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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 article studies the optimal control policy learning for underactuated vertical take-off and landing (VTOL) aerial vehicles subject to the unknown mass and inertia matrix. A novel off-policy integral reinforcement learning (IRL) scheme is presented for simultaneously unknown parameter identification and optimal trajectory tracking. In the outer loop of the VTOL vehicles, a novel off-policy IRL scheme is proposed, where the fixed control policy for data generation is chosen to be different from the iterated control policy and the feedforward term with an unknown mass can be learned along with the optimal control policy. In the inner loop, a hybrid off-policy IRL algorithm is developed to tackle the optimal attitude control policy learning and inertia matrix identification under the hybrid control scheme introduced by the employed inner-outer loop control strategy. A simulation study is finally provided to demonstrate the effectiveness of the proposed algorithm.

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.

A robust adaptive finite-time controller for satellite fast attitude maneuver is proposed in this paper. The finite-time sliding mode is proposed based on standard sliding mode, hence the terminal convergence rate could be largely improved, and the inherent robustness to some typical perturbations is maintained. A new method is proposed to deal with the singularity issue based on the property of Euler rotation. In order to deal with inertia matrix uncertainty, finite-time adaptive law for inertia matrix estimation variables is proposed. Considering that the variable estimation system has no direct feedback, an auxiliary state converging slower than system is designed to achieve finite-time stability. The overall global finite-time stability is proved by Lyapunov method and the performance of the controller is demonstrated by numerical simulation results.

In this paper, a robust control method is proposed for rigid spacecraft attitude stabilization under inertia matrix uncertainties and external disturbances. The attitude stabilization problem is firstly reformulated into an optimal control problem, then a state-dependent indirect Chebyshev pseudospectral (SDICP) method is designed to solve the resultant optimal control problem. It is proved that, by incorporating the uncertainties into the performance index and adaptively estimating the parameters, the stabilization problem can be converted into an infinite horizon optimal control problem. Based on successive state-dependent coefficient parameterization, time domain transformation and Chebyshev spectral discretization, the proposed SDICP method turns the resultant optimal control problem into a sequence of systems of linear equations, which can be efficiently solved by basic matrix operations. Simulation results also verify the effectiveness of the proposed robust adaptive attitude stabilization method.

A smooth version of Sylvester's law of inertia is presented for symmetric matrix functions of constant rank. The techniques used in the proof are constructive but the resulting numerical approaches are unstable, and therefore require stabilization. Two different stabilization techniques are suggested, one based on a descent method and one based on Newton's method. Some numerical tests are included to demonstrate the applicability of the obtained numerical methods.

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.

This paper studies the problem of trajectory tracking control for a class of vehicles (underwater vehicles, some horizontally moving vehicles, indoor airships). The control development is based on some velocity transformation arising from the inertia matrix decomposition, Lyapunov’s direct method and a non-adaptive nonlinear tracking controller in terms of the Generalized Velocity Components (GVC). In the nonlinear controller the control gains are strictly related to the vehicle dynamics (especially dynamical couplings). The general algorithm is presented for a 6 DOF vehicle. In the simulation two trajectories were tested. Moreover, one robustness test was done (corresponding to robustness issue considered in this work). The simulation results obtained for a full airship model show that the proposed control scheme guarantees satisfactory performance.

With the conventional 2D exam of clinical cases, the diagnosis is penalized by the lack of data, not only for vertical or transverse or asymmetrical problems, but for classical cases of anteroposterior dysharmonies. In these cases, the effectively used parameter, ANB angle, seems insufficient. So the authors elaborated a 3D biometry tool. The program of morphological analysis is able to deliver a complete description of dysharmony, supported by Cone Beam data capture. In the first part of this article the authors present the foundation of the model: anatomical reference, skeletal landmarks, teeth location by inertia matrix calculus, parameters, diagnosis and aid to treatment plan. The second part is the presentation, step by step, of the program in function, analyzing a great case of Class II hyperdivergent, border line surgery. All along the diagnosis way, the authors make the assistant discover all the documents given by the computer about complete 3D diagnosis and aid to treatment plan.

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.

