Search

This paper establishes a finite time robust controller for the attitude stabilization of the rigid spacecraft. The spacecraft is subjected to inertia matrix uncertainties, external disturbances, and inaccessibility of the angular velocity measurements. The proposed controller is developed by employing a non-singular fast terminal sliding manifold. The bound on the uncertainties are unknown; therefore, the adaptive law is incorporated in the control design to estimate the controller gains. The angular velocity is estimated using a finite time second-order differentiation observer. The output of this observer is then implemented in the proposed controller as state feedback. The closed-loop stability analysis affirms a finite time convergence of sliding manifold, and the system states to the origin. The numerical analysis demonstrates the effectiveness of the proposed closed-loop control system performance under the aforesaid constraints and uncertainties.

Recently, the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology has been extended to underactuated mechanical systems in implicit port-Hamiltonian representation. The method is not restricted to holonomic systems, does not require a positive-definite target inertia matrix and, under general conditions, avoids the need for solving partial differential equations. In this paper we simplify the conditions for (local) stability and present equivalent matching equations. In addition, we exploit the inherent polynomial structure of implicit systems modeled in Euclidean space, such that the implicit IDA-PBC problem can be cast as a linear matrix inequality problem. The method is applicable to desired Hamiltonians with arbitrary polynomial order. The proposed methodology is validated on the portal crane and the cart-pole system.

The ill-conditioning of the joint-space inertia matrix plays an important role in the dynamic behavior of robot manipulators, as well as in the controllers' performance. Indeed, due to the ill-conditioning, small perturbations in the system can produce large changes in the numerical solutions, which can lead to instability. Moreover, this characteristic is intrinsic to a phenomenon of ill-conditioning in the mechanism itself, which suggests that it may be more difficult to control the mechanism. In this context, this paper proposes an adaptive controller to be used together with an algorithm that ensures better conditioning of the inertia matrix. To evaluate the proposed technique, we compared it with two widely used controllers via statistical analysis. The results showed that the proposed adaptive controller presents a better performance than the one based on the inverse dynamics with feedback linearization, and similar results when compared to a PID controller with gravity compensation.

In this paper, a robust finite time control scheme is introduced for trajectory tracking of robot manipulators based on a new sliding mode control (SMC) and time delay estimation (TDE) technique. The suggested control scheme is independent of the robot dynamics, and the upper and lower bounds of the inertia matrix are enough to design the controller. To confirm this claim, at first the boundedness of the TDE errors is analyzed by Lyapunov-Krasovskii approach. Next, a dual terminal SMC (DTSMC) based on TDE is proposed to achieve desirable tracking performance and fast finite convergence time. Meanwhile, the stability of the closed-loop system with the proposed control algorithm is investigated through the Lyapunov method by choosing the appropriate sliding surface. Finally, the effectiveness of the proposed control scheme is shown by some simulations as well as comparing with other types of TDE based SMC schemes.

In this paper, the time-delayed control (TDC) scheme with a sliding mode controller for a robot manipulator is presented. Since TDC suffers from the selection of an inertia matrix of a robot manipulator, the effect of the constant matrix on the performance is investigated. TDC is designed with the sliding mode controller (SMC) to improve the control performance. For the performance comparison between several control schemes, PD control, SMC, TDC, and TDC-SMC are presented. The performances are compared by simulating the same trajectory tracking task of a three link robot manipulator u nder different control schemes.

With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching., Accepted to the American Control Conference, 2020

Mathematical model of a rigid and flexible 4 degrees of freedom (DOF) joint robotic manipulator with executive electric drives has been developed. The mathematical model of the robotic manipulator is designed based on the Lagrange - Euler formula, and the result of calculating the nonlinear inertia matrix, the matrix of Centrifugal and Coriolis forces, and the Gravitational force vector are presented. The mathematical model of the electromechanical drive is developed based on the two-mass model “executive electric drive - mechanism”. Adaptive systems for rigid and flexible robotic manipulators are designed by syntheses on using computed torque (Li-Stoline) method and backstepping (step-by-step synthesis). The calculation and synthesis algorithm was implemented using the Mathcad and Matlab-Simulink software packages.

