Control Method For Robot Manipulators Research Articles

Event-triggered learning-based robust tracking control for robotic manipulators with uncertain dynamics and non-zero equilibrium

This paper presents a novel optimal tracking control method for robotic manipulators (RMs) with system uncertainties and non-zero equilibrium points. The existing tracking control methods typically require the precise system dynamics and assume the existence of a zero equilibrium point, which may not always be true in practice. To overcome this issue, a new cost function with respect to the first derivative of system states and a known upper bound on the system’s mismatched disturbances is designed, and then an optimal control problem of RMs is formulated. Furthermore, to solve this optimization, an event-triggered critic learning control framework is proposed to estimate the solution of Hamilton–Jacobi-Bellman equation, reducing the computational burden. In the critic learning control designs, novel weight updating laws related to system stability information are proposed to train the critic neural networks, which eliminates the initial stabilization requirement. Theoretical analysis shows that the stability of the closed-loop system in the sense of uniform ultimate boundedness is ensured. It should be emphasized that the proposed control method offers a simplification of the tracking controller design process and removes the restriction on system dynamics. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.

Metaheuristic adaptive control based on polynomial regression and differential evolution for robotic manipulators

Adaptive control of systems consists of the online adjustment of their control parameters to deal with parametric uncertainties and disturbances. Indirect Adaptive Control (IAC) of electromechanical systems and robotic manipulators based on metaheuristic optimization has been shown to be competitive compared to other classical and advanced control schemes. In this approach, the identification of system model parameters is stated as an optimization problem and then solved online by metaheuristics. Subsequently, the identified model is used in a second stage of online metaheuristic optimization to predict the system behavior and tune its control parameters. Therefore, this approach can be computationally expensive and unaffordable for systems with more complex dynamics whose models are just as complex. Due to the above, this work proposes an indirect adaptive control method for robotic manipulators based on differential evolution (DE) optimization, which aims to reduce the computational cost of the online identification stage by using Polynomial Regressors (PR) whose adjustment can be performed through a closed-form solution. The proposed method is tested in simulation for a 2 d.o.f. robotic manipulator and the results are compared against the original indirect adaptive control approach based on metaheuristic optimization and also a controller optimized offline. The post-hoc pair-wise Friedman tests confirm that the proposed approach provides competitive results compared to the original approach, with significant savings in computational resources.

A Model-Free-Based Control Method for Robot Manipulators: Achieving Prescribed Performance and Ensuring Fixed Time Stability

This paper addresses three significant challenges in controlling robot manipulators: improving response time, minimizing steady-state errors and chattering, and enhancing controller robustness. It also focuses on eliminating the need for computing the robot’s dynamic model and unknown functions, as well as achieving global fixed-time convergence and the prescribed performance for the control system. To achieve these objectives, a fixed-time sliding mode function is designed, which uses transformation errors to achieve prescribed control performance, with adjustments made to the maximum overshoot, convergence time, and tracking errors to keep them within predefined bounds. Additionally, a radial basis function neural network (RBFNN) is used to eliminate the need for knowledge of the robot’s dynamical properties and uncertain terms, which also reduces negative chattering. Finally, a novel fixed-time terminal sliding mode control (TSMC) algorithm is developed for robot manipulators without using their dynamical model. The fixed-time stability of the control system is thoroughly demonstrated by applying Lyapunov criteria and conducting simulations on a robot manipulator to showcase its effectiveness.

Taylor‐based adaptive sliding mode control method for robot manipulators

AbstractThis paper develops a novel Taylor‐based adaptive sliding mode control method (ASMC) for robot manipulators. In the first new scheme, sliding mode control (SMC) is effectively enhanced using the Taylor expansion for achieving a less conservative sign‐function gain that enables chattering attenuation. After that, a new Taylor‐based adaptive SMC scheme is proposed without prior knowledge of the upper bound of uncertainty and the Taylor expansion coefficients. Then, a new Taylor‐based boundary layer ASMC scheme is proposed for chattering attenuation. As a fact, no chattering is expected to be observed as long as the sliding surface remains an invariant set. However, the sliding surface will not be an invariant set unless the sign‐function is precisely determined on the sliding surface. It is verified that the sign‐function cannot be precisely determined on the sliding surface due to the presence of uncertainty, hence, the chattering phenomenon. In the new Taylor‐based boundary layer ASMC scheme, the conventional ASMC is modified by removing the sign‐function in the vicinity of the sliding surface and using the Taylor expansion to estimate and compensate for the uncertainty. Compared to a time‐delay ASMC applied to a robot manipulator, the Taylor‐based ASMC scheme exhibits a less conservative sign‐function gain resulting in chattering attenuation.

