Roboticists are becoming increasingly successful at both implementing and analyzing dynamic steady-state legged robotic tasks such as running. Underlying this success is the mathematical understanding that many useful steady-state behaviors can be encoded as stable limit cycles of the controlled hybrid dynamics of the system. The dynamical systems literature has given engineers a wealth of tools for encoding and controlling the asymptotic properties of such systems - for example, to recast the problem of generating stable locomotion as finding a control which brings the Jacobian of an appropriate Poincare map of the system to have eigenvalues with magnitude less than unity at a designated fixed point.
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