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In general, structures with rotational joints and linearized dynamic equations are used to facilitate the control of manipulator robots. However, in some cases, the workspace is limited, which reduces the accuracy and performance of this type of robot, especially when uncertainties are considered. To counter this problem, this work presents a redundant planar manipulator robot with Six-Degree-of-Freedom (6-DoF), which has an innovative structural configuration that includes rotary and prismatic joints. Three control strategies are designed for the monitoring and regulation of the joint trajectory tracking problem of this robot under the action of variable loads. Two advanced control strategies—predictive and Fuzzy-Logic Control (FLC)—were simulated and compared with the classical Proportional–Integral–Derivative (PID) controller. The graphic simulator was implemented using tools from the MATLAB/Simulink software to model the behavior of the redundant planar manipulator in a virtual environment before its physical construction, in order to conduct performance tests for its controllers and to anticipate possible damages/faults in the system mechanics before the implementation of control strategies in a real robot. The inverse dynamics were obtained through the Lagrange–Euler (L-E) formulation. According to the property of symmetry, this model was obtained in a simplified way based on the main diagonal of the inertia matrix of the robot. Additionally, the model includes the dynamics of the actuators and the estimation of the friction forces, both with central symmetry present in the joints. The effectiveness of these three control strategies was validated through qualitative comparisons—performance graphs of trajectory tracking—and quantitative comparisons—the Common Mode Rejection Ratio (CMRR) performance indicator and joint error indexes such as the Residual Mean Square (RMS), Residual Standard Deviation (RSD), and Index of Agreement (IA). In this regard, FLC based on the dynamic model was the most-suitable control strategy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

By considering the different-level time-varying physical limits in joint space, a refined self-motion control scheme via Zhang neurodynamics equivalency (SMCSvZ) of redundant robot manipulators is proposed, analyzed, and investigated in this manuscript. The SMCSvZ is reformulated as a quadratic program with an equation constraint and a unified bound inequation constraint, which meets the self-motion requirements including the end effector keeping immobile and the initial joint-angle velocities being zero. Simulative verifications based on a six-degrees-of-freedom planar redundant manipulator substantiate the efficacy, accuracy, and superiority of the proposed control scheme, additionally by comparing it with two previous self-motion control schemes. Besides, simulative verifications based on a PUMA560 manipulator are carried out to further verify the availability and correctness of the SMCSvZ. [ABSTRACT FROM AUTHOR]

To effectively solve the multi-objective motion planning problem for redundant robot manipulators, a penalty neural multi-criteria optimization (PNMCO) scheme is proposed and investigated. The scheme includes two parts: a constrained multi-criteria optimization (CMCO) subsystem, and a varying-parameter recurrent neural network combined with penalty function (VP-RNN-PF) subsystem. Specifically, the CMCO subsystem is made up of velocity two norm, repetitive motion, and infinity norm. With these criteria, it can achieve energy minimization, repetitive motion, and avoidance of speed peaks. In addition, the CMCO subsystem is then transformed into a standard quadratic programming (QP) problem, and the VP-RNN-PF subsystem is applied to solve the QP problem. Results of computer simulations based on the JACO2 robot manipulator demonstrate that the proposed PNMCO scheme is effective and feasible to plan the multi-objective motion tasks. Comparison experiments of two complex paths tracking between VP-RNN-PF and the traditional neural networks (e.g., simplified linear-variational-inequality-based primal-dual neural network, S-LVI-PDNN) shows that the proposed scheme as well as the neural network is more accurate and more efficient for solving multi-objective motion planning problem.

In order to resist periodic interfere in robot hardware or environment, a Runge–Kutta type discrete-time circadian rhythms neural network (RK-DCRNN) model is proposed, and investigated to plan the motion of redundant robot manipulators. To achieve the optimal control, a quadratic programming-based acceleration-level hybrid tri-criteria (ALHT) scheme is first designed, which simultaneously minimize the acceleration norm, torque norm, and joint-angle shift-free indices. Second, according to the neural dynamic design method, a continuous-time circadian rhythms neural network model is exploited, and then based on the Runge–Kutta numerical differential method, a discrete-time circadian rhythms neural network model is obtained. Third, the convergence of the proposed RK-DCRNN model is proved by detailed mathematical derivation. Fourth, comparative simulations and physical experiments verify that the proposed RK-DCRNN model can suppress the accumulation of position error in the motion planning of manipulators. [ABSTRACT FROM AUTHOR]

