Real-time implementation of regressor-based sliding mode control algorithm for robotic manipulators

A Novel Variable Structure Control Scheme for Robot Trajectory Control

A method for optimal trajectory control of robotic manipulators is considered in this paper. In particular, a control scheme is proposed such that, while the manipulator passes two or more prescribed points, the resulting trajectory of motion is smooth. Such a problem is formulated by employing a criterion of minimum-mean-square acceleration during the entire period of motion. Although the motion of robot manipulators is governed by a system of second-order differential equations which are highly non-linear, it is shown that the control problem can be solved rigorously under such a criterion. The optimal control consists of non-linear compensation terms and other linear feedback terms. The results of computer simulation studies for a two-link manipulator are also included.

Robust trajectories following control of a 2-link robot manipulator via coordinate transformation for manufacturing applications

A discrete-time learning control for robotic manipulators is studied using its pulse transfer function. Firstly, the discrete-time learning stability condition which is applicable to single-input two-outputs systems is derived. Secondly, the stability of the learning algorithm with a position signal is studied. In this case, when the sampling period is small, the algorithm is not stable because of an unstable zero of the system. Thirdly, the stability of the algorithm with position and velocity signals is studied. In this case, we can stabilize the learning control system which is unstable in the case of learning with only the position signal. Finally, simulation results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. The simulation results agree well with the analytical results.

A discrete-time learning control for robotic manipulators is studied from a viewpoint of zeros of a control system. The signal used for learning is a position signal of each joint detected by a pulse encoder. Firstly, we show that when sampling period is small, the learning is unstable because of an unstable zero of the system. Secondly, we show that we can stabilize the learning control system with small sampling period by using a low pass filter, and also show that a tracking error converges not to zero but to a certain value in that case. Finally, experimental results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. These experimental results agree well with the analytical ones.

Radial basis function network (RBFN) is used in this paper for predefined trajectory control of both one-link and two-link robotic manipulators. The updating equations for the RBFN parameters were derived using the gradient descent principle. The other advantage of using this principle is that it shows the clustering effect in distributing the radial centres. To increase the complexity, the dynamics of robotic manipulator is assumed to be unknown, and hence, simultaneous control and identification steps were performed using the RBFNs. The performance of the RBFN is compared with the multilayer feed-forward neural network (MLFFNN) in terms of mean square error, tolerance to disturbance and parameter variations in the system. The efficacy of RBFN as a controller and identification tool is verified by performing the simulation study, and the results obtained reveal the superior performance of RBFN over MLFFNN in both identification and control aspects for one-link and two-link robotic manipulators.

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

In tlus work a nonlinear control method is used for the trajectory control of robotic manipulators. In this method, the correct gain values are obtained using an off-line based numerical optimization method. The results obtained are tested on a two link manipulator whose end effector moves along a circular trajectory. The results show that one can obtain very accurate results using this method

In the present paper, we examine the Model Feedback Control System. Since the Model Feedback Control System is simple, the ModeI Feedback ControI System has been applied to many applications such as the trajectory control of robot manipulator, level control of serially connected tanks and so on. Since the control structure of the ModeI Feedback Control System has constrained, it is likely that the Model Feedback Control System can not represent all of stabilizing controllers for the plant. Nothing has been reported whether or not, the ModeI Feedback Control System can represent all of stabilizing controllers. The purpose of the present paper is to give a solution to the question whether or not, all of stabilizing controllers for the plant are written as the Model Feedback Control structure. Since Model Feedback Control System is applied to many minimum phase systems, in the present paper, we especially clarify the relationship between the ModeI Feedback Control System and the parametrization of all stabilizing controllers for the minimum phase system. First, the relationship between the Model Feedback Control system and the parametrization by Glaria and Goodwin is clarified. Next, for the strictly proper system, the relationship between the Model Feedback Control System and the parametrization by Yamada and Moki is presented. Simple design method of the Model Feedback ControI System to specify control characteristics is shown.

In this paper, a controller for robot manipulators is proposed to guarantee the tracking error of the systems bounded by predefined decreasing boundary. In this control scheme, a multi-layer neural network is used to approximate the unknown non-linear items, and the robustifying control term is used to compensate the approximation errors. The adaptive laws of weights of the neural network and robustifying control term are derived based on the Lyapunov stability analysis, so that, under appropriate assumptions, the transient and steady-state error bounds can be guaranteed. Compared with the existing work, the adaptable parameters in the proposed method do not need an off-line training procedure for better approximation. Simulations performed on a two-link robot manipulator illustrate the developed controller and demonstrate its performance.

In recent years, robotic systems have been widely used in different applications, and this has motivated researchers to develop different control methods. A model-free, intelligent, robust control method for a nonlinear robotic manipulator system is proposed in this work. This paper presents a novel solution for the major drawbacks of the sliding mode control scheme, which are chattering. Prior knowledge is needed about the dynamic model of the controlled system and the upper bound of uncertainty. In this paper, a fuzzy-like PD controller with SMC (FLPDSM) is proposed. The fuzzy-like PD controller was designed according to fuzzy rules and membership functions based on the nominal model of the robot manipulator. A robust control term was added to the control signal to compensate for the system uncertainty, and external disturbances are compensated by adding an auxiliary robust term to the SMC control law. Two methods for designing robust control terms are proposed. The first proposed method assumes that the upper bound of system uncertainty is known although it cannot be exactly determined due to external disturbances and uncertainty. Hence, a second method was proposed that assumes this bound to be unknown, and an adaptive gain based on Lyapunov theory was used to derive the adaptation law. The Lyapunov second method was used to ensure the stability of the closed loop system. Performance tests on the proposed methods were implemented through simulation studies for the two-link robotic manipulator, and the test results were compared with the standard SMC to verify the effectiveness of the proposed method. A good trajectory tracking with a high robustness against parameter variations and external disturbances was observed under the presented control scheme.

The paper presents a new proximate time optimal seek control approach with discrete-time variable structure control theory for a hard disk drive (HDD) servo. It incorporates the time optimal control idea into the time-varying sliding mode control design and derives a class of proximate time optimal control algorithms with robustness. The proposed approach provides one unified framework for both track seeking and track following controller design, it achieves smooth transition from seek control to track-following control naturally, and it eliminates the common chattering and overshoot problem as well. A systematic method is developed for the choice of controller parameters. Simulation results are demonstrated to show the robustness of the proposed method to disturbances, unmodelled dynamics and parameter variations with near time optimal performance.

In this paper, a chattering-free neural sliding mode control (CFNSMC) scheme is proposed for robotic manipulators with considering actuator dynamics. A full-order sliding mode surface is constructed to develop the finite-time controller such that the chattering and singularity problems can lie avoided since the derivatives of terms with fraction powers do not appear in the actual control law. Besides a radial basis function neural network (RBFNN) is employed to approximate the system uncertainties and nonlinearities. With the proposed scheme, no singularity and chattering problems exist in the controller design, and the convergence of the position tracking error is guaranteed via the Lyapunov synthesis. Comparison simulations of a two-link robotic manipulator are provided to verify the effectiveness of the proposed method.

Based on a non-linear model of a computer numerical control (CNC) system, a general adaptive robust controller (ARC) is presented in this paper. The ARC was used to treat problems including the compensation of friction non-linearity, parameter variation, and unmodelled dynamics in the design of a CNC system. It can enhance stability robustness and performance robustness. The simulation results show the effectiveness of the method.

A comparison of model-based machining force control approaches