  This paper proposes a Nonlinear Model-Predictive Control (NMPC) method
capable of finding and converging to energy-efficient regular oscillations,
which require no control action to be sustained. The approach builds up on the
recently developed Eigenmanifold theory, which defines the sets of line-shaped
oscillations of a robot as an invariant two-dimensional submanifold of its
state space. By defining the control problem as a nonlinear program (NLP), the
controller is able to deal with constraints in the state and control variables
and be energy-efficient not only in its final trajectory but also during the
convergence phase. An initial implementation of this approach is proposed,
analyzed, and tested in simulation.
