A modeling and control hierarchy of quadrupedal running with torso compliance

Poulakakis, IoannisA series of quadrupedal robots with different morphologies has been developed in the past forty years to explore the enhanced mobility such platforms may offer. The majority of these robots incorporate rigid, non-deformable torsos, a feature that distinguishes them from their counterparts in the animal world, which owe much of their remarkable locomotion abilities to their flexible bodies. Biological research indicates that torso flexibility may contribute to increased running speed, reduced energy cost and improved gait stability. This thesis proposes a modeling hierarchy that incorporates biological observations within a series of models with increasing complexity, and develops systematic feedback control algorithms for highly dynamic quadrupedal running motions that harness torso flexibility and compliant legs. On a macroscopic level, reduced-order models, or “templates”, can capture the dominant features of an observed locomotion behavior without delving into the fine details of a robot’s (or animal’s) structure and morphology. Templates provide unified, platform-independent descriptions of the desired locomotion task, and they have proved to be indispensable in designing legged robots and in synthesizing controllers for stabilizing highly-agile locomotion behaviors. One representative example is the Spring Loaded Inverted Pendulum (SLIP), which, despite its very simple structure, captures the evolution of kinetic and potential energy associated with running motions, and has informed controller design of many legged robots. However, because of its simple lumped point-mass structure, the SLIP and its immediate extensions cannot describe some of the common quadrupedal gaits that involve pronounced torso oscillations, such as bounding and galloping. Motivated by the capability as well as the limitations of SLIP-type templates, a number of reduced-order quadrupedal models that incorporate non-point-mass torsos has been proposed in the relevant literature to investigate quadrupedal running. However, partly because of the need to describe the torso morphology of the corresponding hardware platforms, and partly because of the need to simplify running dynamics, most of these quadrupedal templates only consider non-deformable, rigid torsos. Although, a few studies with preliminary results on running with torso compliance can be found in the relevant literature, studies on the conditions for generating periodic locomotion behaviors are rather limited while the stability properties of these motions are not carefully examined. As a result, feedback controller design in the presence of torso compliance has not been carefully investigated. Beyond stability and control design, the energetic cost of transport of quadrupedal running and, in particular, the contribution of torso flexibility to running efficiency, has not received adequate attention. This thesis aims at proposing a modeling and control hierarchy that enables the systematic evaluation of the role of torso compliance in quadrupedal running. The proposed templates have different modeling complexities and actuation schemes, and can be used to facilitate the investigation of a number of key issues in quadrupedal running, such as motion generation, gait stability, feedback design, gait transitions and energy efficiency. Through careful analysis of the models, a series of useful conclusions can be drawn; these conclusions pave the way toward synthesizing feedback control laws for legged robots with torso and leg compliance, and provide insight into designing robotic platforms that harness elastic elements to realize high-performance, reliable and natural-like quadrupedal running motions.University of Delaware, Department of Mechanical EngineeringPh.D