Control Of Redundant Robot Manipulators Research Articles

A Discrete Model-Free Scheme for Fault-Tolerant Tracking Control of Redundant Manipulators

Fault tolerance is a critical requirement for robust motion control of redundant robotic manipulators. This article aims to endow the redundant manipulator with the capability to achieve the required path of end-effector in the condition that one or some of its joints’ motion fail. Although many fault-tolerant control algorithms of redundant manipulator have been proposed in recent years. However, few of them are on the basis of the condition that the robotic model is unknown. The complexity of the calculation model limits the efficiency and portability of these algorithms. For the first time, we proposed a discrete model-free fault-tolerant tracking control scheme of redundant manipulator, which takes into account the fault tolerance in the control system of redundant manipulator by formulating it into a quadratic programming (QP) framework. The core of the proposed scheme consists of a discrete kinematic estimator and a discrete QP solver, powered by which the fault-tolerant control problem is transformed into a unified computing problem relaxing the need of knowing the redundant manipulator’s kinematic model. A discrete joint space observer is proposed for the detection of the happening of faulty states. Extensive simulations and experiments based on a redundant manipulator are performed and analyzed to support the verification of the efficiency and effectiveness of the proposed scheme.

Adaptive quadratic optimisation with application to kinematic control of redundant robot manipulators

ABSTRACT The primal-dual gradient dynamics is a broadly investigated approach for handling optimisation problems. In this paper, we provide an extension of such dynamics under the adaptive updating framework for solving equality-constrained quadratic programmes. We show that the performance of the proposed method is theoretically guaranteed and it has asymptotic convergence to the solution of the optimisation problem and the minimum inter-event time is non-trivial. A numerical example and an application show the effectiveness and advantages of the proposed method.

Comparative studies and performance analysis on neural-dynamics-driven control of redundant robot manipulators with unknown models

This paper proposes an inverse-free and model-free control scheme based on gradient neural dynamics (GND), which avoids the calculation of pseudo-inverse, to achieve the tracking control of redundant robot manipulators without knowing their kinematic models. Specifically, two GND models are deployed to solve the inverse kinematics problem and to estimate the unknown Jacobian matrix of manipulators respectively. We prove that the residual tracking error associated with the proposed scheme theoretically converges to an arbitrarily small upper bound in finite-time. Besides, combining GND and zeroing neural dynamics (ZND), this paper also proposes two control schemes based on hybrid neural dynamics to further achieve better performance. Moreover, the proposed continuous-time control schemes are improved to discrete-time algorithms to facilitate the deployment. Finally, the feasibility and merits of the proposed control schemes are revealed by experiments and comparisons.

Two Model-Free Schemes for Solving Kinematic Tracking Control of Redundant Robot Manipulators Based on Cmac Networks

Two Model-Free Schemes for Solving Kinematic Tracking Control of Redundant Robot Manipulators Based on Cmac Networks

Robust model-free control for redundant robotic manipulators based on zeroing neural networks activated by nonlinear functions

Recent studies have verified that zeroing neural network is suitable for model-free feedback control of redundant robot manipulators with excellent convergence and accuracy. Unlike previous studies using a linear activation function, this paper employs zeroing neural networks activated by nonlinear functions to control redundant robots to track desired paths without knowing kinematic models of robots, and systematically investigates the finite-time convergence and robustness of the proposed control scheme. Specifically, two nonlinear-function-activated zeroing neural networks are employed to solve the Jacobian estimation problem and trajectory tracking problem respectively. After introducing a model-free control scheme generally applicable to different types of robots, theoretical analysis proves that the proposed control scheme has finite-time convergence when employing nonlinear activation functions and the tracking error will not exceed the upper bound with the bounded noise interference. Finally, simulations based on a five-link planar robot and a PUMA 560 robot reveal the finite-time convergence of the proposed control scheme and verify that nonlinear functions can effectively increase the error convergence rate and reduce the tracking error caused by noises, compared with conventional method based on linear-function-activated zeroing neural networks.

Acceleration Level Control of Redundant Manipulators with Physical Constraints Compliance and Disturbance Rejection under Complex Environment

Investigation of joint torque constraint compliance is of significance for robot manipulators especially working in complex environments. A lot of which is attributed to that, on the one hand, it is beneficial to the improvement of both safety and reliability of the mission execution. On the other hand, the energy consumption required by the robot to complete the desired mission can be reduced. Most existing schemes do not take the joint torque limit and other inherent physical structure limits in a manipulator into account at the same time. In addition, many unavoidable uncertainties such as the external environmental disturbance and/or electromagnetism interferences in the circuit system may influence the accuracy and effectiveness of the task execution for a robot. In this study, we cast light on the acceleration level control of redundant robot manipulators considering both four physical constraint limits and interference rejection. A robust unified quadratic-programming-based hybrid control scheme is proposed, where the joint torque constraints are converted as two inequality constraints based on the robots’ dynamics equation. A recurrent-neural-network-based controller is designed for solving the control variable. Numerical experiments performing in PUMA 560 manipulator and planer manipulator illustrate that a rational torque distribution is obtained among the joints and the considered physical structural vectors are all restricted to the respective constraint range. In addition, even disturbed by the noise, the manipulator still successfully tracks the desired trajectory under the proposed control scheme.

