The goal of this research is to develop fundamental control theory, dynamic modeling, and control technology for extensible continuum robotic manipulators. These systems often resemble snakes, tentacles, or elephant trunks that are able to bend at any point along their backbone, making modeling and control difficult. Current literature contains partial realizations of these goals but have yet to see advances that allow for extensive application of continuum manipulators. The pursuit of these goals will require the application of linear and nonlinear control techniques, Lagrangian mechanics, state estimation techniques, and system feedback manipulation. Achieving these goals will open the door for reliable control of continuum manipulators and permit Space and exploration applications such as whole-arm grasping, sample manipulation, and crevasse exploration.