| Many legged animals and robots varying in size and morphology produce net ground reaction forces and center-of-mass motions during locomotion similar to those of a monopod bouncing along. However, this analogy and its implications are not fully understood. How and why do diverse multi-legged systems act like a simple passive monopod? How could the understanding of this analogy directly benefit the design and control of legged robots? In this thesis we develop a series of simple mathematical models which begin to answer these questions. We study a passive three-dimensional spring-loaded inverted pendulum 'pogo-stick' model of running, and find that it is unstable everywhere, but can be stabilized with a leg placement control law. We add morphological detail to it to study the affect of leg number, posture, and hip stiffness on center-of-mass motions, and find that these largely passive mechanical schemes can confer dynamic stability. We then move into the horizontal plane to develop an actuated hexapedal model of the cockroach Blaberus discoidalis, and discover that the hexapedal model can produce net force and moment patterns like that of the insect, which a monopod cannot, and that it can stabilize center-of-mass translations coupled with yawing motions. Finally, we study an actuated vertical (sagittal)-plane model of the robotic hexapod RHex, useful for robot analysis and control, and demonstrate qualitative and quantitative agreement with experimental data. Throughout we use the tools of dynamical systems theory---defining Poincare return maps, finding fixed points, and calculating eigenvalues---to analyze the models and derive explicit results where possible, and we use numerical continuation schemes to broaden analysis to non-integrable cases. |