In this paper, a Takagi-Sugeno (T-S) fuzzy descriptor approach for control of a two-link free-floating space manipulator (FFSM) is proposed. The T-S fuzzy descriptor model of the FFSM is first derived from its nonlinear dynamic model, which makes more sense in reality since it avoids the use of joint acceleration measurement and the inversion of inertia matrix. And some nonlinear terms are considered as uncertainties to balance the complexity and accuracy of the model. Then a robust controller based on the Lyapunov stability theory is designed and reformulated as a linear matrix inequality (LMI) optimization problem which can be efficiently solved with the solver SeduMi. Finally, simulation results are carried out with the SimMechanics to demonstrate the effectiveness of the proposed approach.

This paper deals with the problem of trajectory tracking control for some vehicles (underwater vehicles, and indoor airships). The approach uses a velocity transformation which results from the inertia matrix decomposition. Next, a model-based non-adaptive nonlinear tracking controller in terms of the Generalized Velocity Components (GVC) is proposed. An important property of the algorithm is that the control gains are closely related to the dynamics of the vehicle (especially dynamical couplings). The general algorithm was given for a 6 DOF vehicle and tested using simulation. The results obtained for a full airship model have shown that the control scheme guarantees satisfactory performance.

This work presents a Gauss-Newton gradient-based method for identification of the unknown parameters of the dynamic equations of a two-axis gimbal system and design of a suitable fuzzy controller for it. Among the most important uncertain parameters considered in the dynamic equations of a two-axis gimbal, the components of the inertia matrix, the coriolis matrix, the friction matrix and the torque caused by the distance from the center of gravity to the axis of rotation can be named. The input data is measured in response to a known stimulation by the sensors and used as the reference data for the identification process. Regarding the severe sensitivity of inverse problems to measurement errors, using a proper smoothing technique, this undesirable effect is reduced. After identification of the missing parameters, a Mamdani fuzzy controller is used for stabilizing the line of sight of the gimbal. Fuzzy rules are determined according to the dynamic equations and based on the study of the effect of torque changes in the tracking path of the object. Simulation results are given to demonstrate the effectiveness and performance of the proposed fuzzy controller.

This paper considers robust attitude regulation of a rigid spacecraft with both uncertain inertia matrix and dynamic uncertainties. Specifically, we focus on the ignored input unmodeled dynamics, having relative degree zero and being minimum-phase, typical in nonlinear robust control. Instead of the conventional adaptive control approach, we shall develop an inverse optimal robust control design for the problem. Besides, we show strict extensions or applications of the proposed method to the more general attitude tracking control with disturbance rejection. We also present a couple of examples to show efficacy of the proposed results.

Hybrid robots have the time-varying dynamic load characteristics, which can affect the performance of electromechanical system, including the stability and motion accuracy, then determines the spraying quality. In this paper, the dynamic characteristics analysis is performed for a hybrid spray-painting robot with a three-parallelogram structure, taking into account the numerical properties of each component in the dynamic load. Firstly, the dynamic modeling of the mechanism is carried out by the principle of virtual work, and the inertia matrix and gravity matrix are calculated and analyzed. Then, by taking the dynamic load as the disturbance in the servo control system, the transfer function of the electromechanical system of the spray-painting robot is analyzed. The analysis results show that the stability will not change with the motion, and the coupling effect of multi-axis electromechanical systems is weakened under low acceleration conditions. Finally, the motion verification experiment is carried out to show that the gravity and friction are the main components of the driving force, and the motion accuracy will vary with the dynamic load.

A time-delay state feedback controller is designed for an underactuated AUV of three-dimensional stabilization control with input time-delay and model parameter uncertainty. Firstly, by analyzing the sources of the underactuated vehicle’s parameter uncertainty, its uncertainty of inertia matrix coefficient is mainly considered. Under this condition, the state feedback controller with time-delay is improved. Then, the state feedback control law that can guarantee the system to be uniformly asymptotically stable is given. And the feedback gain of the state feedback controller is solved by the LMI method. Finally, a simulation experiment of time-delay stabilization control with bounded parameter perturbation norm is designed. The results show that the proposed control law is robust to parameter perturbation.

