Shape Control of Manipulators with Hyper Degrees of Freedom

Abstract

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.

Dimensionality Reduction in Controlling Articulated Snake Robot for Endoscopy Under Dynamic Active Constraints

“…The center of joint i is adjusted to lie on the centerline at point . By implementing the shape-inverse approach that is proposed in [3], we can obtain the robot configuration closest to the centerline. The angular joint limits are also considered so that the joint space solution will not exceed the range ±q max .…”

“…As shown in Fig. 3(b), j v i=1…4 ∈ ℜ 3×1 are the four vertices of the section arranged in a particular order as follows: (3) where the caret ^ denotes that the vector is normalized with respect to its length. As shown in Fig.…”

“…Given the amount of input motion and the mass of each robot link, the required torque can be computed using inverse dynamics. The kinematics simplicity, e.g., each joint consists of two rotational axes perpendicular to each other with no offset, implies simple formulation of robot dynamics, thus yielding a closed form of inverse dynamics, as reported in [3].…”

“…Hence, the rigid robot links are connected by universal joints, each providing two-degree-offreedom (DoF) rotational movement within ±q max = ±45°. Independent actuation of each provides typical hyper-redundant kinematic structure [3]. Furthermore, the robot uses a modular hybrid micromotor-tendon joint design that allows for the integration of multiple internal instrument channels [4].…”

Distributed Control of the Center of Mass of a Modular Robot

“…With hyperredundant kinematic chains [1][2][3][4] the focus is on solving the inverse kinematics or tracking a reference shape with a robot. Solutions to these problems are computed in a centralized way.…”