A general locomotion control framework for multi-legged locomotors

Abstract

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 generation of arbitrary substrate contact patterns. Second, we extend geometric mechanics, which was originally introduced to study swimming in low Reynolds number, to frictional environments, allowing identification of optimal body-leg coordination in this common terradynamic regime. Our scheme allows the development of effective gaits on flat terrain with diverse number 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.

Self propulsion via slipping: frictional resistive force theory for multi-legged locomotors

“…As discussed in prior work, body undulation can play an important role in multi-legged systems [31,32]. In Fig.…”

“…More recently, studies have demonstrated effective undulatory swimming with no intrinsic drag anisotropy. These works modulated the magnitude of surface traction via either static friction [18,37] or periodic lifting and landing of body appendages [31] to produce undulatory locomotion. Here, we posit that effective undulatory swimming shares the same physical principles between these two scenarios (intrinsic drag anisotropy and friction modulation).…”

“…In other words, by properly controlling the sequence of lifting and landing, we can effectively acquire drag anisotropy in either direction and therefore enable swimming along (direct wave [41]) and against (retrograde wave [41]) the direction of wave propagation. Interestingly, s 1 = 0 also optimizes body-leg coordination as reported in [31] where the body undulation is considered to assist leg retraction. In this paper, we only consider the retrograde-wave terrestrial swimming.…”

“…All combined, each module has three degrees of freedom (DoF): the shoulder lifting joint that controls the contact states of contralateral legs, the shoulder retraction joint that controls the fore/aft positions of leg movements, and the body bending joint that controls the lateral body undulation [30]. The synchronization of these three DoF is coupled using the extended Hildebrand framework ( [31] and SI), which prescribe a leg stepping wave and a body undulation wave, both propagating from head to tail. The amplitude of body undulation, Θ body , the amplitude of leg movement, Θ leg , and the spatial wave number ξ, can then uniquely prescribe the gait of the multi-legged robot.…”

“…Interestingly, we observe that after the transient response (t < 2s) upon the initiation of gait, the trajectory of velocity converge to a limit cycle. To better understand the initial transient response and the limit cycle, we establish a dynamic model (see SI) and a quasi-static model [31] (Fig. 1d).…”