Via the Euler forward-difference rule, an Euler-type discrete-time circadian rhythms neural network model (E-DTCRNN) is proposed, developed, and investigated for motion planning of the redundant robot manipulator affected by periodic noises. In this article, an Euler-type discrete-time zeroing neural network model (E-DTZNN) is presented as comparison. The E-DTCRNN model is 0-stable, consistent, and convergent. In addition, through a hybrid torque and velocity optimization scheme synthesized by the proposed E-DTCRNN and the traditional E-DTZNN, a tracking trajectory is designed and applied to the motion planning of the redundant robot manipulator. Finally, groups of simulations and physical experiments verify the efficacy and noise suppression ability of the proposed E-DTCRNN model for motion planning of the manipulator. [ABSTRACT FROM AUTHOR]

Repetitive path planning (RPP) plays an important role in the operation of redundant robot manipulators. In this study, we investigate a new discrete-time RPP scheme depicted in the pseudoinverse-type formulation for redundant robot manipulators. Such a scheme is derived from the discretization of the previous continuous-time RPP scheme using a special numerical difference formula. Theoretical analysis shows that the proposed RPP scheme has the property of cube pattern in the end-effector planning accuracy. On the basis of a PUMA560 robot manipulator with different examples, comparative simulation results are presented to demonstrate the effectiveness and superiority of the proposed RPP scheme.

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. [ABSTRACT FROM AUTHOR]

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.

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.

Repetitive motion planning (RMP) is a crucial issue encountered in studies on redundant robot manipulators. Numerous RMP schemes have been established in previous studies wherein simulations are assumed to be free of noise. However, noise is ubiquitous and can severely affect RMP schemes to the point of causing failure. This paper attempts address the limitations imposed by noise by providing the first RMP scheme with inherent noise-suppression capability. The new RMP scheme for redundant robot manipulators in a noisy environment is proposed on the basis of an equality criterion that is robust against additive noise. The equality criterion is established by incorporating the proportional and integral information of the desired end-effector path. The proposed scheme is reformulated as a quadratic program and is calculated by using a recurrent neural network. Comparative simulation results obtained with PA10 and four-link robot manipulators illustrate the effectiveness and superiority of the proposed RMP scheme over the traditional RMP scheme. [ABSTRACT FROM AUTHOR]

In this paper, zeroing neural network models are redesigned and analyzed from a control-theoretical framework for online solving time-varying full-rank Moore–Penrose inversions. To solve time-varying full-rank Moore–Penrose inverse problems with different noises in real time, some modified zeroing neural network models are developed, analyzed and investigated from the perspective of control. Furthermore, the proposed zeroing neural network models globally converge to the theoretical solution of the full-rank Moore–Penrose inverse problem without noises, and exponentially converge to the exact solution in the presence of noises, which are demonstrated theoretically. Moreover, in comparison with existing models, numerical simulations are provided to substantiate the feasibility and superiority of the proposed modified neural network for online solving time-varying full-rank Moore–Penrose problems with inherent tolerance to noises. In addition, the numerical results infer that different activation functions can be applied to accelerate the convergence speed of the zeroing neural network model. Finally, the proposed zeroing neural network models are applied to the motion generation of redundant robot manipulators, which illustrates its high efficiency and robustness. [ABSTRACT FROM AUTHOR]

SUMMARY: Repetitive 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recently, a repetitive motion planning (RMP) scheme with guaranteed precision has been developed for redundant robot manipulators. However, the RMP scheme does not consider joint constrains. As a result, such a scheme may not perform effectively when the joint configuration exceeds its physical limit. In this paper, we provide a further study by proposing a new discrete-time RMP (DTRMP) scheme based on the pseudoinverse formulation for redundant robot manipulators with joint constrains. Specifically, by using the direct derivation and by introducing the feedback, the handling of joint physical limit is formulated as an implicit dynamic equation. Then, the combined kinematic equation of the constrained redundant robot manipulators is obtained, and the resultant continuous-time RMP (CTRMP) scheme with the pseudoinverse-based formulation is established. By utilizing a numerical difference rule to discretize the CTRMP scheme, the new DTRMP scheme is thus developed for redundant robot manipulators with joint constrains. Theoretical analysis and computer simulations under a constrained five-link robot manipulator validate the effectiveness and superiority of the proposed DTRMP scheme. The experiment results of implementing the proposed scheme on the constrained practical Panda robot manipulator further indicate the scheme applicability and feasibility. • We propose a new DTRMP scheme for manipulators with joint limits using pseudoinverse. • The new DTRMP scheme ensures joint repeatability and precise end-effector motion. • We theoretically analyze the properties of the proposed DTRMP scheme for consistency. • Simulations on a constrained five-link manipulator prove the scheme's effectiveness. • The proposed scheme's applicability has been validated on the practical Panda robot. • Theory and simulations show the proposed DTRMP scheme's end-effector precision is O (η 4). • It enables precise RMP designs for robots at joint velocity, acceleration, and jerk. [ABSTRACT FROM AUTHOR]

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.

