Barrier Lyapunov function-based robot control with an augmented neural network approximator

Considering the complexity of dynamic and friction modeling, this paper aims to develop an adaptive trajectory tracking control scheme for robot manipulators in a universal unmodeled method, avoiding complicated modeling processes.

An augmented neural network (NN) constituted of radial basis function neural networks (RBFNNs) and additional sigmoid-jump activation function (SJF) neurons is introduced to approximate complicated dynamics of the system: the RBFNNs estimate the continuous dynamic term and SJF neurons handle the discontinuous friction torques. Moreover, the control algorithm is designed based on Barrier Lyapunov Function (BLF) to constrain output error.

Lyapunov stability analysis demonstrates the exponential stability of the closed-loop system and guarantees the tracking errors within predefined boundaries. The introduction of SJFs alleviates the limitation of RBFNNs on discontinuous function approximation. Owing to the fast learning speed of RBFNNs and jump response of SJFs, this modified NN approximator can reconstruct the system model accurately at a low compute cost, and thereby better tracking performance can be obtained. Experiments conducted on a manipulator verify the improvement and superiority of the proposed scheme in tracking performance and uncertainty compensation compared to a standard NN control scheme.

An enhanced NN approximator constituted of RBFNN and additional SJF neurons is presented which can compensate the continuous dynamic and discontinuous friction simultaneously. This control algorithm has potential usages in high-performance robots with unknown dynamic and variable friction. Furthermore, it is the first time to combine the augmented NN approximator with BLF. After more exact model compensation, a smaller tracking error is realized and a more stringent constraint of output error can be implemented. The proposed control scheme is applicable to some constraint occasion like an exoskeleton and surgical robot.