Trajectory Tracking Of Robot Manipulators Research Articles

AdaptivePIDcontrol of robotic manipulators without equality/inequality constraints on control gains

AbstractThis article proposes two novel adaptive PID controllers for the trajectory tracking of robotic manipulators with known or unknown upper bound of the uncertainties, respectively. The designed controllers are shown to be not only robust with respect to the uncertainties but also adaptive with reference to the unknown manipulator and load parameters. Lyapunov stability analysis is included to prove eventual local asymptotic tracking. The salient features of the two proposed adaptive PID controllers are as follows: (1) they guarantee the eventual asymptotic convergence of the manipulator joint position and velocity tracking errors to zero with no need of any equality/inequality constraints on the controller gains when compared with the classical PID controller and the existing adaptive PID controllers; and (2) they offer better robustness against uncertainties than the existing classical PID controller, the adaptive PD controller, the linear active disturbance rejection controller, and the nonlinear disturbance observer based adaptive PID controller. Simulation studies and comprehensive comparisons demonstrate the superiorities of the two proposed adaptive PID controllers.

Sliding Mode with Adaptive Control of Robot Manipulator Trajectory Tracking using Neural Network Approximation

This paper briefly discusses about the Robust Controller based on Adaptive Sliding Mode Technique with RBF Neural Network (ASMCNN) for Robotic Manipulator tracking control in presence of uncertainities and disturbances. The aim is to design an effective trajectory tracking controller without any modelling information. The ASMCNN is designed to have robust trajectory tracking of Robot Manipulator, which combines Neural Network Estimation with Adaptive Sliding Mode Control. The RBF model is utilised to construct a Lyapunov function-based adaptive control approach. Simulation of the tracking control of a 2dof Robotic Manipulator in the presence of unpredictability and external disruption demonstrates the usefulness of the planned ASMCNN.

Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function

This study introduces a design of robust finite-time controllers that aims to solve the trajectory tracking of robot manipulators with full-state constraints. The control design is based on the construction of a distributed state constraint non-singular terminal sliding mode (CNTSM). The CNTSM design includes the gain self-adapting tuning method, which can ensure finite-time convergence to the sliding surface aside from the states to its corresponding reference trajectories. The implementation of the time-varying gain ensures the fulfillment of the accurate tracking for the references while the position and velocity constraints are satisfied permanently. A barrier Lyapunov function is proposed to develop the finite-time stability analysis of the designed controllers. The CNTSM realization uses the tracking error as well as its estimated derivative, which is calculated using a variant of adaptive super-twisting algorithm operating as robust differentiator. The proposed CNTSM is numerically evaluated on a two-link RM with uncertain inertia and Coriolis matrices. Simulation and experimental results evidence the efficiency of the CNTSM controller demonstrating a better tracking performance while the full-state constraints are satisfied in counterpart with the classical non-singular terminal sliding mode which is not able to keep such restrictions.

Adaptive Task-Space Manipulator Control with Parametric Uncertainties in Kinematics and Dynamics

This paper aims to deal with the problem of robot tracking control in the presence of parametric uncertainties in kinematics and dynamics. We propose a simple and effective adaptive control scheme that includes adaptation laws for unknown constant kinematic and dynamic parameters. In addition, instead of convolution-type filtered differentiation, we designed a new observer to estimate velocity in the task space, and the proposed adaptive control requires no acceleration measurement in the joint space. Using the Lyapunov stability and Barbalat’s lemma, we show that by appropriately choosing design parameters, the tracking errors and estimation errors in task space can asymptotically converge to zero. Through numerical simulation on a two-link robot with a fixed camera, we illustrate the design procedures and demonstrate the feasibility of the proposed adaptive control scheme for the trajectory tracking of robot manipulators.

