Nonlinear Inverse and Predictive End Point Trajectory Control of Flexible Macro-Micro Manipulators

The question of end-point trajectory control of flexible macro-micro manipulator based on variable structure control (VSC) and predictive control techniques is considered. A VSC law is derived for the end point trajectory control of the rigid micro manipulator. For the end-point control of the flexible macro manipulator, a predictive control law is derived. The predictive control law is obtained by minimizing a quadratic function of the tip tracking error of the flexible link (macro), the elastic deflection, and the input torque of the macro manipulator. The combination of the VSC and the predictive controllers accomplishes precise end-effector trajectory tracking and elastic mode stabilization. These results are applied to a planar macro-micro manipulator system consisting of one flexible link and two micro rigid links. Simulation results are presented to show that in the closed-loop system time varying end point trajectory control and elastic mode stabilization are accomplished.

This paper presents an application of model reference adaptive control to the position and vibration control of a single-link flexible manipulator. A distributed mass model of the flexible link has been analyzed using the method of modal expansion. The performance of the system with various control schemes has been investigated. It has been demonstrated that effective position/vibration control of a flexible manipulator is achieved by model reference adaptive control.

Tip position control of a two-link flexible robot manipulator based on nonlinear deflection feedback

Adaptive nonlinear vibration control of a Cartesian flexible manipulator driven by a ballscrew mechanism

The manipulating system of modern high-speed industrial robot may often contain the links with lowered mechanical rigidity. As the result, such a manipulating system possesses the increased level of vibrations and link's deformations under it's own weight and load. This leads to additional trajectory control and positioning error of the manipulator arm. So the control of flexible links manipulator is a complex problem. The control algorithm for the flexible link manipulator is offered for further explores. The algorithm is build with the use of model predictive control technique.

SummaryIn this article, we investigate the problem of nonlinear modeling and adaptive boundary vibration control with actuator failure for a flexible rotatable manipulator in three‐dimensional space, which is made up of a rotatable base and a flexible manipulator. In order to accurately reflect the characteristics of the distributed parameters, the Hamilton principle is introduced to derive the dynamic model expressed by partial differential equations (PDEs). Based on the model, an innovative boundary control scheme is proposed to eliminate the deflection and vibration simultaneously, and to guarantee that the rotatable base and the flexible manipulator can track the desired angle respectively. The adaptive law is developed to estimate the loss of the actuator. The effectiveness of the designed controller is verified from both theoretical analysis and numerical simulation.

The paper presents an approach to end point control of elastic manipulators based on the nonlinear predictive control theory. For the derivation of the predictive control law, a vector function s is chosen as a linear combination of the trading error,its higher order derivatives, and the integral of the trading error for robustness. A control law is derived by minimizing a quadratic function of the predicted value of s and control torques. This approach avoids the instability of the zero dynamics encountered in the controller design using feedback linearization and variable structure control techniques for end-point control. Simulation results are presented for a one link flexible manipulator to show that in the closed-loop system accurate end point trajectory control and vibration damping can be accomplished in the presence of uncertainty in the system parameters.

The task of model verification and control implementation for flexible multi-body systems undergoing large-angle displacement can probably be best accomplished using the experiments involved with large flexible multi-link manipulators. In this paper, various kinds of experiments for modeling and control for large flexible manipulators are reviewed. Although most experiments are restricted to either vertical or horizontal planes, and control algorithms are applied to simplified examples, insight gained in this survey will be useful to the advancement of the state-of-the-art for accurate modeling and precision control of flexible multibody manipulators.

The wide availability of microprocessors with much higher computational power capabilities has encouraged many researchers during the last decade to introduce the predictive control techniques to the field of power electronics and motor drives. One technique of predictive control, which is called model predictive control, is introduced in this paper and its application to control a five-phase induction motor is also presented. The mathematical formulation of both model predictive torque control and model predictive speed control algorithms are explained, which shows that the algorithms' equations are intuitive so they can be easily understood and implemented. Since a load torque estimate is needed in the predictive speed controller, an observer based on the minimal-order Gopinath's method is designed to get the load torque value. A comparison between the two techniques is carried out based on a simulation study. Also, the simulation results show the effectiveness of the predictive control in achieving a high dynamic performance control of multiphase induction motor drives.

In this research, the focus is on the adaptive fuzzy neural networks (NNs) control of the single-link flexible robot manipulator, which achieves accurate trajectory tracking and improves the speed of position tracking. Firstly, in order to establish a single-link flexible model, the lumped spring-mass method and Lagrangian equation are used. Secondly, a full-state feedback control is proposed. Aiming at achieving the control objective, the Lyapunov stability method proves that the closed-loop system is uniformly ultimately bounded. Finally, Numerical simulations are carried out to verify the performance of the fuzzy NNs control. Furthermore, the control performance is compared with the proportion derivative control.