The aim of this paper is to address the leader–follower formation control problem for a group of underactuated unmanned surface vehicles (USVs) with non-diagonal inertia matrix subject to modeling uncertainties and limited sensing capabilities. No communication is required among the USVs, but every USV is only equipped with on-board sensors to measure the line-of-sight (LOS) range and the relative bearing angle. The connectivity preserving constraint arisen from the limited sensing capability and the collision avoidance constraint resulting from the safety requirement are imposed on the LOS range and the relative bearing angle between every follower and its leader. These constraints are subsequently incorporated into the tan-type barrier Lyapunov function-based formation control design. Every USV reconstructs the velocity of its leader using the high-gain observer based solely on the available LOS range and relative bearing angle. Based on coordinate transformation, backstepping procedure, dynamic surface control (DSC) technique, and neural network approximation, a singularity-free formation controller is then developed, which guarantees the boundedness of all the closed-loop system signals and achieves satisfaction of prescribed performance specifications on the formation errors. Simulations are performed to verify the effectiveness of the formation control strategy.

Robust control of attitude tracking system between two rigid spacecraft is addressed using nonlinear disturbance observer-based control technique. A relative attitude dynamics model is derived for spacecraft tracking maneuver, where parameter uncertainty and environmental disturbances are considered as disturbance torques. A composite control technique is proposed for robust attitude tracking of a rigid spacecraft about a spacecraft under multiple disturbances by combining a nonlinear disturbance observer with an asymptotic tracking control. The proposed nonlinear disturbance observer is used to enhance the disturbance attenuation ability and robustness performance against uncertain inertia parameter and disturbances by estimating and compensating for the disturbances through feedforward. Stability and tracking performance of the nonlinear disturbance observer are analyzed. Furthermore, the stability of the composed control approach consisting of the asymptotic tracking control and nonlinear disturbance observer is established through Lyapunov method. Simulation results show that the composite control technique can significantly enhance disturbance attenuation ability, robust dynamics performance and the desired relative attitude tracking accuracy of a rigid spacecraft under external disturbances and uncertain inertia matrix.

A combined energy and attitude control system (CEACS) is a synergized system in which flywheels are used as attitude control actuators and simultaneously as a power storage system. This paper, a subsequent to previous research on CEACS, addresses the attitude-tracking problem. Integral Augmented Sliding Mode Control with Boundary-Layer (IASMC-BL), a locally asymptotically stable controller, is developed to provide a robust and accurate solution for the CEACS’s attitude-tracking problem. The controller alleviates the chattering phenomenon associated with the sliding mode using a boundary-layer technique. Simultaneously, it reduces the steady-state error using an integral action. This paper highlights the uncertainty of inertia matrix as a contributing factor to singularity problem. The inversion of the uncertain inertia matrix in simulation of a spacecraft dynamics is also identified as a leading factor to a singular situation. Therefore, an avoidance strategy is proposed in this paper to guarantee a singular-free dynamics behavior in faces of the uncertainties. This maiden work attempts to employ the singularity-free Integral Augmented Sliding Mode Control with Boundary-Layer (IASMC-BL) to provide a robust, accurate and nonsingular attitude-tracking solution for CEACS.

Autonomous close proximity operations are an arduous and attractive problem in space mission design. In particular, the estimation of pose, motion and inertia properties of an uncooperative object is a challenging task because of the lack of available a priori information. This paper develops a novel method to estimate the relative position, velocity, angular velocity, attitude and the ratios of the components of the inertia matrix of an uncooperative space object using only stereo-vision measurements. The classical Extended Kalman Filter (EKF) and an Iterated Extended Kalman Filter (IEKF) are used and compared for the estimation procedure. In addition, in order to compute the inertia properties, the ratios of the inertia components are added to the state and a pseudo-measurement equation is considered in the observation model. The relative simplicity of the proposed algorithm could be suitable for an online implementation for real applications. The developed algorithm is validated by numerical simulations in MATLAB using different initial conditions and uncertainty levels. The goal of the simulations is to verify the accuracy and robustness of the proposed estimation algorithm. The obtained results show satisfactory convergence of estimation errors for all the considered quantities. The obtained results, in several simulations, shows some improvements with respect to similar works, which deal with the same problem, present in literature. In addition, a video processing procedure is presented to reconstruct the geometrical properties of a body using cameras. This inertia reconstruction algorithm has been experimentally validated at the ADAMUS (ADvanced Autonomous MUltiple Spacecraft) Lab at the University of Florida. In the future, this different method could be integrated to the inertia ratios estimator to have a complete tool for mass properties recognition.

