RNN For Solving Time-varying System Of Linear Equations And Its Application To Robots

Neural networks have been generally deemed as important tools to handle kinds of online computing problems in recent decades,which have plenty of applications in science and electronics fields.Generally,in order to handle a problem,RNN is usually counted as a solution algorithm to exploit through constructing an ordinary differential equation(ODE).As a result,the solution to the objective problem is equivalent to the equilibrium point of the dynamical ODE system.Note that most methods for the ODE are able to solve the proposed RNN model.In addition,most of the existing RNN models are related to gradient-based solutions,thus it is simply to fall into the local minimum value,and it is essentially used to solve static non-time-varying problems.It is worth pointing out that time-varying problems play an increasingly important role in practical applications.Firstly,by elaborately constructing a new general framework enhanced by the error-integration information and nonlinear activation functions,an RNN model is proposed and investigated on the basis of the proposed generated framework for solving the time-varying system of linear equations in the presence of different additive noises.In addition,theoretical analyses are provided,which reveal that,perturbed by constant noises and activated by unbounded functions,the proposed RNN model is of global convergence.Moreover,when the value of activation function is strictly limited by bounds,the convergence value of the proposed RNN model is subject to the values of noises and bounds of the activation function.Computer simulation results,as well as robot experiments,verify the superior property of the RNN model for solving the perturbed time-varying system of linear equations,compared with the previously presented models.Subsequently,a joint-drift-free(JDF)scheme synthesized by an RNN model for the motion generation and control of redundant robot manipulators perturbed by disturbances is proposed and analyzed.In the first place,the RNN model could adopt saturated or even nonconvex activation functions.The proposed scheme completely decouples the interferences of joint errors in the joint space and position errors in the Cartesian space.Beyond that,theoretical analyses are conducted in order to validate that the RNN 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 RNN model for remedying joint-drift problems of redundant robot manipulators in noisy environments.Lastly,this paper also proposes an RNN model to handle the perturbed timevarying underdetermined linear system with double bound limits on residual errors and state variables.Beyond that,the bound-limited underdetermined linear system is converted into a time-varying system that consists of linear and nonlinear formulas through constructing a non-negative time-varying variable.Then,theoretical analyses are conducted to verify the superior convergence performance of the proposed RNN model.Furthermore,numerical experiment results and computer simulations demonstrate the superiority and effectiveness of the proposed RNN model for handling the time-varying underdetermined linear system with double bound limits.Then,the proposed RNN model is applied to the physically-limited PUMA560 robot to show its satisfactory applicabilities.