We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is exploited to devise an efficient swing-up strategy for a double pendulum with weak, saturating actuators. Our approach involves stabilizing the system onto periodic orbits associated with the nonlinear modes while gradually injecting energy. Since these modes are autonomous system evolutions, the required control effort for stabilization is minimal. Even with actuator limitations of less than 1% of the maximum gravitational torque, the proposed method accomplishes the swing-up of the double pendulum by allowing sufficient time.

Animals rely on the elasticity of their tendons and muscles to execute robust and efficient locomotion patterns for a vast and continuous range of velocities. Replicating such capabilities in artificial systems is a long-lasting challenge in robotics. By taking advantage of a pitch dynamics decoupling spring potential, this work aims to provide design rules and a control strategy to generate dynamic, efficient locomotion patterns in quadrupeds moving in a sagittal plane. We rely on nonlinear modal theory, which provides the tools to characterize continuous families of efficient oscillations in nonlinear mechanical systems. We provide simulations of an elastic quadruped showing that the proposed solution can robustly excite efficient locomotion patterns under non-ideal conditions.

Advances in exoskeleton technology now enable interacting with rigid objects in a virtual or remote environment using one's hand and fingertips. However, interaction with non-solid materials - such as liquids, sediments and regolith - alongside solids, can greatly extend the versatility of this technology. Rendering rigid objects adequately requires a control loop with high update rates, whereas fluid dynamics equations are computationally expensive. To accommodate this, the fluid dynamics can be simplified - particularly for fluids with high viscosity - resulting in a fast-to-calculate model to enabling haptic rendering of viscous fluids and rigid bodies simultaneously using DLR's Exodex Adam hand exoskeleton. Viscosity as a proprioceptive cue of fluids can be presented to the human through force feedback at multiple points on the human hand - fingers and palm - letting the user interact with a virtual environment in a more natural way and making the experience more immersive. We carry out two user studies to investigate the human perception abilities of virtual fluids rendered with simplified dynamics, and the discernability of different viscosity in virtual fluids compared real fluids. Results show that virtual media can give the user the perception of interacting with a fluid, even with simplified models, at a high update frequency. Furthermore, the material discernibility corresponds well to actual interaction with real viscous fluids. This shows great promise forward for haptic in-hand interaction in fluid and mixed media environments.