This paper describes a method based on an automatic segmentation process to coregister carpal bones of the same patient imaged at different time points. A rigid registration was chosen to avoid artificial bone deformations and to allow finding eventual differences in the bone shape due to erosion, disease regression, or other eventual pathological signs. The actual registration step is performed on the basis of principal inertial axes of each carpal bone volume, as estimated from the inertia matrix. In contrast to already published approaches, the proposed method suggests splitting the 3D rotation into successive rotations about one axis at a time (the so-called basic or elemental rotations). In such a way, singularity and ambiguity drawbacks affecting other classical methods, for instance, the Euler angles method, are addressed. The proposed method was quantitatively evaluated using a set of real magnetic resonance imaging (MRI) sequences acquired at two different times from healthy wrists and by choosing a direct volumetric comparison as a cost function. Both the segmentation and registration steps are not based on a priori models, and they are therefore able to obtain good results even in pathological cases, as proven by the visual evaluation of actual pathological cases.

An approach to forming analytical solutions of the discrete and continuous Sylvester and Lyapunov linear algebraic matrix equations is described. The approach is based on reducing the square matrix to the Jordan normal form. Examples, algorithms, and implementations in Matlab are presented.

The conditions of regularization and the structure of generalized Green’s operator for a re-gularized linear matrix differential-algebraic boundary-value problem are found. To solve the problem of regularization of a generalized matrix differential-algebraic boundary-value problem, the original conditions of solvability and the structure of the general solution of a matrix equation of the Sylvester type are used.

The periodic discrete-time matrix equations have wide applications in stability theory, control theory and perturbation analysis. In this work, the biconjugate residual algorithm is generalized to construct a matrix iterative method to solve the periodic discrete-time generalized coupled Sylvester matrix equations [Formula: see text] The constructed method is shown to be convergent in a finite number of iterations in the absence of round-off errors. By comparing with other similar methods in practical computation, we give numerical results to demonstrate the accuracy and the numerical superiority of the constructed method.

The manipulator control is an important problem in robotics. To work out this problem, a correct dynamic model for the robot manipulator must be in hand. Hence, this work first presents the dynamic model of an existing 4-DOF robot manipulator based on the Euler–Lagrange principle, utilizing the body Jacobian of each link and the generalized inertia matrix. Furthermore, essential properties of the dynamic model are analyzed for the purpose of control. Then, a PID controller is designed to control the position of the robot by decoupling the dynamic model. To achieve a good performance, the differential evolution algorithm is used for the selection of parameters of the PID controller. Feedback linearization scheme is also utilized for the position and trajectory tracking control of the manipulator. The obtained results reveal that the PID control coupled with the differential evolution algorithm and the feedback linearization control enhance the performance of the robotic manipulator. It is also found out that increasing masses of manipulator links do not affect the performance of the PID position control, but higher control torques are required in these cases.

In this paper, some necessary and sufficient conditions are established for the constraint generalized Sylvester matrix equations to have a common solution. The expression of the general common solution is also given under the solvable conditions. In addition, a numerical example is presented to illustrate the presented theory.

The aim of this article is modifying the well-known homotopy perturbation method (HPM) to yield the solution of Sylvester matrix equation. Moreover, conditions are deduced to check the convergence of the homotopy series. The numerical implementations will be conducted to measure the accuracy and speed of the homotopy series. Finally, some applications of this linear matrix equation are given.

The generalized reflexive and anti-reflexive matrices have several applications in engineering and scientific computations. In the present paper, first we propose a conjugate direction (CD) algorithm for finding the generalized reflexive solution X and the generalized anti-reflexive solution Y of the coupled Sylvester matrix equations [Formula: see text] Then, we analyze the convergence properties of the CD algorithm under some plausible assumptions. Finally by applying two numerical examples, we compare the proposed algorithm with other popular iterative solvers in use today.

The U1 matrix and extreme U1 matrix were successfully used to study quadratic doubly stochastic operators by R. Ganikhodzhaev and F. Shahidi [Linear Algebra Appl., 2010, 432: 24–35], where a necessary condition for a U1 matrix to be extreme was given. S. Yang and C. Xu [Linear Algebra Appl., 2013, 438: 3905–3912] gave a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme U1 matrix and investigated the structure of extreme U1 matrices. In this paper, we count the number of the permutation equivalence classes of the n × n extreme U1 matrices and characterize the structure of the quadratic stochastic operators and the quadratic doubly stochastic operators.