Fixed-Time Sliding Mode-Based Active Disturbance Rejection Tracking Control Method for Robot Manipulators

This work investigates the issue of a hybrid trajectory tracking control algorithm (HTCA) for robot manipulators (RMs) with uncertain dynamics and the effect of external disturbances. Following are some proposals for achieving the control target. Firstly, to achieve the active disturbance rejection, we propose a uniform second-order sliding mode disturbance observer (USOSMDO) to obtain directly the lumped uncertainties without their prior upper-bound information. Secondly, a fixed-time singularity-free terminal sliding surface (FxSTSS) is proposed to obtain a fixed-time convergence of the tracking control error (TCE) without the singularity in the control input. Then, using information on the proposed USOSMDO, our HTCA is formed based on the FxSTSS and the fixed-time power rate reaching law (FxPRRL). The control proposal not only stabilizes with the global fixed-time convergence but also attains high tracking accuracy. In addition, the chattering problem also is handled almost completely. Finally, numerical simulations verify the effectiveness and advantages of applying the proposed HTCA to a FARA robot.

Event-Triggered Robust Optimal Control for Robotic Manipulators with Input Constraints via Adaptive Dynamic Programming

This paper proposes an event-triggered robust tracking control method for robotic manipulators with asymmetrical input constraints based on adaptive dynamic programming (ADP). First, the original robust tracking control problem is transformed into an optimal control problem for a nominal system with the help of a novel cost function design. Next, an event-triggered optimal control approach is proposed to solve this optimization problem and obtain the optimal solution to the Hamilton-Jacobi-Bellman (HJB) equation. The classical ADP framework is then used to approximate the optimal cost function and controller. Unlike existing weight adaptive laws, an additional term is introduced for removing the requirement of initial stabilization. Based on the Lyapunov theory, the stability of the original robotic system and the convergence of weight estimation are both guaranteed. Finally, simulation results are presented to demonstrate the effectiveness of the proposed event-triggered optimal control method.

Scaled Jacobian transpose based control for robotic manipulators

This paper presents a scaled Jacobian transpose based control method for robotic manipulators as a modification of a conventional Jacobian transpose based method. The proposed method has several advantages such as it shows faster convergence and better tracking performance than the conventional method, furthermore, it does not have any singularity problem similar to the conventional method. The scaled Jacobian transpose is obtained by collecting each pseudoinverse of the column vector of the Jacobian matrix. The proposed method performs a given task well under singular configurations while minimizing the task error. Finally, a few comparative studies with the conventional method are provided to show the effectiveness of the proposed method through simulations.

Iterative learning-based minimum tracking error entropy controller for robotic manipulators with random communication time delays

A novel feedback control method for robotic manipulators with random communication delays by combining the optimal P-type iterative learning control (ILC) idea with a minimum tracking error entropy control strategy is presented. The control design is formulated as an optimisation problem with a proper performance index and a constraint. In specific, the performance index implies the idea of the minimum entropy control of the closed-loop tracking error. The convergence in the mean-square sense has been analysed for all the signals in the closed-loop system. The convergence condition of such a tracking error under ILC framework is treated as the constraint condition which is satisfied in the optimisation process. It has been shown that the numerical optimal solution per iteration can be obtained by using the well-known particle swarm optimisation techniques. Simulation results are provided to show the effectiveness of the proposed approach.

弾性関節を持つロボットマニピュレータのマルチレートフィードフォワード制御系の実現

This paper introduces a novel multirate feedforward control method for robot manipulators with elastic joints. Perfect tracking control methodology using multirate feedforward control was proposed by H. Fujimoto, et al. Then, A. Shimada, et al. have prsented its application to robot manipulators; however, they only described the controller design process and gave a few simulation results. In addition, they did not provide details on how the state reference should be designed. Even if experiments were attempted, it would be difficult to evaluate control performance since generally manipulators have joint angle sensors mounted on the output side of reduction gears In order to solve this, this paper illustrates the design process for the state reference, and introduces a prototype robot manipulator that has precision rotary encoders installed on the output side of the joints. This means that the manipulator has not only the rotary encoders attached to servo motors but special precision rotary encoders. We describe experimental results obtained by applying this control technique.

A robust adaptive H∞ control for robotic manipulators with input torque uncertainties

This paper proposes an adaptive control method for robotic manipulators with input toque uncertainties. For each link of manipulators, it is assumed that the input torque uncertainties can be divided into unknown parameters term and bounded disturbance term. In addition, all the parameters for input torque uncertainties and robot are unknown. The proposed method ensures that the unknown parameters are estimated adaptively. Moreover, our proposed method can attenuate not only the external input torque disturbances, but also the estimation errors of the unknown parameters in the notion of H∞ control performance. In spite of considering the non-linear adaptive H∞ control problems, the compensator can design without solving the Hamilton-Jacobi-Isaacs equation. Simulation and experimental results are given to illustrate the effectiveness of our proposed method.

