The character of the reaching law approach is utilized to estimate the time-to-go in the first phase.
The surface is then modified to adapt arbitrarily given initial conditions for the reduction of the reaching phase.
Since the inputs of the reaching motion are the hands poses, it is necessary to calculate the whole body configuration of the robot (i.e., inverse kinematics (IK)).
The proposed algorithm is theoretically analyzed, proving the existence of an upperbound of the reaching time to the origin through the considered quantization levels.
The control design adds an exponential reaching law and a disturbance estimator to improve performance, achieving a reduction of the convergence time to the reference, as well as a reduction of the reaching time towards the sliding surface.
Moreover, based on the genetic algorithm (GA) approach to the optimal design of parameters of the reaching law, the reaching dynamics can be significantly improved during the reaching phase.
In this way, we make use of the fuzzy logic to handle uncertainty/disturbance in the design of the equivalent part and provide a chattering free control for the design of the reaching part.
The advantages of the controller include elimination of the reaching movement of traditional sliding mode control, realization of online identification of the fault value, and overcoming of the effect of the actuator faults and time delay.
A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties.
We defined this timing as the end of the reaching.
Following the practice trials, subjects completed ten trials of the reaching task without music followed by ten trials of the reaching task with preferred music.