The solution of the generalized Sylvester real matrix equation XB − AX = CY is important in stability analysis and controller design in linear systems. This paper presents an explicit solution to the generalized Sylvester real matrix equation XB − AX = CY . Based on the derived explicit solution to the considered generalized Sylvester real matrix equation, a new approach is provided for obtaining the solutions to the generalized Sylvester quaternion j-conjugate matrix equation XB − A X ^ = CY using the real representation of a quaternion matrix. The closed form solution is established in an explicit form for this generalized Sylvester quaternion j-conjugate matrix equation. The existing complex representation method requires the coefficient matrix A to be a block diagonal matrix over complex field, while it is any suitable dimension quaternion matrix in the present paper. Therefore, we generalize the existing results.

In this note, we dedicate to solving the forward-time discrete periodic Sylvester matrix equations (FDPSE) and the reverse-time discrete periodic Sylvester matrix equations (RDPSE), which are frequently encountered in the analysis and design of linear discrete-time periodic systems. Explicit and complete parametric solutions to these equations are derived without any constraints on the coefficient matrices. As one of the most important applications of the periodic Sylvester matrix equations, periodic Luenberger-type observers design problem for linear discrete-time periodic systems is solved in the paper. Necessary and sufficient conditions for the existence of Luenberger observers are established, and a parametric design algorithm for Luenberger observers is presented. A numerical example is worked out to illustrate the effectiveness of our results.

Nowadays, one of the most active research fields in space engineering is autonomous relative navigation around uncooperative objects. A common approach used to tackle this problem is through vision-based pose determination techniques. This paper investigates the possibility of using non-linear filtering techniques to improve the attitude estimation performance of vision-based methods. Furthermore, a simulation study is presented to compare the proposed nonlinear techniques with the multiplicative extended Kalman filter for attitude estimation. First-order and second-order nonlinear filters are adapted, implemented and tested for relative attitude estimation. Finally, the consequences of uncertainty in the knowledge of the target inertia matrix are investigated.

This paper proposes a new nonlinear stability analysis for the acceleration-based robust position control of robot manipulators by using Disturbance Observer (DOb). It is shown that if the nominal inertia matrix is properly tuned in the design of DOb, then the position error asymptotically goes to zero in regulation control and is uniformly ultimately bounded in trajectory tracking control. As the bandwidth of DOb and the nominal inertia matrix are increased, the bound of error shrinks, i.e., the robust stability and performance of the position control system are improved. However, neither the bandwidth of DOb nor the nominal inertia matrix can be freely increased due to practical design constraints, e.g., the robust position controller becomes more noise sensitive when they are increased. The proposed stability analysis provides insights regarding the dynamic behavior of DOb-based robust motion control systems. It is theoretically and experimentally proved that non-diagonal elements of the nominal inertia matrix are useful to improve the stability and adjust the trade-off between the robustness and noise sensitivity. The validity of the proposal is verified by simulation and experimental results., Comment: 9 pages, 9 figures, Journal

This chapter deals with the stabilization of nonlinear spacecraft attitude dynamics by solely using magnetic actuation. The considered control problem possesses instantaneous underactuation due to the magnetic torque production mechanism. The aim is to design an observer-based control system by integrating an already existing magnetic sliding mode attitude controller with a nonlinear disturbance observer. In the observer-based controller synthesis, all major environmental disturbances and complete inertia matrix uncertainty are taken into account. It is proven that the obtained controller realizes sliding mode in the system, which implies robustness of the stabilization. An exemplary simulation verifies the theoretical deduction. Comparative simulation results indicate superiority of the ultimate controller to the baseline controller in terms of control effort and chattering while the same state responses are output by both control systems.

This study introduces the Geometric Dynamics Algorithm (GDA) for representing the dynamics of serially linked robots. GDA is non-symbolic, preserves simple formulation, and is convenient for numerical implementation. GDA-based algorithms are deduced for efficient calculation of various dynamic quantities including (1) joint space inertia matrix (JSIM) (2) Coriolis matrix (3) centrifugal matrix (4) and the time derivative of JSIM. The proposed algorithms were analyzed in terms of their computational complexity. Results compare favorably with other methods.

