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

Abstract

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.

Peristalsis by pulses of activity

“…Our results can be used for biomimetic reproduction of wormlike motion in applications ranging from endoscopic diagnostics [46] to pipeline inspection [47]. While in the existing robotic systems activity is imitated by globally synchronized distributed actuators [9,20,36], our focus on local mechanical feedback in muscle-type soft materials opens new avenues in the biomimetic modeling of peristalsis, see also [21,48,49]. The proposed prototypical model can serve only as a proof of concept and future work aimed at quantitative predictions, should incorporate energy supply and dissipation while also accounting for realistic threedimensional geometry.…”

“…where ε n (t ) = (u n+1 (t ) − u n (t ))/a are the strains in the springs, u n (t ) are the displacements of the nodes, and a is the equilibrium length. The inertial term, allowing the system to overcome the discreteness-induced trapping, proved to be important in ultrasoft robotics [30,31,35,36]. In physiological setting the apparent mass density ρ can be viewed as a parameter introducing the activity-related time delay in the response of stretch receptors [37,38].…”

Variations of Saffman's robot: two mechanisms of locomotion?

“…For the purpose of geometrical visualisation one may write that the time-evolution of the shape of spear robot looks somewhat similar to that in the self-propulsion of worms, see e.g. Quillin (1998); Boxerbaum, et al (2012);Ziwang & Jian (2017). Indeed, the worm's peristaltic propulsion is modelled by a wave, consisting of a sequence of radially expanded and radially contracted segments of its long cylindrical body.…”

Peristalsis by pulses of activity

“…where ε n (t) = (u n+1 (t) − u n (t))/a is the strain in a spring whose ends undergo displacements u n (t)and a is the equilibrium length of a spring. The inertial term, allowing the system to overcome the discreteness-induced trapping, proved to be important in ultra-soft robotics [29,30,34,35]. In physiological setting the apparent mass density ρ can be viewed as a parameter introducing an activity-related time delay in the response of stretch receptors [36,37].…”

“…Our results can be used for biomimetic reproduction of wormlike motion in applications ranging from endoscopic diagnostics [45] to pipeline inspection [46]. While in the existing robotic systems activity is usually imitated by globally synchronized distributed actuators [9,20,35] our focus on local mechanical feedback in muscle-type soft deformable materials opens new avenues in the modeling of peristalsis, see also [47][48][49]. The proposed prototypical model can serve only as a proof of concept and future work allowing one to make quantitative predictions, should incorporate energy supply and dissipation and account for realistic 3D geometry.…”