Oscillators are ubiquitous in nature and are usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. We show that the asymptotic phase can be estimated using a carefully chosen series expansion that directly computes the phase response curve (PRC) and provides an algorithm for estimating the coefficients of this series. Unlike previously available data-driven phase estimation methods, our algorithm can use observations that are much shorter than a cycle; has proven convergence rate bounds as a function of the properties of measurement noise and system noise; will recover phase within any forward invariant region for which sufficient data are available; recovers the PRCs that govern weak oscillator coupling; and recovers isochron curvature and recovers nonlinear features of isochron geometry. Our method may find application wherever models of oscillator dynamics need to be constructed from measured or simulated time-series.

Decimeter scale robots in human environments are small relative to obstacles they encounter, making them prone to flipping over and needing to self-right. We present a multifaceted shell that by its geometry alone enables the hexapedal robot MediumANT to passively self-right without the need for additional sensory feedback. We designed the shell by specifying the cross-sectional geometry in the yz and xy planes such that the robot returns to an upright position by rolling around the longitudinal (x) axis, and then tweaked the design to reduce the number of faces. We then attached the shell to the robot by modifying some of its chassis structural plates to extend to and support the shell. We evaluated the effectiveness of the shell in two experimental scenarios: passive righting – balancing the robot on each face of the shell before releasing the robot – and an intentional fall – walking the robot off a ledge at various approach angles. As intended by our design, the robot recovered the upright orientation from all starting faces in the passive righting test and righted itself and continued walking in all falling trials. This work presents an example of using biologically inspired simplicity to solve what would otherwise be a technically challenging problem.

We describe a mobile modular robot system that can generate foam to make structural elements. The mobile platform itself is built of CKBot modules and carries extra modules along with a foam generation device. We demonstrate the system synthesizing new robot morphologies: a snake-like robot and a legged robot. We also use the foam structures to encapsulate and pick-up objects and to modify the environment by blocking a door. Our presentation describes the issues that arose in implementing and using this technique.