Adaptive fuzzy Jacobian control of spacecraft combined attitude and Sun tracking system

PurposeThe paper aims to address the combined attitude control and Sun tracking problem in a flexible spacecraft in the presence of external and internal disturbances. The attitude stabilization of a flexible satellite is generally a challenging control problem, because of the facts that satellite kinematic and dynamic equations are inherently nonlinear, the rigid–flexible coupling dynamical effect, as well as the uncertainty that arises from the effect of actuator anomalies.Design/methodology/approachTo deal with these issues in the combined attitude and Sun tracking system, a novel control scheme is proposed based on the adaptive fuzzy Jacobian approach. The augmented spacecraft model is then analyzed and the Lyapunov-based backstepping method is applied to develop a nonlinear three-axis attitude pointing control law and the adaptation law.FindingsNumerical results show the effectiveness of the proposed adaptive control scheme in simultaneously tracking the desired attitude and the Sun.Practical implicationsReaction wheels are commonly used in many spacecraft systems for the three-axis attitude control by delivering precise torques. If a reaction wheel suffers from an irreversible mechanical breakdown, then it is likely going to interrupt the mission, or even leading to a catastrophic loss. The pitch-axis mounted solar array drive assemblies (SADAs) can be exploited to anticipate such situation to generate a differential torque. As the solar panels are rotated by the SADAs to be orientated relative to the Sun, the pitch-axis wheel control torque demand can be compensated by the differential torque.Originality/valueThe proposed Jacobian control scheme is inspired by the knowledge of Jacobian matrix in the trajectory tracking of robotic manipulators.

An Observer-Based Neural Adaptive $PID^2$ Controller for Robot Manipulators Including Motor Dynamics With a Prescribed Performance

This article proposes a novel prescribed performance-based neural adaptive control scheme for robot manipulators including motor dynamics under model uncertainties without velocity, acceleration, and input current measurements. The prescribed performance function approach is used to transform a constrained tracking problem of the robot model including motor dynamics into an unconstrained third-order error model in Euler-Lagrange form which inherits all properties of the robot dynamics. Then, a projection-type neural adaptive PID <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> controller (a PID controller with the second-order derivative) in conjunction with a velocity-acceleration observer is proposed. Lyapunov's direct method is used to prove that the tracking and state observation errors are semiglobally uniformly ultimately bounded and converge to a small ball around the origin with a prescribed overshoot/undershoot, convergence rate, and final tracking accuracy. Finally, simulation, experimental results on a SCARA robot and comparative studies verify that the proposed controller is effective for the joint position trajectory tracking of robot manipulators in the industrial automation with minimum measurement and hardware requirements.

Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators

To achieve precise trajectory tracking of robotic manipulators in complex environment, the precise dynamic model, parameters identification, nonlinear characteristics, and disturbances are the factors that should be solved. Although parameters identification and adaptive estimate method were proposed for robotic control in many literature studies, the essential factors, such as coupling and friction, are rarely mentioned as it is difficult to build the precise dynamic model of the robotic manipulator. An adaptive backstepping sliding mode control is proposed to solve the precise trajectory tracking under external disturbances with complex environment, and the dynamic response characteristics of a two-link robotic manipulator are described in this paper. First, the Lagrange kinetic method is used to derive the precise dynamic model which includes the nonlinear factor with friction and coupling. Moreover, the dynamic model of two-link robotic manipulator is built. Second, the estimate function for the nonlinear part is selected, and backstepping algorithm is used for analyzing the stabilities of the sliding mode controller by using Lyapunov theory. Furthermore, the convergence of the proposed controller is verified subject to the external disturbance. At last, numerical simulation results are reported to demonstrate the effectiveness of the proposed method.

Adaptive Fuzzy Sliding Mode and Robust Tracking Control for Manipulators with Uncertain Dynamics

In response to the issue of the trajectory tracking control problem of manipulators with uncertain parameters and external disturbance, an adaptive fuzzy sliding mode robust control algorithm is proposed. Sliding mode control (SMC) is adopted to perform robotic manipulator trajectory tracking control. Then, a fuzzy logic system is used for adaptive adjustment of switching gain of the SMC and to reduce the buffeting problem. Next, compensation is made by using the robust controller in consideration of the impacts of unmodeled dynamics and external disturbance. The simulation experiment on a two axes robotic manipulator shows that, with the proposed control method, the sliding mode control input signal is kept smooth, and the manipulator has high trajectory tracking precision.

Finite-time control for rigid robots with bounded input torques

The problem of finite-time trajectory tracking of robot manipulators with uncertain dynamics, external bounded disturbances, and bounded torque inputs is addressed in this paper. In order to achieve finite-time convergence a nonlinear control algorithm based on a second-order sliding mode controller in combination with nonsingular terminal sliding mode is proposed. The proposed controller also exploits the properties of the hyperbolic tangent function. As a result, the control algorithm generates a continuous bounded signal. In addition, the controller structure is simple since it does not require the knowledge of the robot dynamic model. Experimental results are provided to show the performance of the proposed control algorithm.

