Abstmct-A Hyper-Flexible Manipulator (HFM, for short) is a kind of continuum robots with a simple mechanical structure like a cable, rope and string, which are useful tools utilised everywhere in various forms. In this paper, in order to achieve dexterous and useful manipulation hy this type of robot, we discuss kinematics and dynamics of an HFM. We rigorously derive a spatial, nonlinear and continuum dynamics model with an underactuated mechanism using special kinematics based on curve geometry and t h a ory of robot manipulation.
This paper provides a theoretical framework for controlling a manipulator with hyper degrees of freedom (HDOF). An HDOF manipulator has the capability to achieve various kinds of tasks. To make full use of its capability, shape control is proposed here; that is, not only the tip of a manipulator, but also its whole body is controlled. To formulate control objectives for shape control, we define a shape correspondence between an HDOF manipulator and a spatial curve that prescribes a desired shape. The shape correspondence is defined by using solutions of a nonlinear optimization problem termed the shape-inverse problem. We give theorems on the existence of the solutions, and on an existence region that allows us to convert shape-control problems into more tractable ones. A shape-regulation control problem is considered first to bring an HDOF manipulator onto a given time-invariant curve. The idea of estimating the desired curve parameters is the crucial key to solving the problem by Lyapunov design. The derived shape-regulation law includes the estimator, which infers the desired curve parameters corresponding to the desired joint positions on the curve. The idea of the desired curve-parameter estimation is also effective for shape tracking where a time-varying curve is used for prescribing a moving desired shape. Considering an estimator with second-order dynamics enables us to find two shape-tracking control laws by utilizing conventional tracking methods in manipulator control. We show the simulation results of applying the derived shape-tracking control laws to a 20-DOF manipulator.
The Shape Jacobian which is the counterpart of the manipulator Jacobian plays a key role to control the shape of a manipulator with extraordinarily many degrees of freedom. In this paper, we show some significant properties of the Shape Jacobian; the structure, boundedness, determinant and singularity, in geometric pavor.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.