Redundant Robot Manipulators Research Articles

Regressor-free adaptive fuzzy force tracking control of redundant robot manipulator for task space

In this study, an adaptive fuzzy force control of a redundant robot manipulator experiencing system uncertainties and operating in an unknown environment is proposed. This is important not only to provide additional control flexibility for complicated tasks but also to avoid the joint limit of a robot in implementing better dynamics and kinematics. The relation between the task and joint spaces is discussed to derive a dynamic model for force tracking controller design. To treat the system uncertainties, an adaptive fuzzy system approach is established to achieve the adaptive position and force controller design based on a regressor-free approach. Considering that the stiffness coefficient of the environment is assumed to be unknown, the gradient descent method is used to estimate this coefficient to achieve adaptive force tracking. A stability analysis of the closed-loop system and the corresponding update laws are given by the Lyapunov stability theorem. Finally, several apposite simulations using the KUKA lightweight robot are performed to validate our approach and demonstrate the performance and effectiveness of the proposed regressor-free adaptive fuzzy force controller.

A Multi-Level Simultaneous Minimization Scheme Applied to Jerk-Bounded Redundant Robot Manipulators

In this paper, a multi-level simultaneous minimization (MLSM) scheme is proposed and investigated to remedy the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. The proposed scheme is novelly designed within multiple levels and finally resolved at the jerk level for a jerk-bounded robot motion, which is desirable for engineering applications. More importantly, the correctness of the proposed MLSM scheme is guaranteed by the corresponding theorems. Then, the MLSM scheme is formulated as a dynamical quadratic program (DQP) that is solved by a piecewise linear projection equation neural network (PLPENN). Furthermore, the path-tracking simulations based on a 6-degrees-of-freedom (DOF) robot manipulator substantiate the effectiveness and advantage of the MLSM scheme. Comparisons between the MLSM scheme and the minimum jerk norm (MJN) scheme illustrate that the proposed scheme is superior and more applicable. Finally, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is provided for reproducible engineering applications by researchers and practitioners. Note to Practitioners —This paper is motivated by the inverse kinematics problem of jerk-bounded redundant robot manipulators in practical applications. Note that the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as the occurrence of high joint variables always encountered in the traditional norm-based scheme for robot manipulators, which is not suitable for the real-time control of robots. Besides, it would be appealing and desirable to resolve the robot redundancy at the jerk level for industrial robots in engineering. Therefore, an effective, flexible, and stable solution for such robot manipulators is significant for practitioners. This paper proposes a multi-level simultaneous minimization (MLSM) scheme for practitioners interested in robot kinematics to remedy the JAD and NZFJV phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. Unlike traditional single-level schemes, such as the minimum jerk norm (MJN) scheme, the proposed scheme is designed within multiple levels with distinct physical nature and finally resolved at the jerk level to achieve a desirable performance for the jerk-bounded redundant robot manipulators. Besides, for better understanding of practitioners, the corresponding block diagram and principle interpretation of the MLSM scheme are presented. Simulation studies and comparisons are designed and conducted on a 6-degrees-of-freedom (DOF) robot manipulator to substantiate the effectiveness and superiority of the proposed scheme. Extensive tests with different weighting factors fully verify the flexibility and stable performance of the proposed MLSM scheme. For reproducible engineering applications by researchers and practitioners, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is further presented.

New Disturbance Rejection Constraint for Redundant Robot Manipulators: An Optimization Perspective

Due to the property of multiple solutions, redundant robot manipulators are usually required to simultaneously achieve multiple objectives in complex applications. The research of robustness for scheme formulation and optimization becomes an increasingly important issue for motion planning of redundant robot manipulators. From the perspective of optimization, a robust hybrid multiobjective (RHMO) scheme with a new disturbance rejection constraint is proposed in this article to achieve simultaneously four objectives together with the suppression of external time-varying disturbances. Theoretical results on the property of disturbance rejection are shown to confirm the effectiveness and robustness of the proposed RHMO scheme with a new disturbance rejection constraint. The RHMO scheme is then reformulated as dynamical quadratic programming with its solution found via the piecewise-linear projection equation neural network. Numerical experiments, tests, and comparisons on the basis of a PA10 manipulator verify the effectiveness, robustness, and superiority of the RHMO scheme with the new constraint for the motion planning and optimization of redundant robot manipulators against time-varying disturbances.

