  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 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 generation of arbitrary
substrate contact patterns. Second, we use geometric mechanics methods to
facilitates identification of optimal phasing of these undulations to maximize
speed and/or stability. Our scheme allows the development of effective gaits in
multi-legged robots locomoting on flat frictional terrain with diverse number
of limbs (4, 6, 16, and even 0 limbs) and body actuation capabilities
(including sidewinding gaits on limbless devices). By properly coordinating the
body undulation and the leg placement, our framework combines the advantages of
both limbless robots (modularity) and legged robots (mobility). We expect that
our framework can provide general control schemes for the rapid deployment of
general multi-legged robots, paving the ways toward machines that can traverse
complex environments under real-life conditions.