The paper focuses on the preliminary analysis of the requirements imposed to the attitude control system of a space vehicle (SV) aimed at collecting large-size space debris (LSSD) objects. The approximate inertia matrix of Zenit-2 launch vehicle’s second stage is obtained. This object is at present the largest and most massive in LEO among the existing last stages and upper stages. The angular velocities of these objects with respect to their centres of mass are estimated using the data from PPAS photometric catalogue. It is supposed that a new mechanical system appears when an active SV captures a stage, and so the angular motion of this system is studied for SVs of various masses, while the sizes of SVs are taken similar to those of the Soyuz family. An approach for control torque function selection is proposed; the goal of the control is to damp the system’s angular motion over fixed time interval with due account of some technical constraints.

The moment of inertia parameters play a critical role in assuring the spacecraft mission throughout its lifetime. However, determination of the moment of inertia is a key challenge in operating satellites. During satellite mission, those parameters can change in orbit for many reasons such as sloshing, fuel consumption, etc. Therefore, the inertia matrix should be estimated in orbit to enhance the attitude estimation and control accuracy. This paper investigates the use of gyroscope to estimate the attitude rate and inertia matrix for low earth orbit satellite via extended Kalman filter. Simulation results show the effectiveness and advantages of the proposed algorithm in estimating these parameters without knowing the nominal inertia. The robustness of the proposed algorithm has been validated using the Monte-Carlo method. The obtained results demonstrate that the accuracy of the estimated inertia and angular velocity parameters is satisfactory for satellite with coarse accuracy mission requirements. The proposed method can be used for different types of satellites.

Attitude control of a satellite having only two reaction wheels is a challenging issue. To address this problem, previously published researches considered some simplifying assumptions on the satellites such as diagonality of the moment of the inertia matrix. On the other hand, in some works, the total angular momentum of the satellite is assumed to be zero. In this paper, a linear time-variant model predictive control (LTV MPC) is designed to control a satellite with two reaction wheels. This control method can be applied to a satellite with a non-diagonal inertial matrix in the presence of external torques, to rotate the satellite toward the desired directions in the space and orbit. The simulations results show that this method has a small amount of computational cost and enables an under-actuated satellite to perform large real-time maneuvers with acceptable accuracy.

Adaptive control of a quad-rotorcraft is designed to estimate unknown plant parameters online in order to improve the robustness of the system against parametric uncertainties. Using the hierarchical structure of a quadrotor a nonlinear position and an adaptive attitude control law is proposed that can asymptotically track a command signal without the knowledge of inertia matrix. A projection based adaptive law estimates the unknown inertia parameters and ensures that the estimate always stay inside a pre-defined compact set. Adaptive design obeys the underlying principle behind hierarchical control where the vehicle tracks the desired position and compute guided attitudes from a thrust input so that designed rotor torques drives the vehicle towards desired orientation. A rigorous stability analysis proves that the overall system is stable by considering the effect of strong nonlinear coupling between the position and attitude subsystem. Closed-loop error dynamics is asymptotically converging and ensure all signals are bounded in the cascaded control structure. Simulation results demonstrate the theoretical conjecture of the proposed controller.

In this paper, we propose a new feedback vibration suppression controller for active nonlinear TMD using IDA-PBC. We consider a general Hamiltonian system under two kinds of disturbances as the controlled system, whose inertia matrix is the function of displacement, so that we can consider the vibrating system with nonlinear tuned mass damper. The feedback law only uses the information of relative displacements and velocities without accelerometer, and the system is based on the relative coordinate. We derive some constraints and the guideline of parameter selection with respect to the feedback law so that the controller can suppress the vibration caused by basement vibration and force disturbance. The effectiveness is confirmed by some simulations.

In this paper, a novel adaptive model-free attitude tracking control method is investigated for rigid spacecraft with consideration of the external disturbance, unknown inertia matrix, and ...

This paper investigates the problem of attitude tracking control for a nonrigid spacecraft subject to time-varying inertia matrix and external disturbances. Based on the deployable spacecraft with both fuel depletion and mass displacement, the time-varying inertia matrix is characterized with both rigid components and time-dependent components. Not only the direct influences of the fuel depletion and the mass displacement, but also the resulting change of center of mass (CM) are taken into account during the characterization. And the time-varying inertia matrix is applied to the mathematic model of the nonrigid spacecraft’s dynamics. Then, an adaptive attitude tracking control algorithm is proposed for the nonrigid spacecraft. The proposed controller directly compensates for inertia variations and achieves high control accuracy and good system robustness. Furthermore, a theoretical analysis of the system stability is also presented. Finally, numerical simulations are carried out to illustrate the effectiveness and superior control performance of the proposed control scheme.

