Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

@article{Colombo2021StabilizationOP,
  title={Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction},
  author={Giovanni Colombo and Paolo Gidoni and Emilio Vilches},
  journal={Discrete \& Continuous Dynamical Systems},
  year={2021}
}
<p style='text-indent:20px;'>We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger <inline-formula><tex-math id="M1">\begin{document}$ W^{1,2} $\end{document}</tex-math></inline-formula> convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running… 
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References

SHOWING 1-10 OF 26 REFERENCES
Rate-independent soft crawlers
  • P. Gidoni
  • Mathematics
    The Quarterly Journal of Mechanics and Applied Mathematics
  • 2018
This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies
Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler
TLDR
By focusing on the tensions in the elastic segments, this work shows that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity, and shows that specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.
Control of locomotion systems and dynamics in relative periodic orbits
The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as
On the optimal control of rate-independent soft crawlers
Stabilization of the response of cyclically loaded lattice spring models with plasticity
This paper develops an analytic framework to design both stress-controlled and displacement-controlled T-periodic loadings which make the quasistatic evolution of a one-dimensional network of
Existence and stability of limit cycles in the model of a planar passive biped walking down a slope
  • O. Makarenkov
  • Biology, Mathematics
    Proceedings of the Royal Society A
  • 2020
TLDR
The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps and derives a perturbations theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences.
The Role of Symmetry and Dissipation in Biolocomotion
TLDR
This toy model identifies how symmetry reduction and dissipation can conspire to create robust behavior in crawling, and possibly walking, locomotion.
Swimming on limit cycles with nonholonomic constraints
TLDR
This work shows that the governing equations of the Chaplygin sleigh are a very useful surrogate model for the swimming robot, and suggests that there is a close phenomenological and mathematical similarity between the dynamics of swimming robots and those of ground-based nonholonomic robots, which could motivate the development of very low-dimensional mathematical models for the motion of other fish-like swimming robots.
Geometric phases and robotic locomotion
TLDR
This paper describes locomotion in terms of the geometric phase associated with a connection on a principal bundle, and addresses issues such as controllability and choice of gait.
On rate-independent hysteresis models
This paper deals with a general approach to the modeling of rate–independent processes which may display hysteretic behavior. Such processes play an important role in many applications like
...
...