A general locomotion control framework for multi-legged locomotors.

Serially connected robots are promising candidates for performing tasks in confined spaces such as search and rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve mobility. However, a challenge in designing and controlling such devices lies in the coordination of high-dimensional redundant modules in a way that improves mobility. Here we develop a general framework to discover templates to control serially connected multi-legged robots. Specifically, we combine two approaches to build a general shape control scheme which can provide baseline patterns of self-deformation ('gaits') for effective locomotion in diverse robot morphologies. First, we take inspiration from a dimensionality reduction and a biological gait classification scheme to generate cyclic patterns of body deformation and foot lifting/lowering, which facilitate the generation of arbitrary substrate contact patterns. Second, we extend geometric mechanics, which was originally introduced to study swimming at low Reynolds numbers, to frictional environments, allowing the identification of optimal body-leg coordination in this common terradynamic regime. Our scheme allows the development of effective gaits on flat terrain with diverse numbers of limbs (4, 6, 16, and even 0 limbs) and backbone actuation. By properly coordinating the body undulation and leg placement, our framework combines the advantages of both limbless robots (modularity and narrow profile) and legged robots (mobility). Our framework can provide general control schemes for the rapid deployment of general multi-legged robots, paving the way toward machines that can traverse complex environments. In addition, we show that our framework can also offer insights into body-leg coordination in living systems, such as salamanders and centipedes, from a biomechanical perspective.