This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state restrictions in the device articulations; this means the maximum and minimum angular ranges, to avoid any possible damage to the structure. The controller uses an active compensation method to estimate the unknown dynamics of the WBRD by means of an extended state observer. The sequence of movements for the gait cycle of a WBRD is represented as a class of hybrid system by alternative reference frameworks placed at the first and the last link. The stability analysis employs a class of Hybrid Barrier Lyapunov Function to ensure the fulfillment of the angular restrictions in the robotic device. The proposed controller is evaluated using a numerical simulation system based on the virtual version of the WBRD. Moreover, experimental results confirmed that the H-ADRC may endorse the realization of the proposed gait cycle despite the presence of perturbations and modeling uncertainties. The H-ADRC is compared against a proportional derivative (PD) controller and a proportional-integral-derivative (PID) controller. The H-ADRC shows a superior performance as a consequence of the estimation provided by the homogeneous extended state observer.

Purpose: There are common problems in the identification of uncertain nonlinear systems, nonparametric approximation, state estimation, and automatic control. Dynamic neural network (DNN) approximation can simplify the development of all the aforementioned problems in either continuous or discrete systems. A DNN is represented by a system of differential or recurrent equations defined in the space of vector activation functions with weights and offsets that are functionally associated with the input data.Design/methodology/approach: This study describes the version of the toolbox, that can be used to identify the dynamics of the black box and restore the laws underlying the system using known inputs and outputs. Depending on the completeness of the information, the toolbox allows users to change the DNN structure to suit specific tasks.Findings: The toolbox consists of three main components: user layer, network manager, and network instance. The user layer provides high-level control and monitoring of system performance. The network manager serves as an intermediary between the user layer and the network instance, and allows the user layer to start and stop learning, providing an interface to indirectly access the internal data of the DNN.Research limitations/implications: Control capability is limited to adjusting a small number of numerical parameters and selecting functional parameters from a predefined list.Originality/value: The key feature of the toolbox is the possibility of developing an algorithmic semi-automatic selection of activation function parameters based on optimization problem solutions.