Noise-Tolerant and Finite-Time Convergent ZNN Models for Dynamic Matrix Moore–Penrose Inversion

Dynamic (or say, time-varying) problems have been a hot spot of research recently. As a general form of matrix inverse, dynamic Moore–Penrose inverse solving has received more and more attention owing to its broad applications. The approaches based on neural networks have become a popular solution to various dynamic matrix-related problems including dynamic Moore–Penrose inverse. However, existing neural models either only achieve infinite-time instead of finite-time convergence, or are sensitive to noises. Therefore, finite-time convergent neural model, which is simultaneously capable of addressing the noises, is desperately needed for dynamic Moore–Penrose inverse solving. To do that, in this paper, a novel evolution formula is designed based on the widely investigated Zhang neural network (ZNN). Accordingly, two modified ZNN models (MZNN), namely MZNN-R and MZNN-L models, are proposed and analyzed for the right and left dynamic Moore–Penrose inversion of full-rank matrices, respectively. In addition to providing detailed theoretical analyses on the desired finite-time convergence and noise-depression properties of the proposed two models, we also perform two numerical examples for further verification. Furthermore, to illustrate the potential of MZNN models in practical applications, two path-tracking control examples are also presented via a two-dimensional planar three-link and a three-dimensional Kinova Jaco $^2$ redundant robot manipulator. The feasibility, extraordinary efficacy, and superiority of the proposed MZNN models for dynamic Moore–Penrose inverse solving are corroborated by both theoretical results and simulation observations.

Two Hybrid End-Effector Posture-Maintaining and Obstacle-Limits Avoidance Schemes for Redundant Robot Manipulators

To fulfill path tracking tasks with the end-effector posture controlled in a complex environment, maintaining the robot manipulator end-effector posture and avoiding obstacles are two important issues needed to be considered. In this paper, two hybrid end-effector posture-maintaining and obstacle-limits avoidance (hybrid PM-OLA) schemes are proposed and investigated for motion planning of redundant robot manipulators, which are based on the quadratic programming (QP) framework. The end-effector posture-maintaining, obstacle-avoidance, and the joint-angular-limits are formulated as an equality constraint, inequality constraint, and bound constraint into the QP problem. With these hybrid PM-OLA schemes, the robot manipulator can avoid the obstacle and joint physical limits when executing end-effector tasks. The hybrid PM-OLA schemes are finally transformed into linear variational inequalities and solved by a recurrent neural network. Computer simulations and physical experiments substantiate the effectiveness, accuracy, safety, and the practicability of the proposed hybrid PM-OLA schemes. Comparisons with other schemes show that the proposed hybrid PM-OLA schemes are more suitable for applications.

New P-type RMPC Scheme for Redundant Robot Manipulators in Noisy Environment

SUMMARYRepetitive motion planning and control (RMPC) is a significant issue in the research of redundant robot manipulators. Moreover, noise from rounding error, truncation error, and robot uncertainty is an important factor that greatly affects RMPC schemes. In this study, the RMPC of redundant robot manipulators in a noisy environment is investigated. By incorporating the proportional and integral information of the desired path, a new RMPC scheme with pseudoinverse-type (P-type) formulation is proposed. Such a P-type RMPC scheme possesses the suppression of constant and bounded time-varying noises. Comparative simulation results based on a five-link robot manipulator and a PUMA560 robot manipulator are presented to further validate the effectiveness and superiority of the proposed P-type RMPC scheme over the previous one.

Real-Time Kinematic Control for Redundant Manipulators in a Time-Varying Environment: Multiple-Dynamic Obstacle Avoidance and Fast Tracking of a Moving Object

This paper presents a real-time kinematic control strategy to realize fast tracking of redundant robot manipulators in a time-varying environment. An obstacle avoidance method based on the law of conservation of energy is proposed to adjust the motion states of robot manipulators in real time. This method defines that the total energy for the end effector consists of an energy toward object (ETO) and an energy around obstacle (EAO), and that the total energy for each critical point on manipulator composes a relative kinematic energy (RKE) and an energy memory (EM). The total energies remain constant at each sampling period, and the conversions between the ETO and the EAO or between the RKE and the EM are recognized to obey a distance-related S -function. Such considerations ensure the smooth movement of the manipulator and avoid collisions with obstacles. In real-time planning, an unsupervised single neuron PID model is raised to adaptively increase the convergence ratio of moving object tracking via the online learning of the principal component analysis. Then, combined with the dynamic obstacle avoidance method based on conservation of energy, the kinematic control strategy is established for redundant manipulators to track a moving object rapidly in the presence of multiple dynamic obstacles. Theory analysis and various contrast experimental results show that the proposed kinematic control strategy is feasible and has fast convergence.

