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