Improved recurrent neural network-based manipulator control with remote center of motion constraints: Experimental results

In this paper, an improved recurrent neural network (RNN) scheme is proposed to perform the trajectory control of redundant robot manipulators using remote center of motion (RCM) constraints. Firstly, learning by demonstration is implemented to model the surgical operation skills in the Cartesian space. After that, considering the kinematic constraints associated with the optimization control of redundant manipulators, we propose a novel RNN-based approach to facilitate accurate task tracking based on the general quadratic performance index, which includes managing the constraints on RCM joint angle, and joint velocity, simultaneously. The results of the conducted theoretical analysis confirm that the RCM constraint has been established successfully, and accordingly. The corresponding end-effector tracking errors asymptotically converge to zero. Finally, demonstration experiments are conducted in a laboratory setup environment using KUKA LWR4+ to validate the effectiveness of the proposed control strategy.

Adaptive tracking control of robot manipulators with input saturation and time‐varying output constraints

AbstractThis paper investigates adaptive tracking control in task space for robot manipulators with uncertain system dynamics, input saturation, and time‐varying output constraints simultaneously. An auxiliary system is constructed to compensate the effect of the input saturation, and an asymmetric barrier Lyapunov function (BLF) is applied to tackle time‐varying output constraints, while radial basis function (RBF) neural networks (NN) are used to approximate the unknown closed‐loop dynamics. By introducing a disturbance observer (DO), unknown external disturbances from humans and environment are estimated, and NN approximation errors are compensated. A novel adaptive NN tracking controller is designed to guarantee all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (UUB), while the tracking errors and observer errors converge to a small neighborhood of zero, and the time‐varying output constraints are not violated. Moreover, the adaptive tracking control of redundant robot manipulators is studied, and the subtask and task space tracking of redundant robot manipulators are realized simultaneously, while the stability of the system is proved by Lyapunov stability theory. Finally, some simulation results are presented to verify the effectiveness and superiority of the proposed control scheme.

여유자유도 로봇 매니퓰레이터를 위한 동적제어시스템

This paper deals with the dynamic control of redundant robot manipulator. Traditionally, the kinematic control schemes for redundant robot manipulator were developed from the point of speed and used under the assumption that the dynamic control of manipulator is perfect. However, in reality, the precise control of redundant robot manipulator is very difficult due to their dynamics. Therefore, the kinematic controllers for redundant robot manipulator were employed in the acceleration dimension and may be combined with the computed torque method to achieve the accurate control performance. But their control performance is limited by the accuracy of the manipulator parameters such as the link mass, length, moment of inertia and varying payload. Hence in this paper, the proportional and derivative control gains of the computed torque controller are optimized by the genetic algorithm on the typical payloads, and the neural network is applied to obtain the proper control gains for arbitrary loads. The simulation results show that the proposed control method has better performance than the conventional control method for redundant robot manipulator.

New Joint-Drift-Free Scheme Aided with Projected ZNN for Motion Generation of Redundant Robot Manipulators Perturbed by Disturbances

Joint-drift problems could result in failures in executing task or even damage robots in actual applications and different schemes have been presented to deal with such a knotty problem. However, in these existing schemes, there exists the coupling in coefficients for eliminating the drift in the joint space and the equality constraint for completing the given task in the Cartesian space, thereby, theoretically, leading to a paradox in achieving zero joint drift in the joint space and zero position error in the Cartesian space simultaneously. A novel joint-drift-free (JDF) scheme synthesized by a projected zeroing neural network (PZNN) model for the motion generation and control of redundant robot manipulators perturbed by disturbances is proposed and analyzed in this article. Besides, the PZNN model could adopt saturated or even nonconvex projection functions. The proposed scheme completely decouples the interferences of joint errors in the joint space and position errors in the Cartesian space for the first time. Beyond that, theoretical analysis is conducted in order to validate that the PZNN model is of global convergence to the theoretical kinematics solution to the motion generation of robots, and that the joint-drift problems are thus remedied. Moreover, several simulations and physical experiments on the strength of different robot manipulators are carried out to confirm the superiority, efficiency, and accuracy of the proposed JDF scheme synthesized by the PZNN model for remedying joint-drift problems of redundant robot manipulators in noisy environments.

