Extensions of the Principal Fiber Bundle Model for Locomoting Robots

Our goal is to establish a rigorous formulation for modeling the locomotion of a broad class of robotic systems. Recent research has identified a number of systems with the structure of a principal fiber bundle. This framework has led to a number of tools for analysis and motion planning applicable to various robotic configurations in different environments, but it also requires a number of assumptions that limit its usefulness to certain \idealized" systems. Systems that cannot be fully described with a principal fiber bundle or cannot make full use of the subsequent tools include those whose joints are not fully controllable, those with control inputs or dynamics external to their mechanism, and those whose external configurations do not form
a symmetry group. In addition, the motion planning techniques derived from this structure have traditionally assumed a mapping from internal joint configurations to
external position configurations. The reverse of this mapping will be discussed in this thesis, as well as the analysis and solutions for problems violating each of the above
assumptions in turn. For each case, we introduce one or two motivating examples of robotic systems and discuss novel locomotive characteristics that do not previously
appear under the standard assumptions. This thesis expands the applicability of the principal fiber bundle model, as well as derivative tools for analysis and motion
planning, to a larger variety of locomoting systems.