Modeling, Control, and Motion Analysis of a Class of Extensible Continuum Manipulators

In this dissertation, the development of a kinematic model, a configuration-space controller, a master-slave teleoperation controller, along with the analysis of the self-motion properties for redundant, extensible, continuous backbone (continuum) “trunk and tentacle” manipulators are detailed. Unlike conventional rigid-link robots, continuum manipulators are robots that can bend at any point along their backbone, resulting in new and unique modeling and control issues. Taken together, these chapters represent one of the first efforts towards devising model-based controllers of such robots, as well as characterizing their self-motion in its simplest form.;Chapter 2 describes the development of a convenient set of generalized, spatial forward kinematics for extensible continuum manipulators based on the robot's measurable variables. This development, takes advantage of the standard constant curvature assumption made for such manipulators and is simpler and more intuitive than the existing kinematic derivations which utilize a pseudo-rigid link manipulator.;In Chapter 3, a new control strategy for continuum robots is presented. Control of this emerging new class of robots has proved difficult due to the inherent complexity of their dynamics. Using a recently established full Lagrangian dynamic model, a new nonlinear model-based control strategy (sliding-mode control) for continuum robots is introduced. Simulation results are illustrated using the dynamic model of a three-section, six Degree-of-Freedom, planar continuum robot and an experiment was conducted on the OctArm 9 Degree-of-Freedom continuum manipulator. In both the simulation and experiment, the results of the sliding-mode controller were found to be significantly better than a standard inverse-dynamics PD controller.;In Chapter 4, the nature of continuum manipulator self-motion is studied. While use of the redundant continuum manipulator self-motion property (configuration changes which leave the end-effector location fixed) has been proposed, the nature of their null-spaces has not previously been explored. The manipulator related resolved-motion rate inverse kinematics which are based on the forward kinematics described in Chapter 2, are used. Based on these derivations, the self-motion of a 2-section, extensible redundant continuum manipulator in planar and spatial situations (generalizable to n-sections) is analyzed. The existence of a single self-motion manifold underlying the structures is proven, and simple self-motion cases spanning the null-space are introduced. The results of this analysis allow for a better understanding of general continuum robot self-motions and relate their underlying structure to real world examples and applications. The results are supported by experimental validation of the self-motion properties on the 9 Degree-of-Freedom OctArm continuum manipulator.;In Chapter 5, teleoperation control of a kinematically redundant, continuum slave robot by a non-redundant, rigid-link master system is described. This problem is novel because the self-motion of the redundant robot can be utilized to achieve secondary control objectives while allowing the user to only control the tip of the slave system. To that end, feedback linearizing controllers are proposed for both the master and slave systems, whose effectiveness is demonstrated using numerical simulations and experimental results (using the 9 Degree-of-Freedom OctArm continuum manipulator as the slave system) for trajectory tracking as well as singularity avoidance subtask.