Supplementary Note 9. Comparative Experiments with EEAR

A rigid air tank (100 mL) is introduced to the system as the air buffer to achieve EEAR (Figure S9f and g). Here, we should mention that a too-small air buffer may damage the air smoothness of the pipeline for this closed configuration, and on the other hand, a too-large air buffer may result in excessive pressure drop in the buffer during recirculation, reducing recycling capability.
Based on the original system and the system with the air buffer introduced, we test the performance of four actuation modes: DIDO, IEAR, EEAR, and IEAR+EEAR. All the experiments follow the experimental procedures for Double Bellows and Triple Bellows.
Experimental results show the following findings in improving actuation speed and energy efficiency (Figure S9h-k).
        i) IEAR performs better than DIDO and EEAR.
        ii) EEAR hinders the improvement of actuation or efficiency within the range of low pressure,
        even worse than DIDO.
        iii) Actuation performance can benefit from the combination IEAR + EEAR. Especially for the
         range of high pressure, IEAR+EEAR achieves better performance than a single IEAR.
         iv) An adaptable best strategy is optional according to the results, which means adopting IEAR at low pressure and EEAR+IEAR at high pressure for robotic applications.

Supplementary Note 10. Characterization of pump flow \(Q_{pump}\)