RNN for Solving Time-Variant Generalized Sylvester Equation With Applications to Robots and Acoustic Source Localization

Jin, Long; Yan, Jingkun; Du, Xiujuan; Xiao, Xiuchun; Fu, Dongyang

doi:10.1109/tii.2020.2964817

Cited by 131 publications

(42 citation statements)

References 37 publications

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“…Indeed, due to the recurrent information which has been indirectly stored in a neural cell, RNN provides short-term dependencies that create the capability of processing and learning time-varying smooth functions [50,68,69]. Hence, RNN is more applicable to the estimation of the time-evolving condition [70][71][72].…”

Section: A Selecting An Rnn-based Controllermentioning

confidence: 99%

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

et al. 2020

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We develop a new robust control scheme for a non-holonomic spherical robot. To this end, the mathematical model of a pendulum driven non-holonomic spherical robot is first presented. Then, a recurrent neural network-based robust nonsingular sliding mode control is proposed for stabilization and tracking control of the system. The designed recurrent neural network is applied to approximate compound disturbances, including external interferences and dynamic uncertainties. Moreover, the controller is designed in a way that avoids the singularity problem in the system. Another advantage of the proposed scheme is its ability for tracking control while there exists control input saturation, which is a serious concern in robotic systems. Based on the Lyapunov theorem, the stability of the closed-loop system has also been confirmed. Lastly, the performance of the proposed control technique for the uncertain system in the presence of an external disturbance, unknown input saturation, and dynamic uncertainties has been investigated. Also, the proposed controller has been compared with a Fuzzy-PID one. Simulation results show the effectiveness and superiority of the developed control technique.

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Section: A Selecting An Rnn-based Controllermentioning

confidence: 99%

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

et al. 2020

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“…Proof: According to the previous Definitions, employing the equation (12) to discretize the CTZTM model (7) and utilizing the equation (10) to estimate the unknown derivative information. Therefore, the HADTZTM-U (11) with O(τ 4 ) pattern residual error can be given by…”

Section: Definitionmentioning

confidence: 99%

“…In addition, the parameter h of DTZTM (18) must be less than 1. 4) When the derivative informationȦ k andḂ k of HADTZTM-K (9) is unknown, we utilize equation (10) to approximate the termsȦ k andḂ k , from Table 4 and Figure 6 we can obtain that the efficiency and superiority of the HADTZTM-U (11) in the path-tracking of the four-link planar manipulator. The position-error of the HADTZTM-U (11) will decrease with the parameter h increasing from 0.1 to 0.3.…”

Section: Application On Planar Manipulatormentioning

confidence: 99%

“…That is to say, static solvers cannot exhibit satisfactory performance when applied to solve dynamic linear equations. Although a few algorithms have been developed to solve time-varying linear equations [14], the existing ones still have large errors in the application of DSLEs with high time-dependence such as robots [9], localization [10], and signal processing [11], etc. Therefore, research on the stability, accuracy and rapidity of algorithms still have a wide range of significance.…”

Section: Introductionmentioning

confidence: 99%

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Two DTZNN Models of O(τ⁴) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation

et al. 2020

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In this paper, firstly, a high accuracy one-step-ahead numerical differentiation formula with O(τ 4) pattern is proposed for discretization. Meanwhile, a high precision first-order derivative formula of the backward difference rule with O(τ 4) pattern error is given to approximate the derivative information. Then, two high accuracy discrete-time zeroing-type models (HADTZTM) with O(τ 4) pattern, i.e., HADTZTM with derivative information known (HADTZTM-K) and HADTZTM with derivative information unknown (HADTZTM-U), are developed, analyzed and investigated for online solving the dynamic system of linear equations (DSLEs). In addition, the 0-stability, consistency, and convergence of the HADTZTM-K and HADTZTM-U are verified for DSLEs. From a theoretical/numerical viewpoint, the classical models are revisited and analyzed for online solving DSLEs. Ultimately, simulation experiment including an application to the path-tracking of the four-link planar manipulator is conducted to demonstrate the efficiency and superiority of the HADTZTM-K and HADTZTM-U, where the HADTZTM-U overcomes the difficulty of derivative information unknown in practical applications. INDEX TERMS Dynamic system of linear equations (DSLEs), discrete-time zeroing neural network (DTZNN), backward difference formula, theoretical results, steady-state residual error.

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“…Recurrent neural networks (RNNs) have natural advantages in solving real-time problems because they contain hidden layers that can store data from the past, which is conducive to subsequent computations [21]. To date, numerous RNNs have been exploited to solve dynamic optimization problems converted from robotics [22]- [25]. For instance, in [24], a neural algorithm with an estimation on Hessian matrix inversion, as a special kind of RNN, is presented to solve the dynamic unconstrained optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Recurrent Neural Network for State Adjustment of Redundant Manipulators

Jin

Huang

et al. 2020

IEEE Access

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To make joints of a redundant manipulator moving automatically to a target state, a stateadjustment (SA) scheme is studied and modified in this paper. Specifically, owing to the problem of non-zero initial joint velocity in the SA scheme leading to a potential hazard to redundant manipulators, a modified state-adjustment (MSA) scheme is obtained on the basis of the SA scheme. The MSA scheme achieves the state adjustment by minimizing the differences between the joint angles and the target values. For solving the MSA scheme, a recurrent neural network (RNN) model is derived, of which the critical component is to iterate over the joint angles and joint velocities. The MSA scheme solved by the RNN model enables the redundant manipulator to adjust to the target state automatically while ensuring that the initial joint velocity is zero. Beyond that, several comparative simulations demonstrate the availability and accuracy of the MSA scheme solved by the RNN model in controlling the state adjustment of redundant manipulators. INDEX TERMS State-adjustment scheme, recurrent neural network, redundant manipulators.

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RNN for Solving Time-Variant Generalized Sylvester Equation With Applications to Robots and Acoustic Source Localization

Cited by 131 publications

References 37 publications

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

Two DTZNN Models of O(τ⁴) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation

Recurrent Neural Network for State Adjustment of Redundant Manipulators

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RNN for Solving Time-Variant Generalized Sylvester Equation With Applications to Robots and Acoustic Source Localization

Cited by 131 publications

References 37 publications

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

Recurrent Neural Network-Based Robust Nonsingular Sliding Mode Control With Input Saturation for a Non-Holonomic Spherical Robot

Two DTZNN Models of O(τ4) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation

Recurrent Neural Network for State Adjustment of Redundant Manipulators

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Two DTZNN Models of O(τ⁴) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation