Hexapod robots have gained significant attention due to their potential applications in complex terrains and dynamic environments. However, traditional inverse kinematics approaches often face challenges in meeting the precision required for adaptive omnidirectional movement. This work introduces a novel approach to addressing these challenges through the Directed Angular Restitution (DAR) method. The DAR method offers significant innovation by simplifying the calculation of rotational transformations necessary for aligning vectors across different planes, thus enhancing control, stability, and accuracy in robotic applications. Unlike conventional methods, the DAR method extends the range of trigonometric functions and incorporates spin functions to ensure continuous and smooth trajectory tracking. This innovative approach has been rigorously tested on a hexapod robot model, demonstrating superior performance in movement precision and stability. The results confirm that the DAR method provides a robust and scalable solution for the inverse kinematics of hexapod robots, making it a critical advancement for applications in robotics and automation where precise control and adaptability are paramount.

This work presents a nested super-twisting second-order sliding mode speed controller for a brushless direct current motor with a high order sliding mode observer used for back electromotive force (back-EMF) estimation. Due to the trapezoidal nature of the back-EMF, a modified Park transformation is used in order to achieve proper field orientation. Such transformation requires information from the back-EMF that is not accessible. A second-order sliding mode observer is used to estimate the back electromotive forces needed in the modified transformation. Sliding mode control is known to be robust to matched uncertain disturbances and parametric variations but it is prone to unmatched perturbations that affect the performance of the system. A nested scheme is used to improve the response of the controller in presence of unmatched disturbances. Simulations performed under similar conditions to real-time experimentation show a good regulation of the rotor speed in terms of transient and steady-state responses along with a reduced torque ripple.

A super-twisting sliding mode controller is developed for speed control of a brushless direct current motor using a nested scheme. The non-sinusoidal nature of the back electromotive forces in this electrical machine presents the need of a modification to Park transformation for accurate field orientation. An extension to Park transformation is used in this work that requires information from the back electromotive forces to compensate position and magnitude variations resulting from the transformation. To obtain the information needed in the modified transformation, a sliding mode observer is designed to estimate the back electromotive forces from the motor. To improve the performance of the controller, a nested sliding mode algorithm is implemented that allows robustness to unmatched perturbations such as load torque variations. Simulations are used to show the performance of the controller under similar real-time conditions with parametric and load torque variations.

This work introduces an impulsive neural control algorithm designed to mitigate the spread of epidemic diseases. The objective of this paper is the development of a vaccination strategy based on a PIN-type impulsive controller based on an online-trained neural identifier to control the spread of infectious diseases under a complex network approach with time-varying connections where each node represents a population of individuals whose dynamics are defined by the MSEIR epidemiological model. Considering an unknown model of the system, a neural identifier is designed that provides a nonlinear model for the complex network trained through an extended Kalman filter algorithm. Simulation results are presented by applying the proposed control scheme for a complex network parameterized as infectious diseases.