Significant payload variations often occur in many practical tasks for robotic applications. But its adequate control is a formidable challenge to control designers, and previous research works have exhibited either limited performance or noticeable difficulties in implementation. In this paper, we have proposed an adaptive PID control that is simple, model-free, and robust against payload variations. These advantages, already verified from the adaptive time-delay control (TDC), have been inherited to the proposed PID control through the equivalence relationship between the two controls. As a result, the proposed PID shares the simplicity, robustness, and the model free property, as well as the high levels of stability and performance with the adaptive TDC. In particular, the selection of its gains becomes especially simple and straightforward, while the adaptation becomes efficient under substantial payload variations. These positive attributes have been verified through simulations and experiments on robots under substantial payload variation. In particular, the proposed PID control was applied to the control of a WAM robot holding a baseball bat, with a result better than a standard PID control.INDEX TERMS Adaptive control, payload variations, PID control, robot manipulator, time-delay estimation.

The time-delay control (TDC) has recently been spotlighted as an effective solution owing to model-free, efficient, and robust properties thanks to a time-delay estimation (TDE) technique. The gain of TDC usually denoted byM is crucial for its stability and performance, and it is reported that the constant gain of TDC does not always guarantee the best performance. To cope with this problem, this paper proposes an effective gain adaptation together with a nonlinear desired error dynamics and a new sliding variable. The resulting adaptive gain dynamics is combined with the TDC to form the proposed control, whose closed-loop stability is proved. Through simulation and experiment, we have shown that the proposed control enables to transferM from an unstable initial value to a stable one, better than a best-tuned gain by trial and error. As a result, the proposed control is model-free, able to achieve time responses as fast as the inclusive enhanced TDC (IETDC)-arguably the fastest TDC-and tracking accuracy better than the IETDC. The proposed method has shown a strong potential to significantly relieve the burden of gain selection. INDEX TERMS Adaptive control, robot manipulator, sliding mode control, time-delay estimation.

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Brain activation has been used to understand brain-level events associated with cognitive tasks or physical tasks. As a quantitative measure for brain activation, we propose entropy in place of signal amplitude and beta value, which are widely used, but sometimes criticized for their limitations and shortcomings as such measures. To investigate the relevance of our proposition, we provided 22 subjects with physical stimuli through elbow extension-flexion motions by using our exoskeleton robot, measured brain activation in terms of entropy, signal amplitude, and beta value; and compared entropy with the other two. The results show that entropy is superior, in that its change appeared in limited, well established, motor areas, while signal amplitude and beta value changes appeared in a widespread fashion, contradicting the modularity theory. Entropy can predict increase in brain activation with task duration, while the other two cannot. When stimuli shifted from the rest state to the task state, entropy exhibited a similar increase as the other two did. Although entropy showed only a part of the phenomenon induced by task strength, it showed superiority by showing a decrease in brain activation that the other two did not show. Moreover, entropy was capable of identifying the physiologically important location.