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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 …