Fault tolerance is important for a redundant robot manipulator, which endows the robot with the capability of finishing the end-effector task even when one or some of joints’ motion fails. In this paper, a varying-parameter neural control architecture is designed to achieve fault tolerance for redundant robot manipulators. Specifically, a quadratic programming (QP)-based fault-tolerant motion planning scheme is formulated. Second, a varying parameter recurrent neural network (VP-RNN) is proposed to resolve the standard QP problem, which can make the remaining healthy joints to remedy the whole system which is effected by faulty joints and complete the expected end-effector path. Theoretical analysis based on Lyapunov stability theory proves that the proposed VP-RNN solver can globally converge to the optimal solution to the fault-tolerant motion planning scheme, and the joint motion failure problems are solved successfully. Computer simulations and physical experiments based on a 6 degrees-of-freedom Kinova Jaco2 robot substantiate the effectiveness of the proposed varying-parameter neural control architecture for fault-tolerant motion planning scheme to 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. [ABSTRACT FROM AUTHOR]

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A novel varying-parameter recurrent neural network [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed and investigated to solve time-varying convex quadratic programing (QP) problems and applied to solve nonrepetitive problems of redundant robot manipulators in this brief. First, the nonrepetitive problems of redundant robot manipulators are reformulated as a QP scheme. Second, the QP scheme is reformulated as a matrix equation. Third, the proposed VP-CDNN is applied to solve the matrix equation as well as the original QP problem. To illustrate the advantages of VP-CDNN solver, comparison simulations between the VP-CDNN and the fixed-parameter convergent-differential neural network (FP-CDNN) are constructed based on a six-degrees-of-freedom robot manipulator. Two end-effector tasks employed by the VP-CDNN with linear activation function and sinh activation function verify the effectiveness and advantages of the proposed VP-CDNN and its better expansibility. The results of computer simulations and physical experiments demonstrate that the VP-CDNN solver is more effective and accurate than the FP-CDNN solver to solve nonrepetitive problems of redundant robot manipulators. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Avoiding obstacle(s) is a challenging issue in the research of redundant robot manipulators. In addition, noise from truncation, rounding, and model uncertainty is an important factor that affects greatly the obstacle avoidance scheme. In this paper, based on the neural dynamics design formula, a new scheme with the pseudoinverse-type formulation is proposed for obstacle avoidance of redundant robot manipulators in a noisy environment. Such a scheme has the capability of suppressing constant and bounded time-varying noises, and it is thus termed as the noise-tolerant obstacle avoidance (NTOA) scheme in this paper. Theoretical results are also given to show the excellent property of the proposed NTOA scheme (particularly in noise situation). Based on a PA10 robot manipulator with point and window-shaped obstacles, computer simulation results are presented to further substantiate the efficacy and superiority of the proposed NTOA scheme for motion planning of redundant robot manipulators.

Abstract Constrained optimization problems arise in numerous scientific and engineering applications, and many papers on the online solution of constrained optimization problems using projection neural networks have been published in the literature. The purpose of this paper is to provide a comprehensive review of the research on projection neural networks for solving various constrained optimizations as well as their applications. Since convergence and stability are important for projection neural networks, theoretical results of projection neural networks are reviewed in detail. In addition, various applications of projection neural networks, e.g., the motion generation of redundant robot manipulators, coordination control of multiple robots with limited communications, generation of winner-take-all strategy, model predictive control and WSN localizations, are discussed and compared. Concluding remarks and future directions of projection neural networks as well as their applications are provided. Highlights • The work constructs a bridge between mathematical optimization and neural networks. • A comprehensive review of the research on projection neural networks is presented. • Various applications of projection neural networks are discussed and compared. [ABSTRACT FROM AUTHOR]

Recently, a new formula with noise-tolerant capability has been designed by Zhanget 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. [ABSTRACT FROM AUTHOR]

By 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. [ABSTRACT FROM AUTHOR]

