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The Optimal Locomotion of a Self-Propelled Worm Actuated by Two Square Waves

1 and 1,2,*
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Department of Aeronautics and Astronautics, Fudan University, 220 Handan Road, Shanghai 200433, China
Author to whom correspondence should be addressed.
Micromachines 2017, 8(12), 364;
Received: 30 October 2017 / Revised: 8 December 2017 / Accepted: 13 December 2017 / Published: 16 December 2017
(This article belongs to the Special Issue Locomotion at Small Scales: From Biology to Artificial Systems)
PDF [3603 KB, uploaded 16 December 2017]


Worm-like locomotion at small scales induced by propagating a series of extensive or contraction waves has exhibited enormous possibilities in reproducing artificial mobile soft robotics. However, the optimal relation between locomotion performance and some important parameters, such as the distance between two adjacent waves, wave width, and body length, is still not clear. To solve this problem, this paper studies the optimal problem of a worm’s motion induced by two peristalsis waves in a viscous medium. Inspired by a worm’s motion, we consider that its body consists of two segments which can perform the respective shape change. Next, a quasi-static model describing the worm-like locomotion is used to investigate the relationship between its average velocity over the period and these parameters. Through the analysis of the relationship among these parameters, we find that there exist four different cases which should be addressed. Correspondingly, the average velocity in each case can be approximately derived. After that, optimization is carried out on each case to maximize the average velocity according to the Kuhn–Tucker Conditions. As a result, the optimal conditions of all of the cases are obtained. Finally, numerical and experimental verifications are carried out to demonstrate the correctness of the obtained results. View Full-Text
Keywords: worm-like locomotion; two square waves; two-segment worm; self-propulsion; optimization worm-like locomotion; two square waves; two-segment worm; self-propulsion; optimization

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Jiang, Z.; Xu, J. The Optimal Locomotion of a Self-Propelled Worm Actuated by Two Square Waves. Micromachines 2017, 8, 364.

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