Abstract
The rapid development of technology in the past century has produced robots that are increasingly versatile to perform a wide range of challenging tasks: dexterous manipulation, stable traverse through unknown terrain, and parkour, to name a few. Accompanied with these achievements is the intricate robot construction that complicates the basic formulation of dynamics, the core behind many robots that have ever been built. Besides, the expansion of robots’ working space leads to the inevitable interaction between the robots and the open environment, leading to abundant behaviors that are intermittent, nonsmooth, and hybrid. As the evolution of robots goes naturally towards complexity, understanding the fundamental hybrid, nonsmooth dynamics behind these manmade machines becomes crucial. This thesis presents a complete framework to study hybrid dynamics in nonsmooth mechanical systems, with a particular focus on legged robots. We provide insightful results in analytical modeling, numerical simulation, system design, and physical experiments, all of which contribute to the more profound understanding of the hybrid phenomenon that is prevalent in many robotic systems nowadays. In particular, we propose an analytical formulation that simplifies the dynamic representation of the nonsmooth systems subject to changing constraints. We develop a non-recursive algorithm to predict the collision results from multiple simultaneous impacts, an intricate physical phenomenon that leads to complex nonsmooth behaviors. The proposed formulation and algorithm are subsequently implemented as a simulation program, where we lay down key implementation details to address numerical-specific challenges. We demonstrate the utility of the program by simulating classic nonsmooth behaviors, including legged locomotion. To study nonsmooth systems experiment-4 ally, we design and build two physical robots: a single-leg hopping robot and a quadruped named TorQ, a modular, direct-drive robot built with simplicity in structure and form, robustness to handle dynamic interaction, and versatility to be reconfigured. These robots display intermittent nonsmooth dynamics resulting from impact and contact at a single or multiple locations, making them excellent examples to be studied under the nonsmooth framework proposed in this thesis. Motivated by this fact, we first detail the system design and hardware implementation of these robots. We then conduct a series of experiments on these robots, controlled by a torque-based method to achieve dynamic locomotion. The results collected from the experiments are further analyzed and discussed. The thesis is completed with an outline of planned work in the future. Figure