障害物回避のための視覚に基づくマニピュレータ冗長制御と画像特徴推定

We propose a new redundancy control method for robot manipulators based on visual servoing, which enables obstacles to be avoided while positioning an end-effector in its target position. The control inputs to the manipulator are calculated both from the image features of the end-effector, other parts of the manipulator and obstacles, that are obtained from a stereo vision system, and from the known kinematic manipulator model. Moreover, our method enables the manipulator to avoid singular configurations simultaneously while taking joints limits of the manipulator into consideration. However, it is not easy to obtain all necessary image features of the manipulator by image processing in a real workspace. We estimate image features that cannot be obtained by image processing or which are hidden by some obstacles. Necessary image features of the manipulator are estimated from calibrated camera parameters and the known kinematic model of the manipulator for obstacle avoidance. Experimental and simulation results reveal the validity and effectiveness of our proposed redundancy control method for avoiding obstacles and singular configurations.

Robust control of robot manipulators based on dynamics decomposition

This paper presents a new robust saturation-based control method for robot manipulators and related experimental results. The proposed method distinguishes between uncertainty in the inertia, Coriolis and centripetal forces, gravity and friction. A robust compensator is designed for each type of uncertainty, and each control parameter is directly related to a specific behavior of the closed-loop robot system and can be adjusted accordingly. The goal is to achieve better performance by using this fine-tuning capability of the control law. The proposed control method has been implemented on a direct-drive robot arm. Experiments were conducted to investigate the effectiveness of the proposed method, and the results are reported in this paper.

Classification and Examination of Adaptive Control Methods for Robots

The different adaptive control methods for robot manipulators are critically examined and compared, under various conditions. In order to perform the comparison suitable criteria are chosen. The different adaptive control methods are classified according to their properties, and examined according to the criteria chosen. The comparison between the methods is mainly analytical, but is confirmed with simulations. Advantages and disadvantages of the different control, adaptation and identification methods are presented.

Asymptotically normal state estimators of adaptive models of robot manipulators

We describe an adaptive control method for robot manipulators using a linear simplified model with unknown parameters. Convergence and asymptotic normality of the state estimators is proved.

An addendum on “Robust control of robots by the computed torque method”

We reinterprete and improve recent results on robust control of robots by the computed method. The methods and ideas used are inspired by ‘passivity based’ control methods for robot manipulators and lead to a significant increase in freedom of controller implementation, thereby providing more flexibility to the designer of robot control systems.

Learning Control of Robotic Manipulators Based on Neurological Model CMAC

A learning control method for robotic manipulators is proposed by using the CMAC (Cerebeller Model Arithmetic Computer), a neurological model of cerebellum. The control system consists of a feedforward controller with the CMAC and a fixed-gain linear feedback controller. This system is designed in such a way that desired hand trajectories which are specified in the operational space can be tracked directly without being converted into the ones in the joint space, thus so-called inverse kinematics problems need not be solved. Moreover this system requires no knowledge on manipulator dynamics for which an internal model is to be built in the control system by learning. Feasibility of the method is studied through various kinds of computer simulation experiments by using a 2-DOF planar manipulator. Desired trajectories are generated from the data measured in experiments of human handwriting motion, and are fairly complex for the model manipulator. Such simulation experiments demonstrate high control system performance from the viewpoints of the convergence in repetitive motions as well as of the so-called generalization phenomenon in learning.

Force control of a robotic manipulator by application of a neural network

In this paper, a force control method for robotic manipulators which utilize a neural network model is proposed with consideration of the dynamics of objects. The proposed system consists of a standard PID controller and a multilayered neural network model, which optimizes a set of controller's parameters via a process of learning. The neural network model has not yet been applied to force control problems, but the proposed method is shown to be applicable to force/compliance control problems. The stability of this system and a wider applicability are verified by simulation studies.

A Splines–Based Control Method for Robot Manipulators

SUMMARYIn this paper, a new splines–based control method for robot manipulators is presented and discussed. The above method can be effectively used for path planning and control of rigid and flexible robots. The computational simplicity of the proposed algorithm, together with its flexibility and its high–level intelligence built in, can be considered as promising tools for achieving the goals of modem robot manipulator design.

Robust Controller Design for Robot Manipulators

In this paper we give a control method for robot manipulators which takes account of both the command response and the robustness in a systematic way by utilizing two-degree-of-freedom controller configuration. A simulation result is given to show the validity of our method.