This researching work presents the design of an adaptive controller implementing the solution of the trajectory tracking for a robotic micromanipulator based on a three degrees of freedom arm that carries a piezoelectric- based gripper. The robotic arm is aimed to place the gripper at the correct position. From this spot, the gripper can handle objects of millimetric and micrometric scales. The proposed adaptive controller implements state dependent gains that drives all the articulations of the arm smoothly towards their corresponding references. The design of these gains is obtained using a class of control Lyapunov function. The type of the developed controller is also working to control the motion of the microgripper using the main mode of the piezoelectric actuators, represented by ordinary differential equations that takes into account the relation with the robotic arm. The proposed controller is tested over an actual robotic arm and evaluated considering the performance comparison with respect to a traditional state feedback control form. The experimental results confirm the effective tracking of the reference trajectories showing neither transient oscillations nor overshoots. These evaluations justify the application of the proposed method with the state dependent gains. The manipulation of millimetric objects is also used to evaluate the functionality of the developed robotic arm with its piezoelectric based gripper.

This study is summarising the design of an output hybrid feedback controller for biped robots where the motion range for each joint is being considered. The design considers the hybrid nature of biped device when it is developing an entire gait cycle including the interaction with the environment touching the support floor. A simplified hybrid model is proposed to represent the dynamics of the robotic device in a realistic form. The proposed biped device is driven using linear actuators with a motion transfer system. A hybrid formulation for the control with adaptive state dependent gains regulates the articulations motion considering the limits of actuator motion. The dynamics of the adaptive gains is obtained with the application of a control barrier-like Lyapunov function for hybrid systems. The explicit structure of these gains are derived in a formal way. A set of numerical simulations is used to demonstrate the applicability of the developed controller analysing the tracking of bio-inspired reference trajectories obtained from reported biomechanical information. The numerical simulations used a virtual model of a biped robotic device where the interaction with the environment was considered for analysing the effect of hybrid evolution. A comparison between trajectories produced by the hybrid controller and a traditional state feedback offers a class of validation for the application of the restricted barrier inspired output feedback control strategy,

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories.

The aim of this study was to design and evaluate an output based adaptive rejection controller (ADRC) for a biped robot. The controller considers the application of an extended state observer which serves for either estimate the velocity of the legs articulation angles as well as to estimate the disturbances affecting the robot dynamics. The observer design considered the angles constrains which naturally appear in the movement of a biped robot. A class of hybrid observer appeared as solution for the estimation of angles values and their positions. The control design (proposed in a distributed structure) used the constrained estimation of velocity to solve the tracking trajectory problem associated to the gait cycle of the biped robot. A set of numerical evaluations over a simulated biped robotic system proved that active disturbance rejection controller using the estimated state constrains tracked the reference angles of articulation. The comparison of the controller proposed in this study overcame the tracking results attained by the classical ADRC where the estimated velocities were freely estimated without taking into account the angles constrains.