Recently, the approach based on recurrent neural network (RNN) has been considered a powerful alternative to mathematical problem solving. In this study, a new discrete-time RNN (DTRNN) is proposed and investigated to determine an exact solution of dynamic nonlinear equations. Specifically, the resultant DTRNN model is established for solving dynamic nonlinear equations by utilizing a Taylor-type difference rule. This DTRNN model is then theoretically proven to have an $O(\tau ^4)$ error pattern, where $\tau$ denotes the sampling gap. Comparative numerical results are illustrated to further substantiate the efficacy and superiority of the proposed DTRNN model in comparison with the existing approach. Finally, the proposed DTRNN model is applied to redundant robot manipulators by solving the system of dynamic nonlinear kinematic equations, indicating the application prospect of the proposed model. [ABSTRACT FROM AUTHOR]

Avoiding obstacle(s) is a challenging issue in the research of redundant robot manipulators. In addition, noise from truncation, rounding, and model uncertainty is an important factor that affects greatly the obstacle avoidance scheme. In this paper, based on the neural dynamics design formula, a new scheme with the pseudoinverse-type formulation is proposed for obstacle avoidance of redundant robot manipulators in a noisy environment. Such a scheme has the capability of suppressing constant and bounded time-varying noises, and it is thus termed as the noise-tolerant obstacle avoidance (NTOA) scheme in this paper. Theoretical results are also given to show the excellent property of the proposed NTOA scheme (particularly in noise situation). Based on a PA10 robot manipulator with point and window-shaped obstacles, computer simulation results are presented to further substantiate the efficacy and superiority of the proposed NTOA scheme for motion planning of redundant robot manipulators. [ABSTRACT FROM AUTHOR]

The problem of dynamic task allocation in a distributed network of redundant robot manipulators for path-tracking with limited communications is investigated in this paper, where k fittest ones in a group of n redundant robot manipulators with n>k are allocated to execute an object tracking task. The problem is essentially challenging in view of the interplay of manipulator kinematics and the dynamic competition for activation among manipulators. To handle such an intricate problem, a distributed coordination control law is developed for the dynamic task allocation among multiple redundant robot manipulators with limited communications and with the aid of a consensus filter. In addition, a theorem and its proof are presented for guaranteeing the convergence and stability of the proposed distributed control law. Finally, an illustrative example is provided and analyzed to substantiate the efficacy of the proposed control law. [ABSTRACT FROM AUTHOR]

In order to solve the joint-angular-drift problems of redundant robot manipulators, a novel varying-parameter convergent-differential neural network (VP-CDNN) is proposed and exploited. To do so, a quadratic program (QP)-based feedback-considered joint-angular-drift-free (FC-JADF) scheme is first designed and presented. The FC-JADF scheme adopted in this paper is composed of an optimization criterion simultaneously optimizing quadratic and linear terms, and a velocity layer kinematic equation with adding feedback. Second, the FC-JADF scheme is formulated as a standard QP. Third, the VP-CDNN is proposed to solve the resultant standard QP problem. The Lyapunov theory proves that the proposed VP-CDNN solver can globally converge to an optimal solution to the standard QP problem corresponding to redundant robot manipulators, and the joint-angular-drift problems are solved. Two computer simulations and physical experiments based on a six-degree-of-freedom Kinova Jaco$^2$ robot, i.e., a starfish path and a cardioid path, verify the effectiveness, accuracy, safety, and practicability of the QP-based FC-JADF scheme and the VP-CDNN solver for solving the joint-angular-drift problems of redundant robot manipulators. [ABSTRACT FROM PUBLISHER]

In this paper, a hybrid multi-objective scheme is proposed to complete simultaneously four objectives, i.e., the specified primary task for the end-effector, obstacle avoidance, joint-physical limits avoidance, and repetitive motion of redundant robot manipulators. In addition, corresponding theoretical analysis is given, which guarantees the validity of the proposed scheme. Then, the proposed hybrid multi-objective scheme is reformulated as a dynamical quadratic program (DQP) problem. The optimal solution of the DQP problem is found by the PLPE (piecewise-linear projection equation) neural network, i.e., PLPENN, and also by the corresponding numerical algorithm implemented on the computer. Furthermore, simulation and comparison based on a six-link planar redundant robot manipulator substantiate the effectiveness and accuracy of the proposed scheme. At last, a hardware experiment is conducted on a six-link physical robot manipulator system, which substantiates the physical realizability, operational stability, and safety of the proposed hybrid multi-objective scheme. [ABSTRACT FROM PUBLISHER]

