Nonlinear modes are a well investigated concept in dynamical systems theory, extending the celebrated modal analysis of linear mechanical systems to nonlinear ones. The present work moves a first step in the direction of combining control theory and nonlinear modal analysis towards the implementation of hyper-efficient oscillatory behaviors in mechanical systems with non-Euclidean metric. Rather than forcing a prescribed evolution, we first investigate the regular behaviors that can be autonomously expressed by the system, and then we design a controller that excites them. A first implementation of this concept is proposed, analyzed, and tested in simulation.

Nonlinear modes are a well investigated concept in dynamical systems theory, extending the celebrated modal analysis of linear mechanical systems to nonlinear ones. This letter moves a first step in the direction of combining control theory and nonlinear modal analysis towards the implementation of hyper-efficient oscillatory behaviors in mechanical systems with non-Euclidean metric. Rather than forcing a prescribed evolution, we first investigate the regular behaviors that can be autonomously expressed by the system, and then we design a controller that excites them. A first implementation of this concept is proposed, analyzed, and tested in simulation.

Eigenmanifolds extend eigenspaces to nonlinear mechanical systems with possibly non-Euclidean metrics. Recent work has shown that simple controllers can excite hyper-efficient oscillations by simultaneously stabilizing an Eigenmanifold and regulate the total energy. Yet, existing techniques require imposing assumptions on the system dynamics that the controlled system may not fulfill. This paper overcomes these limitations by allowing for partial dynamic compensation, which produces a good decoupling of the system's dynamics. This decoupling happens in a convenient set of coordinates induced by the modal characterization of the mechanical system. Two control algorithms taking advantage of this property are proposed and validated in simulation.

Thanks to their body elasticity, articulated soft robots promise to produce effective and robust oscillations with low energy consumption. This in turn is an important feature which can be exploited in the execution of many tasks, as for example locomotion. Yet, an established theory and general techniques allowing to excite and sustain these nonlinear oscillations are still lacking. A possible solution to this problem comes from nonlinear modal theory, which defines curved extensions of linear Eigenspaces called Eigenmanifolds. Stabilizing these surfaces is equivalent to exciting regular hyper-efficient oscillations in the robotic system. This paper proposes a first experimental validation of the Eigenmanifold stabilization technique. It also proposes a simple yet effective means of injecting energy into the system, so to sustain the oscillations in presence of damping. We consider as experimental setups a single robotic leg, and a full soft quadruped. Preliminary locomotion results are provided with both systems.