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• W140813413 abstract "The singular nature of contact makes walking a difficult problem to analyze mathematically. To overcome this, we consider a simple triple mass-spring system as a model for a walker and we regularize the ground contact. We prove that under small periodic forcing, this system exhibits a robustly stable, relatively periodic orbit. More specifically, we introduce a regularized model of ground contact using a smooth repulsive potential energy and a smooth dissipative friction force. In a symmetry reduced phase space we then prove the existence of a limit cycle when the system is periodically actuated. In the unreduced phase space, the lifted trajectory is stable and relatively periodic, wherein each period is related to the previous by an $x$-translation. In conclusion, we have constructed a model which is complex enough to capture behavior characteristic of walking, yet simple enough to prove rigorous results. This may serve as a case study for more complex models by identifying core-mechanisms of limit cycle walking." @default.
• W140813413 created "2016-06-24" @default.
• W140813413 creator A5040086724 @default.
• W140813413 creator A5058709078 @default.
• W140813413 date "2012-12-10" @default.
• W140813413 modified "2023-09-27" @default.
• W140813413 title "Limit cycle walking on a regularized ground" @default.
• W140813413 hasPublicationYear "2012" @default.
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