On Generalized RMP Scheme for Redundant Robot Manipulators Aided With Dynamic Neural Networks and Nonconvex Bound Constraints

In this paper, in order to analyze the existing repetitive motion planning (RMP) schemes for kinematic control of redundant robot manipulators, a generalized RMP scheme, which systematizes the existing RMP schemes, is presented. Then, the corresponding dynamic neural networks are derived, which leverage the gradient descent method with the velocity compensation with the feasibility proven theoretically. Given that the position errors of the end-effector should be tiny enough in the applications of redundant robot manipulators when executing a given task, especially for a precision instrument, the performance analyses on the control schemes are urgently desirable. In this paper, the upper bound of the position error on the existing RMP schemes is deduced theoretically and verified by computer simulations, with the relationship between the position error and the manipulability derived. In addition, dynamic neural networks are constructed to solve the generalized RMP schemes, with the joint velocity limits in RMP schemes extended to the nonconvex constraint. Finally, computer simulations based on different redundant robot manipulators and comparisons based on different controllers are conducted to verify the feasibility of the generalized RMP scheme and the proposed dynamic neural networks.

Feedback-Added Pseudoinverse-Type Balanced Minimization Scheme for Kinematic Control of Redundant Robot Manipulators

In this paper, a new feedback-added pseudoinverse-type balanced minimization (FPBM) scheme is proposed and studied for the kinematic control of redundant robot manipulators. Such a scheme is designed by combining the minimum acceleration norm (MAN) solution and the weighted minimum velocity norm (WMVN) solution and by introducing the feedback. With the MAN and WMVN combination, the proposed FPBM scheme can not only remedy the phenomena of high velocity and acceleration but also generate a near-zero velocity after task execution. With the feedback introduction, the proposed FPBM scheme can guarantee a nondivergent end-effector tracking error. Based on a four-link robot manipulator, the simulation results are presented to show the effectiveness of the proposed FPBM scheme.

Robustness Analysis and Robotic Application of Combined Function Activated RNN for Time-Varying Matrix Pseudo Inversion

As a typical representative of the recurrent neural network (RNN), Zhang neural network (ZNN) has been proved as a powerful parallel-processing neural solver for time-varying matrix problems. Recent studies have shown that, in the absence of noise, the ZNN model activated by a combined activation function (CAF), which is the linear combination of sign-bi-power (SBP) and linear functions (termed CAF-ZNN), can achieve much better finite-time convergence compared with other ZNN models for time-varying matrix pseudoinversion. This paper investigates for the first time the influence of noises on such a CAF-ZNN model. We not only present the upper bound of steady-state solution error synthesized by the noise-polluted CAF-ZNN model for time-varying matrix pseudoinversion but also derive the finite convergence time for the solution error reaching the upper bound. Both the theoretical analyses and simulation observation reveal that the solution error can be made arbitrarily small by choosing some design parameters of CAF-ZNN. At last, a robotic application is successfully performed to further illustrate the feasibility of the CAF-ZNN model to kinematic control of redundant robot manipulator.

The Application of Noise-Tolerant ZD Design Formula to Robots’ Kinematic Control via Time-Varying Nonlinear Equations Solving

Recently, a new formula with noise-tolerant capability has been designed by Zhang et al. , and the resultant Zhang dynamics (ZD) models have been developed to solve different types of time-varying problems. Based on previous research, this paper presents and investigates the application of such a noise-tolerant ZD design formula to kinematic control of redundant robot manipulators via time-varying nonlinear equations solving. Specifically, by exploiting this ZD design formula to solve the system of time-varying nonlinear kinematic equations involved in robot control, the redundancy-resolution scheme is established. Such a scheme contains the proportional, integral, and derivative information of the desired Cartesian path of the robot end-effector and can thus be viewed as a nonlinear proportional-integral-derivative controller for redundant robot manipulators. Then, theoretical results are given to show that the redundancy-resolution scheme has the capability of noise suppressing. Simulation results based on a four-link planar robot manipulator and a PA10 robot manipulator with zero, constant, and bounded time-varying noises further substantiate the efficacy and superiority of the redundancy-resolution scheme, and show the application prospect of the noise-tolerant ZD design formula.

Adaptive control of redundant robot manipulators with null-space compliance

PurposeThe purpose of this paper is to propose an adaptive control for a redundant robot manipulator interacting physically with the environment, especially with the existence of humans, on its body.Design/methodology/approachThe redundant properties of the robot manipulator are used and a reference velocity variable is introduced to unify the operation-space tracking control and the null-space impedance control under one common framework. Neural networks are constructed to deal with unstructured and unmodeled dynamic nonlinearities. Lyapunov function is used during the course of control design and simulation studies are carried out to further illustrate the effectiveness of the proposed strategies.FindingsSatisfying tracking performance in the operation-space and compliance behavior in the null-space of the redundant robot manipulator are ensured simultaneously.Originality/valueThe design procedure of redundant robot manipulators control can be greatly simplified, and the framework of multi-priority control can be transformed into a joint-space velocity tracking problem via the introducing of a reference velocity variable.

