Modeling of Asynchronous Mode-Dependent Delays in Stochastic Markovian Jumping Modes Based on Static Neural Networks for Robotic Manipulators

Abstract

Over the past 20 years, many specialists in the business have become interested in managing flexible joint robotics. Considering flexibility in joints in the control scheme of inflexible robots is challenging because it eliminates certain structural properties that facilitate control, such as full activation, distinct control for every socket, and passivity of the torque generated by the motor for coupling velocity. In this research, the authors analyze asymptotic stability for neural models of fixed stochastic process that have time-varying delays, which depend on jumping modes; their derivatives no longer need to be smaller than one. Secondly, by applying a stochastic setup, the researchers explore fixed neutral models with Markovian jump variables based upon mode-dependent time-varying delays for modeling flexible joint robots. Thirdly, this research develops various stability circumstances with delay-dependent conditions based on linear matrix inequalities (LMIs) by combining the novel Lyapunov theory with the convex polyhedron technique, concluding with two numerical examples illustrating their use. As a result, an optimization problem can be addressed to calculate a control law created for implementing the stochastically stable platform. As a final step, the proposed method is verified using a quadruple-tank model and for modeling flexible joint robots. Note to Practitioners—Neural network controllers are frequently employed in the medical field, automation industry, robotics sector, and other industries where certain jobs cannot be completed by autonomous or human robotics. By increasing flexibility, refining control technique, relaxing stability conditions, and promoting human-robot collaboration, this research seeks to create novel solutions to important problems in industrial robotic manipulators. In order to maintain the system’s stability in both motion states-coupling velocity and torque motion and meet the associated position and velocity synchronization goals, this paper suggests a NN-based control technique that can manage random process and variable time-delays signals. More straightforward structures, fewer tuning factors, and improved control behaviors are some of the benefits of this approach that make engineering applications easier. Lastly, a simulation using a realistic strategy is demonstrated to validate the theoretical assertions.