For the control of 2-link flexible joint manipulators, a control method based on the singular perturbation theory and the Udwadia-Kalaba (U-K) method was proposed. The control design was implemented by 2 steps. First, the system order was reduced based on the singular perturbation method and the system was divided into fast and slow sub-systems, to simplify the solution process and overcome the system flexibility. Second, the state feedback constraint following control law for the fast and slow sub-systems was designed with the U-K method, to make the constraint following errors of the fast and slow sub-systems converge to zero, even if the system can't initially satisfy the constraints. The proposed method can deal with holonomic and nonholonomic servo constraints at the same time without the auxiliary variables of the Lagrange multiplier and the pseudo generalized velocity. The method was applied to 2-link flexible joint manipulator systems to solve the flexible oscillation and constraint following problems. Through simulations on MATLAB, and was compared with the traditional PID control, to verify the effectiveness and superiority.

Flexible Manipulators (FMs) provide a number of benefits, containing reduced weight due to the thinness of the robot’s linkages. Although the initial plan was to use actual robots’ flexibility or slenderness to their advantage, the complex dynamics of the systems piqued interest in using an experimental flexible manipulator as a testing ground for various modeling or control strategies. A review is essential for researchers who want to align their study objectives with those of the field because the literature is extensive and diverse. Due to the widespread usage of flexible manipulators in different mechatronic and robotic applications over the past few decades, many academics worldwide are now interested in researching this topic. Studies are categorized here according to the control and modeling technologies of flexible manipulators and methodologies. Review of recent works on analysis, modeling, mechanical vibration, control algorithms, gyroscope technology and applications, difficulties in managing flexible manipulators and their anticipated future, and the majority of the notable evolutionary and optimization algorithms, including Genetic Algorithm (GA), Differential Evolution (DE), and Fuzzy Logic (FL), as well as modification approaches and techniques, are discussed and underlined. This study examines many publications, thoroughly reviewing the analytical, mathematical, dynamical modeling, mechanical vibration control techniques and most of the notable evolutionary and optimization algorithmic approaches of Robotic Flexible Manipulator (RFM) structures.

This paper introduces a novel control strategy for managing the uncertainties in flexible joint manipulators, incorporating a Radial Basis Function Neural Network (RBFNN) with Adaptive Dynamic Surface Control (ADSC). This strategy innovatively utilizes RBFNN to precisely approximate uncertain system dynamics and integrates a nonlinear damping term to effectively counteract external disturbances, enhancing the overall control accuracy. We have also developed an adaptive law that updates neural network weights and system parameters in real-time, ensuring the system's adaptability to dynamic changes. The application of the Lyapunov method ensures that all signals within the closed-loop system remain semi-globally uniformly bounded, significantly reducing tracking errors. Moreover, we introduce the use of Long Short-Term Memory (LSTM) networks for predictive analysis of state data, which further confirms the robustness and effectiveness of our control method through extensive simulations. The distinctive integration of these technologies and their practical validation through comparative simulations underscore the innovative aspects of our approach in addressing real-world challenges in flexible manipulators.

A new method is proposed for the end-effector motion control of flexible manipulators. The dynamic equations of flexible robot manipulators are partitioned as pseudostatic equilibrium equations and deviations from them. The pseudostatic equilibrium considered here is defined as a hypothetical state where the end-effector motion variables have their desired values while the elastic deformations are instantaneously constant. Then, the control torques for the pseudostatic equilibrium are computed and the feedback stabilization of the deviation equations is achieved using strain gage and joint variable or tip point variable measurements. A planar two link robot with flexible forearm is taken into consideration for demonstration of the method. The elasticity of the forearm is approximately described by the first two modes and a controller is designed using this two-mode model. Furthermore, in order to investigate the effects of modeling discrepancies, a “submodel controller” is considered using a model that has only the first mode. The performances of these two controllers are compared by means of simulations. It is observed that the proposed control method does not seem to be sensitive to the number of modes included in the model of the manipulator.

With the rapid development of smart campus, this paper studies the attitude tracking control of flexible manipulator (FM) in colleges and universities under elastic vibration and external disturbances. First, different from the traditional modeling based on ordinary differential equations (ODEs), the partial differential equations (PDEs) dynamic model of a manipulator system is established based on the Hamilton principle (HP). Second, the boundary control condition of the end system of the manipulator is introduced to adjust the vibration of the manipulator. Furthermore, a Proportional-Derivative (PD) boundary control (PDBC) strategy is proposed by the Lyapunov function to suppress the vibration of the manipulator. Finally, a numerical comparison simulation based on MATLAB/SIMULINK further verifies the robustness and anti-disturbance performance of the control method proposed in this paper.