Design and Comprehensive Analysis of a Noise-Tolerant ZNN Model With Limited-Time Convergence for Time-Dependent Nonlinear Minimization

Zeroing neural network (ZNN) is a powerful tool to address the mathematical and optimization problems broadly arisen in the science and engineering areas. The convergence and robustness are always co-pursued in ZNN. However, there exists no related work on the ZNN for time-dependent nonlinear minimization that achieves simultaneously limited-time convergence and inherently noise suppression. In this article, for the purpose of satisfying such two requirements, a limited-time robust neural network (LTRNN) is devised and presented to solve time-dependent nonlinear minimization under various external disturbances. Different from the previous ZNN model for this problem either with limited-time convergence or with noise suppression, the proposed LTRNN model simultaneously possesses such two characteristics. Besides, rigorous theoretical analyses are given to prove the superior performance of the LTRNN model when adopted to solve time-dependent nonlinear minimization under external disturbances. Comparative results also substantiate the effectiveness and advantages of LTRNN via solving a time-dependent nonlinear minimization problem

Robust control for a tracked mobile robot based on a finite-time convergence zeroing neural network

IntroductionSince tracked mobile robot is a typical non-linear system, it has been a challenge to achieve the trajectory tracking of tracked mobile robots. A zeroing neural network is employed to control a tracked mobile robot to track the desired trajectory.MethodsA new fractional exponential activation function is designed in this study, and the implicit derivative dynamic model of the tracked mobile robot is presented, termed finite-time convergence zeroing neural network. The proposed model is analyzed based on the Lyapunov stability theory, and the upper bound of the convergence time is given. In addition, the robustness of the finite-time convergence zeroing neural network model is investigated under different error disturbances.Results and discussionNumerical experiments of tracking an eight-shaped trajectory are conducted successfully, validating the proposed model for the trajectory tracking problem of tracked mobile robots. Comparative results validate the effectiveness and superiority of the proposed model for the kinematical resolution of tracked mobile robots even in a disturbance environment

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS

Active Sensing of Robot Arms Based on Zeroing Neural Networks: A Biological-Heuristic Optimization Model

Conventional biological-heuristic solutions via zeroing neural network (ZNN) models have achieved preliminary efficiency on time-dependent nonlinear optimization problems handling. However, the investigation on finding a feasible ZNN model to solve the time-dependent nonlinear optimization problems with both inequality and equality constraints still remains stagnant because of the nonlinearity and complexity. To make new progresses on the ZNN for time-dependent nonlinear optimization problems solving, this paper proposes a biological-heuristic optimization model, i.e., inequality and equality constrained optimization ZNN (IECO-ZNN). Such a proposed IECO-ZNN breaks the conditionality that the solutions via ZNN for solving nonlinear optimization problems can not consider the inequality and equality constraints at the same time. The time-dependent nonlinear optimization problem subject to inequality and equality constraints is skillfully converted to a time-dependent equality system by exploiting the Lagrange multiplier rule. The design process for the IECO-ZNN model is presented together with its new architecture illustrated in details. In addition, the conversion equivalence, global stability as well as exponential convergence property are theoretically proven. Moreover, numerical studies, real-world applications to robot arm active sensing, and comparisons sufficiently verify the effectiveness and superiority of the proposed IECO-ZNN model for the time-dependent nonlinear optimization with inequality and equality constraints

An L₁-Norm Based Optimization Method for Sparse Redundancy Resolution of Robotic Manipulators

For targeted motion control tasks of manipulators, it is frequently necessary to make use of full levels of joint actuation to guarantee successful motion planning and path tracking. Such way of motion planning and control may keep the joint actuation in a non-sparse manner during motion control process. In order to improve sparsity of joint actuation for manipulator systems, a novel motion planning scheme which can optimally and sparsely adopt joint actuation is proposed in this paper. The proposed motion planning strategy is formulated as a constrained L1 norm optimization problem, and an equivalent enhanced optimization solution dealing with bounded joint velocity is proposed as well. A new primal dual neural network with a new solution set division is further proposed and applied to solve such bounded optimization which can sparsely adopt joint actuation for motion control. Simulation and experiment results demonstrate the efficiency, accuracy and superiority of the proposed method for optimally and sparsely adopting joint actuation. The average sparsity (i.e., -||˙θ||p where θ denotes the joint angle) of the joint motion of the manipulator can be increased by 39.22% and 51.30% for path tracking tasks in X-Y and X-Z planes respectively, indicating that the sparsity of joint actuation can be enhanced

A recurrent neural network applied to optimal motion control of mobile robots with physical constraints

