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\u27 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\u27s 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

A hyper-redundant manipulator

“Hyper-redundant” manipulators have a very large number of actuatable degrees of freedom. The benefits of hyper-redundant robots include the ability to avoid obstacles, increased robustness with respect to mechanical failure, and the ability to perform new forms of robot locomotion and grasping. The authors examine hyper-redundant manipulator design criteria and the physical implementation of one particular design: a variable geometry truss

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry-truss manipulator (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. A solution is presented to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm was developed primarily for variable-geometry-truss manipulators, it is general enough for application to a number of manipulator designs

Kinematic Analysis of a Flexible Tensegrity Robot

Conference Paper presented at The Joint International Conference of the XII International Conference on Mechanisms and Mechanical Transmissions (MTM) and the XXIII International Conference on Robotics (Robotics ’16)In the field of parallel kinematics few designs use highly deformable elements to obtain the end effector movement. Most compliant mechanisms rely on notches or shape changes to simulate a standard kinematic joint. In this work a kinematic model of a simple parallel continuum mechanism that combines a deformable element and cable is presented. The kinematic model is used to study the workspace of the manipulator and is validated by experimental measurements of a prototype.The authors wish to acknowledge the financial support received from the Spanish Government through the Ministerio de Economía y Competitividad (Project DPI2015-64450-R) and the Regional Government of the Basque Country through the Departamento de Educación, Universidades e Investigación (Project IT445-10) and UPV/EHU under program UFI 11/29