This paper studies a passivity-based active disturbance rejection control scheme for trajectory tracking control of an omnidirectional mobile robot (OMR). The proposed control design effectively exploits the natural structure of robot dynamics. First, the passivity property of the OMR is analyzed based on the dynamic model. Then the controller is designed, consisting of two parts. One part is used to compensate the disturbances estimated by a modified reduced-order extended state observer, which avoids the inverse operation of the inertia matrix in control design. The other part is passivity-based trajectory tracking controller, which is designed based on the energy shaping plus damping approach. In addition, stability analysis of the proposed control system is presented. Finally, simulation results show the effectiveness of the proposed control design in improving tracking performances, compared with traditional active disturbance rejection control.

In this paper the design, analysis and implementation of improved first-order continuous adaptive sliding mode control (CASMC) based on online estimation of the lumped time-varying uncertainties for tracking control of the robot manipulators is presented. The proposed method allows to address the main drawbacks of conventional sliding mode control: the chattering phenomenon, and the requirement for a priori knowledge of the bounds of the uncertainties, and also the chattering problem associated with adaptive discontinuous sliding mode controllers, while the robustness property of the conventional sliding mode control is preserved. Furthermore, in the previously published version of the controller [1], the estimate of robot inertia matrix is needed to realize the adaptive component of the control law. In this work, the skew-symmetry property (passivity property) of robot dynamic is used to eliminate that requirement. The global stability and robustness of the proposed controller are established in the presence of time-varying uncertainties using Lyapunov's approach and fundamentals of sliding mode theory. The robustness is achieved without knowing the bound of uncertainties. The dynamic model of a two-degrees of freedom (2-DOF) rigid robot is used for simulation study and a 2-DOF flexible-link robot is used as an experimental test-bed to evaluate the performance, and robustness of the controller. Based on the simulations and experimental results, the proposed controller performs remarkably well in terms of the tracking error convergence, estimation of lumped uncertain parameter. And it is robust against un-modeled dynamics and external disturbances.

Robotics: Science and Systems (To Appear); International audience; Rigid body dynamics is a well-established framework in robotics. It can be used to expose the analytic form of kinematic and dynamic functions of the robot model. So far, two major algorithms, namely the recursive Newton-Euler algorithm (RNEA) and the articulated body algorithm (ABA), have been proposed to compute the inverse dynamics and the forward dynamics in a few microseconds. Evaluating their derivatives is an important challenge for various robotic applications (optimal control, estimation, co-design or reinforcement learning). However it remains time consuming, whether using finite differences or automatic differentiation. In this paper, we propose new algorithms to efficiently compute them thanks to closed-form formulations. Using the chain rule and adequate algebraic differentiation of spatial algebra, we firstly differentiate explicitly RNEA. Then, using properties about the derivative of function composition, we show that the same algorithm can also be used to compute the derivatives of ABA with a marginal additional cost. For this purpose, we introduce a new algorithm to compute the inverse of the joint-space inertia matrix, without explicitly computing the matrix itself. All the algorithms are implemented in our open-source C++ framework called Pinocchio. Benchmarks show computational costs varying between 3 microseconds (for a 7-dof arm) up to 17 microseconds (for a 36-dof humanoid), outperforming the alternative approaches of the state of the art.

This paper addresses the path-following formation keeping of a network of multiple autonomous underwater vehicles (AUVs) under unknown and possible time-varying disturbances, while achieving the fault tolerant control. We formulate this problem as the Port-controlled Hamiltonian form, and a feedback control is introduced to symmetrize the non-symmetric part of the inertia matrix caused by the forward speed. And fault tolerant is necessary to be considered due to the fact communication faults occur in the complex ocean environment. In the presence of time-varying disturbances, the internal model is applied to tackle the uncertainties. The passivity enables the closed-loop systems to converge to steady states. Numerical simulation results are given to illustrate the effectiveness of the approach.