Conventional solutions, such as the conventional recurrent neural network (CRNN) and gradient recurrent neural network (GRNN), for the motion control of mobile robots in the unified framework of recurrent neural network (RNN) are difficult to simultaneously consider both criteria optimization and physical constraints. The limitation of the RNN solution may lead to the damage of mobile robots for exceeding physical constraints during the task execution. To overcome this limitation, this paper proposes a novel inequality and equality constrained optimization RNN (IECORNN) to handle the motion control of mobile robots. Firstly, the real-time motion control problem with both criteria optimization and physical constraints is skillfully converted to a real-time equality system by leveraging the Lagrange multiplier rule. Then, the detailed design process for the proposed IECORNN is presented together with the neural network architecture developed. Afterward, theoretical analyses on the motion control problem conversion equivalence, global stability, and exponential convergence property are rigorously provided. Finally, two numerical simulation verifications and extensive comparisons with other existing RNNs, e.g., the CRNN and the GRNN, based on the mobile robot for two different path-tracking applications sufficiently demonstrate the effectiveness and superiority of the proposed IECORNN for the real-time motion control of mobile robots with both criteria optimization and physical constraints. This work makes progresses in both theory as well as practice, and fills the vacancy in the unified framework of RNN in motion control of mobile robots

Tracking control of redundant mobile manipulator: An RNN based metaheuristic approach

In this paper, we propose a topology of Recurrent Neural Network (RNN) based on a metaheuristic optimization algorithm for the tracking control of mobile-manipulator while enforcing nonholonomic constraints. Traditional approaches for tracking control of mobile robots usually require the computation of Jacobian-inverse or linearization of its mathematical model. The proposed algorithm uses a nature-inspired optimization approach to directly solve the nonlinear optimization problem without any further transformation. First, we formulate the tracking control as a constrained optimization problem. The optimization problem is formulated on position-level to avoid the computationally expensive Jacobian-inversion. The nonholonomic limitation is ensured by adding equality constraints to the formulated optimization problem. We then present the Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm to solve the optimization problem efficiently using very few mathematical operations. We present a theoretical analysis of the proposed algorithm and show that its computational cost is linear with respect to the degree of freedoms (DOFs), i.e., O(m). Additionally, we also prove its stability and convergence. Extensive simulation results are prepared using a simulated model of IIWA14, a 7-DOF industrial-manipulator, mounted on a differentially driven cart. Comparison results with particle swarm optimization (PSO) algorithm are also presented to prove the accuracy and numerical efficiency of the proposed controller. The results demonstrate that the proposed algorithm is several times (around 75 in the worst case) faster in execution as compared to PSO, and suitable for real-time implementation. The tracking results for three different trajectories; circular, rectangular, and rhodonea paths are presented

Model-based recurrent neural network for redundancy resolution of manipulator with remote centre of motion constraints

Redundancy resolution is a critical issue to achieve accurate kinematic control for manipulators. End-effectors of manipulators can track desired paths well with suitable resolved joint variables. In some manipulation applications such as selecting insertion paths to thrill through a set of points, it requires the distal link of a manipulator to translate along such fixed point and then perform manipulation tasks. The point is known as remote centre of motion (RCM) to constrain motion planning and kinematic control of manipulators. Together with its end-effector finishing path tracking tasks, the redundancy resolution of a manipulators has to maintain RCM to produce reliable resolved joint angles. However, current existing redundancy resolution schemes on manipulators based on recurrent neural networks (RNNs) mainly are focusing on unrestricted motion without RCM constraints considered. In this paper, an RNN-based approach is proposed to solve the redundancy resolution issue with RCM constraints, developing a new general dynamic optimisation formulation containing the RCM constraints. Theoretical analysis shows the theoretical derivation and convergence of the proposed RNN for redundancy resolution of manipulators with RCM constraints. Simulation results further demonstrate the efficiency of the proposed method in end-effector path tracking control under RCM constraints based on an industrial redundant manipulator system

Neural Network Model-Based Control for Manipulator: An Autoencoder Perspective

Recently, neural network model-based control has received wide interests in kinematics control of manipulators. To enhance learning ability of neural network models, the autoencoder method is used as a powerful tool to achieve deep learning and has gained success in recent years. However, the performance of existing autoencoder approaches for manipulator control may be still largely dependent on the quality of data, and for extreme cases with noisy data it may even fail. How to incorporate the model knowledge into the autoencoder controller design with an aim to increase the robustness and reliability remains a challenging problem. In this work, a sparse autoencoder controller for kinematic control of manipulators with weights obtained directly from the robot model rather than training data is proposed for the first time. By encoding and decoding the control target though a new dynamic recurrent neural network architecture, the control input can be solved through a new sparse optimization formulation. In this work, input saturation, which holds for almost all practical systems but usually is ignored for analysis simplicity, is also considered in the controller construction. Theoretical analysis and extensive simulations demonstrate that the proposed sparse autoencoder controller with input saturation can make the end-effector of the manipulator system track the desired path efficiently. Further performance comparison and evaluation against the additive noise and parameter uncertainty substantiate robustness of the proposed sparse autoencoder manipulator controller