Output Feedback Adaptive Fractional-Order Super-Twisting Sliding Mode Control of Robotic Manipulator

In this study, trajectory tracking of robotic manipulators with uncertainties and external disturbances is obtained by proposing model-free adaptive fractional super-twisting sliding mode control (AOFSTSM). The proposed AOFSTSM method is composed of an adaptive super-twisting sliding mode control integrated with fractional-order (FO) control. An adaptive tuning control is utilized to evaluate the uncertain unknown dynamics of the system without relying on the prior knowledge of the upper bounds. Moreover, FO control and super-twisting sliding mode control are used to achieve the fast finite-time convergence, chatter-free control inputs, better tracking performance and robustness. An output feedback (OF) is proposed and the state estimation is obtained by robust exact differentiator. Furthermore, the stability of the overall system is investigated and derived from the Lyapunov stability criterion. Finally, to validate the effectiveness and robustness of the developed control method, comparative simulations of state-feedback and OF of proposed method with fractional-order nonsingular fast terminal sliding mode control are realized to demonstrate the performance of AOFSTSM.

Adaptive Fractional High‐order Terminal Sliding Mode Control for Nonlinear Robotic Manipulator under Alternating Loads

AbstractIn this study, trajectory tracking of robotic manipulators under varying loads with uncertainties and external disturbances is obtained by proposing model‐independent adaptive fractional high‐order terminal sliding mode control (AFO‐HoTSMC). The proposed AFO‐HoTSMC method is composed of an adaptive high‐order terminal sliding mode control integrated with fractional‐order (FO) control. An adaptive tuning control is utilised to evaluate the uncertain unknown dynamics of the system without relying on the prior knowledge of the upper bounds. FO control and HoTSMC are used to achieve the fast finite‐time convergence, chatter‐free control inputs, better tracking performance and robustness. The finite‐time stability of the overall system is investigated and derived from the Lyapunov stability criterion. Finally, to validate the effectiveness and robustness of the developed control method, comparative simulations with H∞‐Adaptive control, intelligent PD (iPD), intelligent PID (iPID) and adaptive third‐order SMC (ATOSMC) are realized to demonstrate the performance of AFO‐HoTSMC.

Strict Lyapunov functions for finite-time control of robot manipulators

Motivated by the energy shaping framework and the properties of homogeneous systems, we introduce a methodology to derive strict Lyapunov Functions (LFs) for a class of global finite-time (FT) controllers for robot manipulators. As usual in the energy shaping methodology, these controllers are described by the gradient of the controller potential energy plus the gradient of (nonlinear) energy dissipation-like functions. Sufficient conditions on the controller potential energy and energy dissipation-like functions are provided in order to obtain, in a straightforward manner, strict LFs ensuring global FT stability at the desired equilibrium. As an important practical outcome, we illustrate the proposed methodology by constructing strict LFs for some particular FT controllers. The construction of such strict LFs allows us to solve the open problem of FT trajectory tracking of robot manipulators with continuous control laws to track any bounded trajectory.

Sectorial Fuzzy Controller Plus Feedforward applied to the Trajectory Tracking of Robot Manipulators

Abstract In this paper, we propose a novel sectorial fuzzy controller plus feedforward for the trajectory tracking control of robot manipulators. An outline of the stability proof via Lyapunov criterion of the proposed controller is given. Experimental results are presented in comparison to its classical counterpart: The Proportional-Derivative (PD) plus feedforward controller, from which this new proposal is based. The results obtained using the proposed controller indicate a better performance in terms of joint position error and tolerance to parametric variations.

Estimation-Based Quadratic Iterative Learning Control for Trajectory Tracking of Robotic Manipulator With Uncertain Parameters

In this paper, we consider iterative learning control for trajectory tracking of robotic manipulator with uncertainty. An improved quadratic-criterion-based iterative learning control approach (Q-ILC) is proposed to obtain better trajectory tracking performance for the robotic manipulator. Besides of the position error information, which has been used in existing Q-ILC methods for robotic control, the velocity error information is also taken into consideration such that a new norm-optimal objective function is constructed. Convergence and error sensitivity properties for the proposed method are also analyzed. To deal with uncertainty, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are incorporated for estimation of uncertain parameters by constructing extended system states. The performances between the two filters are also compared. Simulations on a 2DOF Robot manipulator demonstrate that the improved Q-ILC with parameter estimators can achieve faster convergence and better transient performance compared to the original Q-ILC, in the presence of measurement noise and model uncertainty.

