Generation of multi-steps limit cycles for rabbit using a low dimensional nonlinear predictive control scheme

In this paper, a new nonlinear predictive control scheme is proposed for a planar under-actuated walking robot. The basic feature in the proposed strategy is to use online optimization in order to update the tracked trajectories in the completely controlled variables in order to enhance the stability of the remaining indirectly controlled ones. The stability issue is discussed using the Poincare´s section tool leading to a computable criterion that enables the stability of the overall scheme to be investigated as well as the computation of a candidate region of attraction. The whole framework is illustrated through a simulation case-study.