Exploiting Discontinuities for Stabilization of Recurrent Motions

Harry Dankowicz, Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA, USA
Petri T Piiroinen, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden

A rigorous mathematical technique is presented for exploiting the presence of discontinuities in nonsmooth dynamical
systems in order to control the local stability of periodic or other recurrent motions. The methodology is illustrated
with examples from impacting systems, namely a model hopping robot, a Braille printer head, and a class of passive
bipedal walkers. It is shown how initially strongly unstable motions can be successfully stabilized at negligible cost
and without active energy injection.