At the outset, a nonlinear dynamic system for the generalized robots with input constraint is given to design an adaptive fixed-time fault-tolerant constraint control (AFTFTCC) for trajectory tracking. The proposed AFTFTCC includes a nonlinear filtering tracking error, which can shape the system response. As the operating point is in the neighborhood of the zero nonlinear filtering tracking error, nonlinear filtering gains are increasing to accelerate its tracking ability. The skew-symmetric matrix's condition for the time-derivative of the inertia matrix and Coriolis and centrifugal force matrix is not required. The upper bound of uncertainties is learned to improve system performance. The stabilities of the closed-loop system are verified by the Lyapunov stability theory. Without true force feedback, the cooperative task of multiple robots with multiple arms is also addressed by the proposed AFTFTCC. Finally, two examples, including the trajectory tracking control of planar three-link robot arm and the cooperative control of dual planar three-link robot arms, are employed to validate the effectiveness and robustness of the proposed control.

In this article, the problem of fault-tolerant attitude-tracking control of spacecraft with quantized control torque is addressed. Actuator faults/failures, an uncertain inertia matrix and unknown disturbances are considered in the attitude controller design of the spacecraft. A dynamical quantization strategy is developed to quantize the signals of the control torque, which can reduce the data transmission rate. An adaptive fault-tolerant controller based on sliding mode techniques is constructed to address the impacts of the actuator faults/failures, quantization errors, inertia matrix uncertainties and unknown disturbances. The developed control strategy with a quantizer can ensure that the entire closed-loop system is asymptotically convergent and achieves satisfactory attitude-tracking performance. Finally, simulation results are provided to show the effectiveness of the proposed method.

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.

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work, the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four-dimensional modulo-permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point-masses at infinity is also investigated. Applications of these ideas to rigid body dynamics are considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation.

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.

International audience; Control of robots with kinematic constraints like loop-closure constraints or interactions with the environment requires solving the underlying constrained dynamics equations of motion. Several approaches have been proposed so far in the literature to solve these constrained optimization problems, for instance by either taking advantage in part of the sparsity of the kinematic tree or by considering an explicit formulation of the constraints in the problem resolution. Yet, not all the constraints allow an explicit formulation and in general, approaches of the state of the art suffer from singularity issues, especially in the context of redundant or singular constraints. In this paper, we propose a unified approach to solve forward dynamics equations involving constraints in an efficient, generic and robust manner. To this aim, we first (i) propose a proximal formulation of the constrained dynamics which converges to an optimal solution in the least-square sense even in the presence of singularities. Based on this proximal formulation, we introduce (ii) a sparse Cholesky factorization of the underlying Karush-Kuhn-Tucker matrix related to the constrained dynamics, which exploits at best the sparsity of the kinematic structure of the robot. We also show (iii) that it is possible to extract from this factorization the Cholesky decomposition associated to the so-called Operational Space Inertia Matrix, inherent to task-based control frameworks or physic simulations. These new formulation and factorization, implemented within the Pinocchio library, are benchmark on various robotic platforms, ranging from classic robotic arms or quadrupeds to humanoid robots with closed kinematic chains, and show how they significantly outperform alternative solutions of the state of the art by a factor 2 or more.

In order to solve the buffeting problem of 7 DOF Manipulator caused by external disturbance in the motion process, the dynamic equation of the manipulator is given, the estimated inertia matrix is selected, and the RBF neural network fitting characteristics are used to fit the required items to reduce the difficulty of modeling. Based on the estimated dynamic model, a neural network adaptive control method with time-varying constraint state is proposed; The control law is designed, and the Lyapunov function equation and asymmetric term are established to derive its convergence. The angular displacement, angular velocity, angular acceleration, input torque and disturbance fitting are analyzed according to the joint state tracking results of the manipulator by using Simulink and gazebo simulation. The system simulation results show that the chattering phenomenon can be suppressed by using this method in the case of disturbance.

In this paper, decentralized adaptive attitude synchronization and tracking control of spacecraft formation flying without angular velocity measurement is considered. The objective is to have the spacecraft track the time-varying attitude of a virtual leader in a synchronous manner. To cope with uncertain inertia matrix of the spacecraft, an adaptive term is incorporated into control signal of each spacecraft based on the linear regression structure. It is well-known that measurement of angular velocity suffers from the drift phenomena and noise. To escape angular velocity measurement, semi-velocity signals are constructed using self and relative lead filters. For a more realistic modelling of the system, the dynamics of the reaction wheel actuators are also considered in this paper. Stability of the proposed control methodology are provided using Lyapunov theorem. Finally, simulation results illustrate efficiency of the proposed control scheme.

The article considers a method of examining the influence of dynamic couplings contained in the underwater vehicle model on the movement of this vehicle. The method uses the inertia matrix decomposition and a velocity transformation if the fully actuated vehicle is described in the earth-frame representation. Based on transformed equations of motion, a controller including dynamic couplings in the gain matrices is designed. In the proposed method, the control algorithm is used for the test vehicle dynamics model taking into account disturbances. The approach is useful for simulating the model of an underwater vehicle and improving it, thus avoiding unnecessary experiments or planning them better. The procedure is shown for a full model of an underwater vehicle, and its usefulness is verified by simulation.

