Fault Accommodation Control for a Biped Robot Using a Recurrent Wavelet Elman Neural Network

A model-based fault accommodation control scheme that uses a recurrent wavelet Elman neural network (RWENN) is proposed to achieve satisfactory control without performance degradation for biped robot locomotion with unknown uncertainties and faults. In the fault accommodation scheme, a computed torque control is the main control that is used to track the desired trajectory when there is no fault; and a compensation control is used to eliminate the unknown model uncertainties. The proposed RWENN has an input from a context layer with self-feedback and an output recurrent layer to the hidden layer, which increases the precision and convergence time of the network compared with a recurrent neural network, a recurrent fuzzy neural network, and a recurrent wavelet neural network, so that any dynamic change, such as a fault on the system, can be estimated properly. Thus, it enhances the capability of fault accommodation. The adaptive laws of the RWENN-based fault accommodation control are derived from the Lyapunov theorem; hence, the stability of the system can be guaranteed. Finally, a case study of biped robot control with multiple faults and uncertainties is analyzed, and the effectiveness of the proposed fault accommodation scheme is demonstrated by simulation results. Its superiority is also assessed by a numerical comparison with other neural-network-based control schemes.

Nomenclature

Inertia matrix.

Coriolis/centrifugal matrix.

Vector of gravity.

Nominal system parameters.

Vector of external torque.

Vectors of the joint positions, velocities, and accelerations.

Computed torque controller, input torque vector, compensation controller.

Desired trajectory vectors.

Tracking error vectors.

Diagonal matrix of the position.

Diagonal matrix of the damping gain.

Unknown uncertainty.

Uncertainty boundary, estimation error of the bound, estimated error bound.

Sliding surface and its derivative.

Learning rate of the estimation bound.

Positive constant matrix.

Time profile of the faults.

Unknown time of the fault occurrence.

Estimation of the angular velocity vector of the joints.

Scalar constant.

Estimation of the fault.

Estimation error of the velocity vector.

Input of the node.

Output of the node.

Index of neuron for input, context, output feedback, and hidden layers.

Iteration number.

Number of input neurons and output feedback and output layer neurons.

Self-connection feedback gain.

Number of both context and hidden layer neurons.

Associated translation of the wavelet functions.

Dilation parameters of the wavelet functions.

Summation of the firing strengths.

Mother wavelet.

Connective weight between the th hidden layer and the th output layer.

Robust fault-tolerant controller.

Optimal recurrent wavelet Elman neural network (RWENN) estimator.

Optimal constant parameter matrix and vectors of , , , and .

Estimated parameter matrix and vectors of , , , and .

Estimation error of the fault, weight, and hidden layer output.

Vector of higher order terms.

Lumped uncertainty term.

Approximation error.

Learning rates of RWENN.

Lyapunov function candidate.

TRMSE

Total root-mean-square error.

ISE

Integral square error.

ITAE

Integral time-weighted absolute error.

IAE

Integral absolute error.