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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. [ABSTRACT FROM AUTHOR]

For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme (termed the acceleration-level obstacle-avoidance scheme). The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming (QP). Two important ‘bridge’ theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation (PLPE). A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme. [ABSTRACT FROM PUBLISHER]

The quadratic programming (QP) problems of redundant robot manipulators, which have high requirement for real-time calculation, are subject to equality, inequality and bound constraints. For solving such QP problems with these constraints, we present and study two numerical algorithms (named as E47 and 94LVI). Such QP problems are converted equivalently to piecewise-linear projection equations (PLPE). Resultant PLPE can be solved by E47 and 94LVI algorithms, and thus the optimal numerical solutions to the QP problems are obtained. In addition, by means of abundant numerical experiments, the performances of these two algorithms on QP solving for redundant robot manipulators are proved. Comparative numerical results of E47, 94LVI and those of the conventional active-set algorithms are also presented. Finally, the efficiency and superiority of the E47 and 94LVI algorithms for QP solving are well validated. [ABSTRACT FROM AUTHOR]

Differential kinematic is one of the most important solution methods in robot kinematics. The main advantage of the differential kinematic method is that it can be easily implemented any kind of mechanisms. Also, an accurate and efficient kinematic based trajectory tracking application can be easily implemented by using this method. In differential kinematic method, we use Jacobian as a mapping operator in the velocity space. Inversion of Jacobian matrix transforms the desired trajectory velocities, which are the linear and angular velocities of the end effector, into the joint velocities. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Therefore, the performance of the trajectory tracking application of the robot manipulator is directly affected by the chosen numerical integration method. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Several widely used numerical integration methods are implemented into the trajectory tracking application of the 7‐DOF redundant robot manipulator named PA‐10 and simulation results are given.

In J Robot Syst 13(3):177-185 (), Ma proposed an efficient technique to stabilize local torque optimization solution of redundant manipulators, which prevents occurrence of high joint-velocity and guarantees the final joint-velocity to be near zero. To prevent the same problems, a different-level simultaneous minimization scheme is proposed in this paper for robotic redundancy resolution, which combines the minimum two-norm joint-velocity and joint-torque solutions via two weighting factors. Physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are also taken into consideration in such a scheme-formulation. Moreover, the proposed different-level simultaneous minimization scheme is resolved at the joint-acceleration level and reformulated as a general quadratic program (QP). Computer-simulation results based on the PUMA560 robot manipulator performing different types of end-effector path-tracking tasks demonstrate the validity and advantage of the proposed different-level simultaneous minimization scheme. Furthermore, experimental verification conducted on a practical six-link planar robot manipulator substantiates the effectiveness and the physical realizability of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: To remedy the joint-torque instability/divergence phenomenon arising in the conventional infinity-norm torque-minimization (INTM) scheme, and prevent the occurrence of high joint-velocity and joint-acceleration as well, a different-level bi-criteria minimization scheme is proposed and investigated in this paper for redundant robot manipulators with physical constraints (e.g., joint-angle limits, joint-velocity limits and joint-acceleration limits) considered. Such a scheme combines the minimum two-norm joint-velocity and infinity-norm joint-torque solutions via a weighting factor, which guarantees the final joint-velocity of the motion to be near zero (more acceptable for engineering application). In addition, the different-level scheme is reformulated as a general quadratic program (QP) and resolved at the joint-acceleration level. Computer-simulation results based on the PUMA560 robot manipulator further demonstrate the effectiveness and advantages of the proposed different-level bi-criteria minimization scheme for robotic redundancy resolution. [Copyright &y& Elsevier]

Differential kinematic is one of the most important solution methods in robot kinematics. The main advantage of the differential kinematic method is that it can be easily implemented any kind of mechanisms. Also, an accurate and efficient kinematic based trajectory tracking application can be easily implemented by using this method. In differential kinematic method, we use Jacobian as a mapping operator in the velocity space. Inversion of Jacobian matrix transforms the desired trajectory velocities, which are the linear and angular velocities of the end effector, into the joint velocities. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Therefore, the performance of the trajectory tracking application of the robot manipulator is directly affected by the chosen numerical integration method. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Several widely used numerical integration methods are implemented into the trajectory tracking application of the 7-DOF redundant robot manipulator named PA-10 and simulation results are given. [ABSTRACT FROM AUTHOR]