This paper is concerned with developing a DP control system in the presence of thruster rate limits and saturation constraints. The proposed control system consists of a robust controller together with an extended-state observer (ESO) so that only an acceptable estimate of inertia matrix is required for control system design. Extended-state observer is used to estimate unknown dynamics and velocities of ROV. A robust controller based on sliding mode methods is proposed for DP control system. Furthermore, thrust allocation algorithm is considered in DP control system synthesis to take into account thruster system constraints namely, saturation and rate limits. Three sets of simulations are carried out to evaluate the performance of the proposed control system and comparisons are made with simple PD-type controllers. The results show that thruster constraints have stringent effects on performance of DP control systems. It is also shown that robust controllers maintain better accuracies despite these limits and constraints and compensate for these discrepancies more effectively.

Whenrobots physically interact with the environment, compliant behaviors should be imposed to prevent damages to all entities involved in the interaction. Moreover, during physical interactions, appropriate pose controllers are usually based on the robot dynamics, in which the ill-conditioning of the joint-space inertia matrix may lead to poor performance or even instability. When the control is not precise, large interaction forces may appear due to disturbed end-effector poses, resulting in unsafe interactions. To overcome these problems, we propose a task-space admittance controller in which the inertia matrix conditioning is adapted online. To this end, the control architecture consists of an admittance controller in the outer loop, which changes the reference trajectory to the robot end-effector to achieve a desired compliant behavior; and an adaptive inertia matrix conditioning controller in the inner loop to track this trajectory and improve the closed-loop performance. We evaluated the proposed architecture on a KUKA LWR4+ robot and compared it, via rigorous statistical analyses, to an architecture in which the proposed inner motion controller was replaced by two widely used ones. The admittance controller with adaptive inertia conditioning presents better performance than with a controller based on the inverse dynamics with feedback linearization, and similar results when compared to the PID controller with gravity compensation in the inner loop.

In this study, a method of active disturbance rejection controller (ADRC) is presented for 2-DOF underwater manipulator. The ADRC basically does not rely on the accurate mathematical model of the object and can decouple the model. This method can eliminate the influence of model errors, time-varying parameters and external interference on the control effect. Firstly, the manipulators is divided into two subsystems. For each joint subsystem, the hydrodynamic force, coupling term between joints and unknown environment disturbances are considered as the total disturbance. Subsequently, an extended state observer (ESO) is designed to estimate and compensate the total disturbance. Moreover, in order to improve the disturbance observation effect of the extended state observer, the inertia matrix of the manipulator system is used to decouple the static part. Finally, the effectiveness of ADRC is verified by simulation and it is demonstrated that ADRC’s control effect outperforms PD and CSMC in either accuracy, dynamic characteristics or robustness.

In order to solve the joint chattering problem of the manipulator in the process of motion, a novel dynamics model is established based on the dynamics model of the manipulator, by fitting parameters of the neural network and combining with the estimated value of the inertia matrix. We proposed a neural network adaptive control method with a time-varying constraint state based on the dynamics model of estimation. We design the control law, establish the Lyapunov function equation and the asymmetric term, and derive the convergence of the control law. According to the joint state tracking results of the manipulator, the angular displacement, angular velocity, angular acceleration, input torque, and disturbance fitting of the manipulator are analyzed by using the Simulink and Gazebo. The simulation results show that the proposed method can effectively suppress the chattering amplitude under the environment disturbances.

Traditionally, the energy shaping for mechanical systems requires the elimination of holonomic and nonholonomic constraints. In recent years, it was argued that such elimination might be unnecessary, leading to a possible simplification of the matching conditions in energy shaping. On the other hand, the partial feedback linearization (PFL) approach has been widely applied to unconstrained mechanical systems, but there is no general result for the constrained case. In this regard, this paper formalizes the PFL for mechanical systems with kinematic constraints and extends the energy shaping of such systems by including systems with singular inertia matrix and non-workless constraint forces, which can arise from the coordinate selection and PFL. We validated the proposed methodology on a 5-DoF portal crane via simulation.

Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) related to kinetic and potential energy shaping shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs relevant to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solving this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including pendubot, VTOL aircraft, and 2D SpiderCrane.

