N.F. Lepora et al. (Eds.): Living Machines 2013, LNAI 8064, pp. 59–70, 2013.
© Springer-Verlag Berlin Heidelberg 2013
Stable Heteroclinic Channels
for Slip Control of a Peristaltic Crawling Robot
Kathryn A. Daltorio
1
, Andrew D. Horchler
1
, Kendrick M. Shaw
2
,
Hillel J. Chiel
2
, and Roger D. Quinn
1
1
Department of Mechanical Engineering, Case Western Reserve University,
10900 Euclid Ave, Cleveland, Ohio 44106-7222
rdq@case.edu
2
Department of Biology, Department of Neurosciences,
and The Department of Biomedical Engineering, Case Western Reserve University,
10900 Euclid Ave, Cleveland, Ohio 44106
Abstract. Stable Heteroclinic Channels (SHCs) are continuous dynamical
systems capable of generating rhythmic output of varying period in response to
sensory inputs or noise. This feature can be used to control state transitions
smoothly. We demonstrate this type of controller in a dynamic simulation of a
worm-like robot crawling through a pipe with a narrowing in radius. Our SHC
controller allows for improved adaptation to a change in pipe diameter with
more rapid movement and less energy loss. In an example narrowing pipe, this
controller loses 40% less energy to slip compared to the best-fit sine wave
controller.
Keywords: stable heteroclinic channels, biologically-inspired control, worm-
like robots, peristalsis.
1 Introduction
Coordinated oscillators can generate life-like motion in biologically-inspired robots.
These oscillators are often based on limit cycles, systems of equations that stabilize
into a regular periodic output. Changing the relative phase of an oscillator can change
the locomotory gait [1]. These controllers may be similar to the way animals control
their bodies because groups of neurons connect to generate repeating cycles, often
referred to as central pattern generators (CPGs). See [2] for a review of controllers
inspired by this concept. One of our previous papers was based on the Wilson-Cowan
model to adjust the speed and spatial resolution of traveling waves [3]. We added
feedback to limit radial expansion in [4]. However, we want variable dwell times at
phases in the oscillation cycle in response to environmental feedback, which led us to
use a different mathematical oscillator: stable heteroclinic channels.
Stable heteroclinic channels (SHCs) are a framework for continuous dynamic
oscillation that can produce regular intervals of steady output [5–7]. In other words,
the system can “pause” near defined equilibrium points. This allows a designer to
treat the equilibrium points as a sequence and yet the dynamic equations provide