An Adaptive Fuzzy Recurrent Neural Network for Solving the Nonrepetitive Motion Problem of Redundant Robot Manipulators

In order to effectively decrease the joint-angular drifts and end-effector position accumulation errors, a novel adaptive fuzzy recurrent neural network (AFRNN) is proposed and exploited to solve the nonrepetitive motion problem of redundant robot manipulators in this paper. First, a quadratic programming (QP)-based repetitive motion scheme is designed according to the kinematics constraint of redundant robot manipulators. Second, the QP-based repetitive motion scheme is converted to a matrix equation according to the Lagrangian multiplier method. Third, inspired by the neural-dynamic and fuzzy control theory, the AFRNN model is designed, which can effectively solve the matrix equation as well as the original nonrepetitive motion problem of redundant robot manipulators. Computer simulation results verify the effectiveness, high accuracy, and robustness to resist external disturbance of the proposed AFRNN scheme.

Compatible Convex–Nonconvex Constrained QP-Based Dual Neural Networks for Motion Planning of Redundant Robot Manipulators

Redundant robot manipulators possess huge potential of applications because of their superior flexibility and outstanding accuracy, but their real-time control is a challenging problem. In this brief, a novel compatible convex–nonconvex constrained quadratic programming (CCNC-QP)-based dual neural network (DNN) scheme is proposed for motion planning of redundant robot manipulators. The proposed CCNC-QP-DNN scheme not only has the advantages of DNN, e.g., parallel processing and real-time control, but also possesses the advantages of CCNC-QP, such as the zeroing initial error, considering convex or nonconvex constraints. Being different from most neural networks, the proposed approach is training-free and is able to track reference signals with superior accuracy and speedability. The detailed derivation process and theoretical analysis are presented. Computer simulations with five end-effector tasks verify the effectiveness and accuracy of the proposed control method in both the convex constraints condition and nonconvex constraints condition whether an initial error exists or not.

Calculation of the inverse kinematics solution of the 7-DOF redundant robot manipulator by the firefly algorithm and statistical analysis of the results in terms of speed and accuracy

ABSTRACTIn this study, the inverse kinematics solution of a 7-DOF redundant robot manipulator was performed by using firefly algorithm that is a swarm optimization technique. In order to show the power of this technique, a redundant robotic arm which is inadequate inverse kinematic solution by conventional methods has been chosen. Both speed and accuracy are two important factors in robotic studies. For this reason, the comparison of the method used in this study in terms of speed and accuracy has been carried out in depth. The scenario used is as follows: Firstly, the position equations of this manipulator are derived with the DH parameters. Afterward, the position of the end effector is obtained in the work space according to the forward kinematic calculation. Finally, the joint angles that will be directed to the calculated position values with the least error are obtained by the firefly algorithm and the obtained result is compared with other swarm algorithms such as particle swarm optimization and artificial bee colony.

New Recurrent Neural Network for Online Solution of Time-Dependent Underdetermined Linear System With Bound Constraint

Recurrent neural network (RNN) has recently been viewed as a significant alternative to online mathematical problem solving. This paper offers important improvements by proposing the first RNN model to solve the time-dependent underdetermined linear system with bound constraint. In particular, by introducing a time-dependent nonnegative vector, the bound-constrained underdetermined linear system is initially transformed into a time-dependent system that comprises linear and nonlinear equations. The newly constructed RNN model can thus zero in on the time-dependent equations. Then, the model is theoretically proven to have convergence properties, and the simulation results further substantiate the efficacy of the proposed RNN model to solve the time-dependent underdetermined linear system with bound constraint. Finally, the proposed RNN model is applied to physically constrained redundant robot manipulators, thereby indicating the applicability of the proposed model.

An Extended Jacobian-Based Formulation for Operational Space Control of Kinematically Redundant Robot Manipulators With Multiple Subtask Objectives: An Adaptive Control Approach

In this study, an extended Jacobian matrix formulation is proposed for the operational space tracking control of kinematically redundant robot manipulators with multiple subtask objectives. Furthermore, to compensate the structured uncertainties related to the robot dynamics, an adaptive operational space controller is designed, and then, the corresponding stability analysis is presented for kinematically redundant robot manipulators. Specifically, the proposed method is concerned with not only the stability of operational space objective but also the stability of multiple subtask objectives. The combined stability analysis of the operational space objective and the subtask objectives are obtained via Lyapunov based arguments. Experimental and simulation studies are presented to illustrate the performance of the proposed method.

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.

Discrete-Time ZND Models Solving ALRMPC via Eight-Instant General and Other Formulas of ZeaD

Repetitive motion planning and control (RMPC) of redundant robot manipulators is a fundamental and important problem widely existing in industrial manufacturing. In this paper, the acceleration-level RMPC (ALRMPC) is studied and solved in a discrete-time manner. For solving this problem, a new ALRMPC scheme with feedback control term is derived and presented at first. Then, by adopting Lagrange’s undetermined multipliers method and zeroing neural dynamics (ZND), a continuous-time ZND model, which is based on the new ALRMPC scheme, is developed and proposed. Besides, an eight-instant general formula with high precision is constructed, proposed and analyzed. By using this eight-instant general formula and other multiple-instant Zhang et al discretization (ZeaD) formulas to discretize the continuous-time ZND model, four discrete-time ZND (DTZND) models for solving ALRMPC are thus obtained. Finally, theoretical analyses and computer simulation experiment results further substantiate the effectiveness and accuracy of the proposed DTZND models.

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.

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.

Varying-Parameter RNN Activated by Finite-Time Functions for Solving Joint-Drift Problems of Redundant Robot Manipulators

Joint-drift problem may lead to task execution failure or robot damage. To solve this problem, a finite-time varying-parameter recurrent neural network (FT-VP-RNN) is proposed and investigated in this paper. First, a quadratic programming (QP) based joint-drift-free (JDF) scheme is developed, which consists of an optimization criterion and a kinematic equation at velocity layer. A feedback control is then added into the kinematic equation as the equality constraint, and a feedback-considered joint-drift-free (FC-JDF) scheme is obtained. Second, a novel FT-VP-RNN is designed to solve the FC-JDF scheme and a corresponding finite-time convergence theorem is proposed. The outstanding advantages of the proposed FT-VP-RNN are the real-time computation, exponential convergence, and the ability to eliminate the initial errors. Finally, three path-tracking simulations and comparisons are conducted to verify the effectiveness, accuracy, practicability, and safety of the proposed FT-VP-RNN for solving the joint-drift problems of redundant robot manipulators.

Neural-Dynamic Based Synchronous-Optimization Scheme of Dual Redundant Robot Manipulators.

In order to track complex-path tasks in three dimensional space without joint-drifts, a neural-dynamic based synchronous-optimization (NDSO) scheme of dual redundant robot manipulators is proposed and developed. To do so, an acceleration-level repetitive motion planning optimization criterion is derived by the neural-dynamic method twice. Position and velocity feedbacks are taken into account to decrease the errors. Considering the joint-angle, joint-velocity, and joint-acceleration limits, the redundancy resolution problem of the left and right arms are formulated as two quadratic programming problems subject to equality constraints and three bound constraints. The two quadratic programming schemes of the left and right arms are then integrated into a standard quadratic programming problem constrained by an equality constraint and a bound constraint. As a real-time solver, a linear variational inequalities-based primal-dual neural network (LVI-PDNN) is used to solve the quadratic programming problem. Finally, the simulation section contains experiments of the execution of three complex tasks including a couple task, the comparison with pseudo-inverse method and robustness verification. Simulation results verify the efficacy and accuracy of the proposed NDSO scheme.

New Pseudoinverse-Based Path-Planning Scheme With PID Characteristic for Redundant Robot Manipulators in the Presence of Noise

In this paper, a new path-planning scheme based on pseudoinverse-type formulation for redundant robot manipulators with the existence of noise is proposed and investigated. Such a pseudoinverse-based path-planning (PPP) scheme contains the proportional, integral, and derivative information of the desired Cartesian path (of the end-effector), and can thus be viewed as a nonlinear proportional–integral–derivative (PID) controller for redundant robot manipulators. In other words, the proposed PPP scheme has the PID characteristic in terms of the desired Cartesian path. Theoretical results are given to show that the Cartesian error synthesized by the proposed PPP scheme has the property of global and exponential convergence (that is to say, the error trajectory is asymptotically stable) and to indicate that such a scheme has the capability to suppress noise. Simulation results based on a four-link planar robot manipulator with the existence of zero, constant, and bounded time-varying noises are presented to further substantiate the efficacy and superiority of the proposed PPP scheme for the path planning of redundant robot manipulators. The physical realizability of the proposed PPP scheme is also demonstrated by applying this scheme to a practical six-link planar robot manipulator.

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.