Non-singular Terminal Sliding Mode Control of Robot Manipulators with $$H_\infty $$ Trajectory Tracking Performance

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

Addressing Control Implementation Issues in Robotic Systems Using Adaptive Control

SummaryThis paper addresses three control implementation issues for trajectory tracking of robotic manipulators: unmodeled dynamics, unknown input saturation and peaking effects during the transient phase. A model-free first-order robust-adaptive control method is used to deal with the unmodeled dynamics. Robust optimality and stability of the controller are proved using the 𝓗∞ technique and the game-algebraic Riccati equation. An intuitive approach is devised to incorporate the unknown input saturation by modifying the speed of the desired trajectory. The trajectory scaling is performed by using only the state errors. Furthermore, two different techniques are utilized to suppress peaking during the transient response of the trajectory tracking. The first method adds an extra term in the input while the second method uses variable gain to improve the transient response. A systematic procedure for finding the controller parameters is formulated using features, such as rise time and settling time. A three-degree-of-freedom robot manipulator is used for the validation of the proposed controller in simulations and experiments.

Adaptive neural network control with optimal number of hidden nodes for trajectory tracking of robot manipulators

In this paper, an adaptive neural network control with optimal number of hidden nodes and less computation is proposed for approximating the system uncertainty and tracking the trajectory of robot manipulators. Unlike the existing researches on adaptive neural network for robot manipulators, whose number of hidden nodes is fixed and determined through the trial and error, a new approach is proposed to obtain the optimal number of hidden nodes, in which the number of hidden nodes adapts to the trajectory variations and is capable of catching up with the optimal value and minimizing the tracking error. The proposed control scheme can avoid overfitting and underfitting problems and guarantee a better trajectory tracking. Mathematical proof for stability and convergence of the system is presented using Lyapunov method. In the end, simulations are performed to illustrate the effectiveness of the proposed approach.

Fixed-Time Inverse Dynamics Control for Robot Manipulators

This paper concerns with global fixed-time trajectory tracking of robot manipulators. A simple nonlinear inverse dynamics control (IDC) is proposed by using bi-limit homogeneity technique. Lyapunov stability theory and geometric bi-limit homogeneity technique are employed to prove global fixed-time tracking stability. It is proved that there exists a convergence time that is uniformly bounded a priori and such a bound is independent of the initial states such that the tracking errors converge to zero globally. The appealing advantages of the proposed control are that it is fairly easy to construct and has the global fixed-time tracking stability featuring faster transient and higher steady-state precision. Numerical simulation comparisons are provided to demonstrate the improved performance of the proposed approach.

Adaptive second-order fast nonsingular terminal sliding mode control for robotic manipulators

This paper presents an adaptive chattering-free sliding mode controller for trajectory tracking of robotic manipulators in the presence of external disturbances and inertia uncertainties. To achieve fast convergence and desirable tracking precision, a second-order fast nonsingular terminal sliding mode (SOFNTSM) controller is designed to guarantee system performance and robust stability. Chattering is eliminated using continuous control law due to high-frequency switching terms contained in the first derivative of actual control signals. Meanwhile, uncertainties are compensated by introducing the adaptive technique, whose prior knowledge about upper bound is not required. Finally, simulation results validate the effectiveness of the proposed control scheme.

Nonlinear PD plus sliding mode control with application to a parallel delta robot

Abstract In this paper, a hybrid nonlinear proportional-derivative-sliding mode controller (NPD-SMC) is developed for the trajectory tracking of robot manipulators. The proposed controller combines the advantage of the easy implementation of NPD control and the robustness of SMC. The gains of PD control are tuned on-line in order to increase the convergence rate, whereas the SMC term is introduced to reject the external disturbances without requiring to know the system dynamics. The stability of the NPD-SMC is proved using Lyaponuv theorem, and it is demonstrated that the tracking error and the tracking error rate converge asymptotically to zero. Experiments are carried out on the parallel Delta robot to illustrate the effectiveness and robustness of the proposed approach. It is also shown the superiority of the NPD-SMC control over the NPD control and PD-SMC control.