Through the use of Eigenmanifold theory, unforced periodic trajectories called nonlinear normal modes can be identified and excited in nonlinear mechanical systems. Applying this to repetitive tasks in robotic systems with elastic components can drastically reduce energy consumption, as normal modes in steady-state require no additional control effort. However, existing control methods for exciting nonlinear normal modes have so far only assumed full actuation. Consequently, these techniques are incompatible with series elastic joint robots, even though they represent a significant subclass of physical systems with elastic elements. Additionally, the calculation and parameterization of Eigenmanifolds for high-dimensional systems generally remains a complex task and is difficult to scale. While existing literature aims to avoid forced evolutions or model cancellation, we instead lean into this approach. By rephrasing Eigenmanifold-based control as a trajectory tracking problem, standard techniques for elastic joint robot trajectory tracking control can be employed. Furthermore, obtaining theoretical guarantees on global stability becomes possible. In this work, a new modular control architecture is presented that integrates trajectory tracking feedback control with Eigenmanifold theory to dynamically generate and track hyper energy-efficient oscillatory movements in underactuated systems. This approach enables the excitation of nonlinear normal modes using standard trajectory tracking controllers, while preserving energy-efficient properties desired from Eigenmanifold-based controllers. We first discuss the theoretical validity and energy-efficiency of this control architecture, and then test the architecture in simulation for a variety of use-cases and controllers.

Soft continuum robots provide a compelling solution for safe interactions with unknown and unstructured environments, owing to their compliance and infinite degrees of freedom. However, the non-linear deformation and inherent underactuation pose a persistent challenge for real-time control and state estimation. To date, continuum structures are typically discretized using a fixed-parameter kinematic model, introducing a trade-off between model accuracy and computational efficiency.

This letter presents an adaptive kinematic modeling framework to address the challenge of underactuation in a different way - not by increasing model resolution or complexity - but by making the model parametric with respect to a set of parameters that are dynamically adapted using a novel inverse kinematic adaptive controller.

We formally prove stability of the adaptive controller and validate its performance through simulations and experiments, considering setpoint reaching tasks with variable end-effector payloads. Even though the approach introduces additional challenges, in comparison to the conventional fixed-parameter models presented in literature, the proposed solution enhances shape representation, redundancy resolution, and state inference while mitigating model complexity.