This paper presents the robust control scheme of improving the poor tracking performance owing to the defects of the time-delayed control (TDC) for robot manipulators. The defects of TDC include inaccurate estimation of an inertia matrix model and joint accelerations required to formulate the TDC scheme. The accuracy of estimating the inertia matrix and accelerations plays an important role in the control performance as well as the stability of TDC. To improve the estimation, the inertia matrix is identified by the recursive least square (RLS) method and the acceleration signals are estimated by a state observer (SOB). Tracking control performances of a manipulator by the proposed scheme are empirically tested and compared.

U ovom radu proučavamo plohe drugog reda. Glavni cilj rada je uz pomoć linearne algebre i kvadratne forme klasificirati plohe drugog reda u realnom afinom prostoru. Iskazan je Sylvesterov zakon inericije te je pomoću njega na primjerima ilustirano kako odrediti vrstu plohe drugog reda. Takoder, opisan je geometrijski pristup određivanja vrsta ploha drugog reda. Drugi dio bavi se osnovnim definicijama i teoremima iz diferencijalne geometrije i teorije ploha. Dane su definicije ploha drugog reda i njihovi presjeci koordinatnim ravninama. Opisali smo rotacijske i translacijske plohe, a u zasebnom poglavlju definirali zakrivljenost plohe te ju pročili na pravčastim plohama. Na kraju dajemo primjere veličanstvenih gradevina moderne arhitekture u kojima vidimo primjenu ploha drugog reda. In this thesis our main concern will be surfaces of second order. Using linear algebra and quadratic form theory our main goal is to provide classification of quadric surfaces in real affine space. In examples we illustrate how to determine the surface using the Sylvester’s law of inertia. Furthermore, we describe geometrical approach of determinating quadric surfaces. The second chapter deals with definitions and theorems in differential geometry and surface theory. We defined second-order surfaces and presented their intersections with coordinate planes. Rotational and translational surfaces are described and in a separate section we defined surface curvature which we study on ruled surfaces. Finally, we provide examples of magnificent buildings in modern architecture in which we can see the implementation of this quadric surfaces.

In this work, an effort is made to propose a chattering mitigating sliding mode controller for attitude maneuver control of a rigid modelled spacecraft. Unit quaternion is used here to represent the attitude kinematics. Firstly, a new sliding output function is defined that have relative degree two and then, control law is formulated in second order sliding mode using homogeneity controller. The proposed controller can ensure quick convergence to equilibrium and limit the chattering in control and states. Simulation is conducted for different initial settings of unit quaternion and angular velocity with external disturbances and inertia matrix uncertainty subjected. Results show the controller efficacy in maintaining both transient and steady state performance.

This paper addresses the problem of position control or waypoint tracking for an underactuated quadrotor. The proposed control law is what is known as reaction based in the way that the attitude system reacts to errors in the translational motion. This methodology requires no generation of desired attitude or angular velocity and the resulting control law is model-independent in that it does not require the knowledge of the inertia matrix. In addition the controller has a very simple structure making it suitable for small quadrotor platforms. Simulation results are provided and discussed to demonstrate the proposed method.

An adaptive attitude tracking control law based on an event-triggered control strategy is proposed to discuss the problem of plug-and-play satellite attitude tracking maneuvers with limited data transmission among independent models. In this scheme, the controller is updated aperiodically only in the case that a designed event-triggered condition is satisfied, so unnecessary communication among modules can be avoided and the sampling frequency is optimized. Also, the control problem is under the condition of inaccurate knowledge of inertial matrix. Considering the uncertainty of system parameter, inertia matrix, an adaptive control is used to avoid using the real value of inertia matrix. The proposed control scheme not only ensure stability of attitude tracking closedloop control system but also a positive lower bound between adjacent triggered instant to avoid Zeno behavior. Finally, the numerical simulation results verify the effectiveness of the designed controller.

This paper presents a robust nonlinear H∞ output-feedback control approach for attitude manoeuvring of flexible spacecraft with external disturbances, inertia matrix perturbation and input constraints. By applying Lyapunov stability theory and using the generalized S-procedure and sum of squares (SOS) techniques, the robust H∞ output-feedback attitude control problem is converted into a convex optimization problem with SOS constraints when the flexible spacecraft is modelled as a polynomial state-space equation with polytope uncertainties. As a result, it overcomes the difficulty in constructing Lyapunov function and implementing numerical computation caused by the non-convexity of output-feedback H∞ control design for nonlinear systems. Moreover, it enables the state-observer and the controller to be designed independently and hence the complexity of the control algorithm is reduced remarkably. A numerical example illustrates the effectiveness and feasibility of the proposed approach.

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).