EigenMPC: An Eigenmanifold-Inspired Model-Predictive Control Framework for Exciting Efficient Oscillations in Mechanical Systems

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.

Automated summary

This paper proposes a Nonlinear Model-Predictive Control method that can find and converge to energy-efficient regular oscillations without any control action. The approach is based on the Eigenmanifold theory, which defines the oscillations of a robot as an invariant submanifold of its state space. By formulating the control problem as a nonlinear program, the controller can handle constraints in the state and control variables and achieve energy efficiency during the convergence phase.