Neural Dynamics for Cooperative Control of Redundant Robot Manipulators

In this paper, a neural-dynamic distributed scheme is proposed for the cooperative control of multiple redundant manipulators with limited communications. It is guaranteed that, with the communication network being connected, all manipulators can jointly reach the same desired motion. The proposed distributed scheme is rearranged as a time-varying quadratic program and solved online by a Zhang neural network. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, an explicit bound relationship between the control input noise and the end-effector position error is analytically derived. Furthermore, numerical comparisons substantiate the superiority, effectiveness, and accuracy of the proposed distributed scheme.

Bi-criteria minimization with MWVN–INAM type for motion planning and control of redundant robot manipulators

SUMMARYThis study proposes and investigates a new type of bi-criteria minimization (BCM) for the motion planning and control of redundant robot manipulators to address the discontinuity problem in the infinity-norm acceleration minimization (INAM) scheme and to guarantee the final joint velocity of motion to be approximate to zero. This new type is based on the combination of minimum weighted velocity norm (MWVN) and INAM criteria, and thus is called the MWVN–INAM–BCM scheme. In formulating such a scheme, joint-angle, joint-velocity, and joint-acceleration limits are incorporated. The proposed MWVN–INAM–BCM scheme is reformulated as a quadratic programming problem solved at the joint-acceleration level. Simulation results based on the PUMA560 robot manipulator validate the efficacy and applicability of the proposed MWVN–INAM–BCM scheme in robotic redundancy resolution. In addition, the physical realizability of the proposed scheme is verified in practical application based on a six-link planar robot manipulator.

The Application of ZFD Formula to Kinematic Control of Redundant Robot Manipulators With Guaranteed Motion Precision

Zhang et al. recently design a special difference formula called the Zhang finite-difference (ZFD) formula. This paper applies the ZFD formula for the kinematic control of redundant robot manipulators, due to its good performance in approximating first-order derivatives. Specifically, the ZFD formula is employed to discrete the pseudoinverse-based (P-based) kinematic control scheme; a new P-based kinematic control scheme with guaranteed motion precision is developed for redundant robot manipulators. Simulation results based on a five-link planar robot manipulator, which performs different end-effector paths, validate the effectiveness of the new scheme and indicate the application prospects of the ZFD formula.

Intelligent Tracking Control of Redundant Robot Manipulators including Actuator Dynamics

In this paper, the trajectory tracking control problem of redundant robot manipulators at the actuator level is studied. In the proposed control scheme, RBF (Radial Basis Function) neural network and adaptive bound part is combined with the model based controller. All the existing uncertainties are learned with the RBF neural network without offline learning. The uncertain parameters, the bounded external disturbances and the neural network reconstruction error are approximated by the adaptive bound part. The hybrid controller is designed in such a way that both the trajectory tracking error and subtask task tracking error converges to zero as well as it controls the DC motors that are used to provide the required currents and torques. Finally, the Lyapunovs stability analysis is used to prove the overall closed loop system to be asymptotically stable.

Analysis, Verification and Comparison on Feedback‐Aided MA Equivalence and Zhang Equivalency of Minimum‐Kinetic‐Energy Type for Kinematic Control of Redundant Robot Manipulators

AbstractBy following and generalizing Ma et al.'s inspiring work and Zhang et al.'s inspiring work, this paper proposes and investigates three kinds of equivalent relationships with error‐feedback information incorporated for the minimum‐kinetic‐energy (MKE) redundancy resolution. Specifically, these three equivalent relationships are divided into two big classes in terms of scheme formulations: one is termed MKE‐type Ma equivalence (MKE‐ME); the other is MKE‐type Zhang equivalency (MKE‐ZE), which can be further subdivided into MKE‐ZE‐I and MKE‐ZE‐II. Also, the equivalent analyses as well as the primary distinctions about three such equivalent relationships are presented. The simulation results based on a PUMA560 robot manipulator and a three‐link planar robot manipulator not only verify the efficacy of the corresponding velocity‐level and acceleration‐level schemes of MKE‐ME, MKE‐ZE‐I and MKE‐ZE‐II, but also substantiate their reasonableness and effectiveness of these three equivalent relationships. More importantly, the comparative numerical results show their respective characteristics and advantages for kinematic control of redundant robot manipulators.