International audience; This paper brings an identified model for a 6 degrees of freedom (dof) industrial robot, the Denso VP-6242G robot, with an end-effector composed of a spherical handle, fixed on a force sensor. This robot is intended to experiments in the field of Physical Human-Robot Interactions (PHRIs), for co-manipulation purposes. The control algorithms that are necessary to achieve a good PHRI, require a good knowledge of the robot dynamical model, especially the inertia matrix which should be positive definite whatever the configuration of the robot. However, most of industrial robots are supplied without any datasheet containing the inertial parameters nor Computer-Aided-Design (CAD) model. Hence, we propose to apply an identification procedure to experimental data, based on the Inverse Dynamic model Identification Method (IDIM). To ensure the positive definiteness of the inertia matrix, the used optimization step addresses the problem of nonlinear Weighted Least Squares (WLS), derived from the mathematical formulation of the identification problem, under a set of nonlinear constraints in the parameters. A validation step permits to check the efficiency of this approach for the Denso robot.

This paper is concerned with orbital and attitude cooperative control problems of small satellite in formation flying operation. At first, positional and attitude error dynamics model of small satellite relative to a target satellite is derived. Then, considering the uncertain inertia matrix and mass of small satellite, we design an adaptive output feedback control law and its stability is proved. Finally, numerical simulation validate the performance of the proposed output feedback control strategy.

The article of record as published may be found at http://dx.doi.org/10.3389/frobt.2018.00041 The paper provides a step-by-step tutorial on the Generalized Jacobian Matrix (GJM) approach for modeling and simulation of spacecraft-manipulator systems. The General Jacobian Matrix approach describes the motion of the end-effector of an underactuated manipulator system solely by the manipulator joint rotations, with the attitude and position of the base-spacecraft resulting from the manipulator motion. The coupling of the manipulator motion with the base-spacecraft are thus expressed in a generalized inertia matrix and a GJM. The focus of the paper lies on the complete analytic derivation of the generalized equations of motion of a free-floating spacecraft-manipulator system. This includes symbolic analytic expressions for all inertia property matrices of the system, including their time derivatives and joint-angle derivatives, as well as an expression for the generalized Jacobian of a generic point on any link of the spacecraft-manipulator system. The kinematics structure of the spacecraft-manipulator system is described both in terms of direction-cosine matrices and unit quaternions. An additional important contribution of this paper is to propose a new and more detailed definition for the modes of maneuvering of a spacecraft-manipulator. In particular, the two commonly used categories free-flying and free-floating are expanded by the introduction of five categories, namely floating, rotation-floating, rotation-flying, translation-flying, and flying. A fully-symbolic and a partially-symbolic option for the implementation of a numerical simulation model based on the proposed analytic approach are introduced and exemplary simulation results for a planar four-link spacecraft-manipulator system and a spatial six-link spacecraft manipulator system are presented.

In this paper, we examine dynamic advantages of singular configurations for a three-degree-of-freedom robot manipulator by numerical simulations and theoretical analysis. When the manipulator performs a task of moving or lifting up a heavy object, the joint torques necessary during the task can be reduced significantly by passing through or reaching singular configurations. The energy required for the task can be efficiently supplied from joint torques near singular configurations because of the large anisotropy of inertia matrix.

We present an iterative method based on the Hermitian and skew-Hermitian splitting HSS for solving the continuous Sylvester equation. By using the HSS of the coefficient matrices A and B, we establish a method which is practically inner/outer iterations, by employing a conjugate gradient on the normal equations CGNR-like method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent splitting of the coefficient matrices. Via this method, a Sylvester equation with coefficient matrices and which are the skew-Hermitian part of A and B, respectively is solved iteratively by a CGNR-like method. Convergence conditions of this method are studied and numerical examples show the efficiency of this method. In addition, we show that the quasi-Hermitian splitting can induce accurate, robust and effective preconditioned Krylov subspace methods.

Recently, Xue etc. (37) discussed the Smith method for solving Sylvester equation AX + XB = C, where one of the matrices A and B is at least a nonsingular M-matrix and the other is an (singular or nonsingular) M-matrix. Furthermore, in order to nd the minimal non-negative solution of a certain class of non-symmetric algebraic Riccati equations, Gao and Bai (17) considered a doubling iteration scheme to inexactly solve the Sylvester equations. This paper discusses the iterative error of the standard Smith method used in (17) and presents the prior estimations of the accurate solution X for the Sylvester equation. Furthermore, we give a new version of the Smith method for solving discrete-time Sylvester equation or Stein equation AXB + X = C, while the new version of the Smith method can also be used to solve Sylvester equation AX + XB = C, where both A and B are positive denite. We also study the convergence rate of the new Smith method. At last, numerical examples are given to illustrate the eectiveness of our methods.