Designing responsive pattern generators: stable heteroclinic channel cycles for modeling and control.

A striking feature of biological pattern generators is their ability to respond immediately to multisensory perturbations by modulating the dwell time at a particular phase of oscillation, which can vary force output, range of motion, or other characteristics of a physical system. Stable heteroclinic channels (SHCs) are a dynamical architecture that can provide such responsiveness to artificial devices such as robots. SHCs are composed of sequences of saddle equilibrium points, which yields exquisite sensitivity. The strength of the vector fields in the neighborhood of these equilibria determines the responsiveness to perturbations and how long trajectories dwell in the vicinity of a saddle. For SHC cycles, the addition of stochastic noise results in oscillation with a regular mean period. In this paper, we parameterize noise-driven Lotka-Volterra SHC cycles such that each saddle can be independently designed to have a desired mean sub-period. The first step in the design process is an analytic approximation, which results in mean sub-periods that are within 2% of the specified sub-period for a typical parameter set. Further, after measuring the resultant sub-periods over sufficient numbers of cycles, the magnitude of the noise can be adjusted to control the mean period with accuracy close to that of the integration step size. With these relationships, SHCs can be more easily employed in engineering and modeling applications. For applications that require smooth state transitions, this parameterization permits each state's distribution of periods to be independently specified. Moreover, for modeling context-dependent behaviors, continuously varying inputs in each state dimension can rapidly precipitate transitions to alter frequency and phase.

Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots.

In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress