Learning to crawl: benefits and limits of centralized vs distributed control

Abstract: We present a model of a crawler consisting of several suckers distributed along a straight line and connected by springs. Both proprioception and control are binary: the system responds to the elongation vs compression of its springs and the suckers can either adhere or remain idle. A central pattern generator delivers a traveling wave of compression, and the crawler is tasked to learn how to control adhesion to effectively ride the wave in order to crawl. We ask what are the benefits and limitations of distributed vs centralized learning architectures. Using tabular Q-learning we demonstrate that crawling can be learned by trial and error in a purely distributed setting where each sucker learns independently how to control adhesion, with no exchange of information among them. We find that centralizing control of all suckers enhances speed and robustness to failure by orchestrating smoother collective dynamics and partly overcoming the limitations of rudimentary proprioception and control. However, since the computational cost scales exponentially with the number of suckers, centralized control quickly becomes untreatable with the size of the crawler. We then show that intermediate levels of centralization, where multiple control centers coordinate subsets of suckers, can negotiate fast and robust crawling while avoiding excessive computational burden. Our model can be further generalized to explore the trade-offs between crawling speed, robustness to failure, computational cost and information exchange that shape the emergence of biological solutions for crawling and could inspire the design of robotic crawlers.