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.

翻译：本文提出了一种非线性模型预测控制（NMPC）方法，能够发现并收敛到无需任何控制作用即可维持的高能效规则振荡。该方法基于近期发展的特征流形理论，该理论将机器人的线状振荡集合定义为其状态空间中一个不变的两维子流形。通过将控制问题表述为非线性规划（NLP），该控制器能够处理状态变量和控制变量的约束，不仅在最终轨迹上，而且在收敛阶段也能实现高能效。本文提出了该方法的初始实现，并在仿真中进行了分析验证。