This paper proposes a periodic event-triggered control (PETC) design applied to nonlinear robotic systems for joint space stabilization. The update of the control signal is based on a predefined triggering mechanism that periodically considers state measurements. So, continuous state measurements required in the continuous event-triggered control (CETC), are no longer needed in this proposal. The main advantages of the proposal are: 1) to assure the convergence of the closed-loop trajectories to a compact ball centered in the origin of the error space, and 2) the relaxation of continuous measurements for the evaluation of the event condition which implies a more suitable design for real-time implementation purposes. Experimental comparative results of the proposed design with a time-triggered control (TTC) scheme show that the PETC can present suitable performance with a significant reduction of 82.20% of the controller updates mainly given in the steady-state of the closed-loop system. This implies a decrement of the computation resources due to information transfer.
In the classical approach of Time-Triggered Control (TTC), the control signal is updated at each sampling time as well as the system states to be controlled, which could imply a redundancy in the computational calculation as well as in the transfer of information in the regulation objective. On the other hand, the Event-Triggered Control (ETC) approach performs the same task in an asynchronous way, i.e,, it only updates the control signal when a performance requirement is violated and the states are updated at each sampling time. This reduces the amount of computational calculation without affecting the performance of the closed loop system. For this reason, in the present work the ETC is developed for the stabilization of a manipulator robot with three Degree of Freedom (DoF) in the joint space where a Lyapunov Control Function (LCF) is proposed to formulate the event function (e¯), which indicates whether or not is required the control signal updating. Simulation results show the reduction of the updates compared with a TTC.
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