properties are greatly exploited for control design purposes. The problem of task space control with minimum (point-wise) power dissipation subject to all physical constraints is transcribed into a quadratically constrained quadratic programming that can be solved by barrier methods. Experimental results are appended to comparatively demonstrate the efficiency and performance of the optimal controller.

Summary The concept of input-to-state stability (ISS) is important in robust control, as the state of an ISS system subject to disturbances can be stably regulated to a small region around the origin. In this study, the ISS property of the rigid-body attitude system with quaternion representation is thoroughly investigated. It has been known that the closed loop with continuous controllers is not ISS with respect to arbitrarily small external disturbances. To deal with this problem, hybrid proportional-derivative controllers with hysteresis are proposed to render the attitude system ISS. The controller is far from new, but it is investigated in a new aspect. To illustrate the applications of the results about ISS, 2 new robust hybrid controllers are designed. In the case of large bounded time-varying disturbances, the hybrid proportional-derivative controller is designed to incorporate a saturated high-gain feedback term, and arbitrarily small ultimate bounds of the state can be obtained; in the case of constant disturbances, a hybrid adaptive controller is proposed, which is robust against small estimate error of inertia matrix. Finally, simulations are conducted to illustrate the effectiveness of the proposed control strategies.

Algorithms of the Bartels–Stewart type for the numerical solution of Sylvester matrix equations of modest size are modified for the case where the linear operators associated with these equations are normal. The superiority of the modified algorithms over the original ones is illustrated by numerical results.

This paper presents a control law that can counter both random disturbance and inertia matrix perturbation in quadrotor attitude stabilization. The control law consists of an ordinary proportional-derivative control and a disturbance compensation. The disturbance compensation is designed by creating a virtual force that always attracts the quadrotor’s state variables back to the equilibrium point. Numerical simulations demonstrate that the control law can counter the effect of the disturbance and perturbation by reducing the upper bound of solution and reducing the vibration effectively.

Finite time controllers robust to inertia matrix uncertainty for satellite attitude stabilization control and attitude tracking control are developed in this paper. A three-stage finite sliding mode is constructed to improve system convergence rate. The singularity issue is solved by using the property of Euler Axis when it's paralleled to angular velocity. Based on this finite time sliding mode, finite time controller is developed to ensure the system state could reach the sliding mode in finite time. System inertia matrix uncertainty and disturbance torque is considered in this paper. The control torque constraint is also considered to ensure the norm of control torque does not exceed system upper bound. Finite time stability of the controller is proved and the controller performance is demonstrated by simulation results.

By keeping in mind the great number of applications of generalized Sylvester matrix equations in systems and control theory, in this paper we establish some necessary and sufficient conditions for the solvability to a system of eight generalized Sylvester matrix equations over the quaternion algebra. The general solution to this system is also constructed when it is solvable. Moreover, an algorithm and a numerical example are also given to make the results of this paper more practical in various fields of engineering. The findings of this paper generalize previous results in the literature.

With the closed-loop structure, parallel manipulators possess some inherent advantages, such as high stiffness, enhanced dynamics, and compact structure. As a result, parallel manipulators gradually gain wide application. In the great variety of parallel manipulators, a kind of high-speed parallel robot, the limb of which is composed of active pendulum and passive parallelogram, gets popular and has realized industrial application firstly. Dynamic performance is the core of the high-speed parallel manipulator, which is usually illustrated through dynamic performance analysis with the aid of the index. Thus, developing reasonable dynamic performance indices is of great theoretical and practical significance for the high-speed parallel manipulator. In this paper, the Coefficient of Variation of joint-space Inertia (CVI) index is proposed to illustrate the acceleration consistency of each limb of the parallel manipulator. By taking the X4 high-speed pick-and-place parallel manipulator as object, the dynamic model and joint-space inertia matrix is established, and the dynamic performance analysis is carried out with the proposed CVI index and the existing Joint-Reflected Inertia (JRI) index. Simulation results illustrate changes of the dynamic performance of the X4 parallel manipulator, and reveal that the JRI index is well complemented with the CVI index. Finally, the workspace with good dynamic performance is discussed. This paper provides a new approach for dynamic analysis and optimal design of high-speed parallel manipulator. Limb Jacobian matrices of the X4 manipulator are given.Dynamic model and inertia matrix of the X4 manipulator are deduced.The CVI index is proposed to evaluate the dynamic performance.Dynamic performance of the X4 mahipulator is analyzed with indices.The workspace with good dynamic performance is disscussed.

In this work, we provide a tracking controller formulation for dynamically positioned surface vessels with an asymmetric added mass terms that affects the overall system dynamics at the acceleration level. Specifically a novel continuous robust controller is proposed for surface vessels that in addition to unstructured uncertainties in its dynamics, contains added mass effects in its inertia matrix. The proposed controller compensates the overall system uncertainties while ensuring asymptotic tracking by utilizing the knowledge of the leading principal minors of the input gain matrix. Stability of the closed–loop system and asymptotic convergence are proven via Lyapunov based approaches. Simulation studies are also presented to illustrate the viability of the proposed method.

An algorithm for computing the antitriangular factorization of symmetric matrices, relying only on orthogonal transformations, was recently proposed. The computed antitriangular form straightforwardly reveals the inertia of the matrix. A block version of the latter algorithm was described in a different paper, where it was noticed that the algorithm sometimes fails to compute the correct inertia of the matrix. In this paper we analyze a possible cause of the failure of detecting the inertia and propose a procedure to recover it. Furthermore, we propose a different algorithm to compute the antitriangular factorization of a symmetric matrix that handles most of the singularities of the matrix at the very end of the algorithm. Numerical results are also given showing the reliability of the proposed algorithm.

A new 3-node triangular hybrid displacement function Mindlin-Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses.