Coil function control problem for a hyperredundant robot

Abstract

The paper focuses on the control problem of a hyperredundant robot that performs the coil function of grasping. First, the dynamic model of a hyperredundant arm with continuum elements produced by flexible composite materials in conjunction with active-controllable electrorheological fluids is analyzed. Secondly, both problems, i.e. the position control and the force control are approached. The difficulties determined by the complexity of the non-linear integral-differential equations are avoided by using a basic energy relationship of this system. Energy-based control laws are introduced for the position control problem. A force control method is proposed, namely the DSMC method in which the evolution of the system on the switching line by the ER fluid viscosity is controlled. Numerical simulations are also presented.

Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review

“…Integral Representation. While differential curve representations other than F-S are possible (see, e.g., Bishop (1975)), another approach given in Chirikjian and Burdick (1994) is the integral representation of a curve, also used in the dynamics formulation of Ivanescu et al (2007). This integral formulation avoids difficulties which arise in the F-S formulas when ¼ 0 and avoids the necessity of solving a differential equation to extract the curve, given arc length parameterized curvature and torsion functions.…”

“…A particularly challenging emerging area of research involves deriving and practically applying dynamic models of continuum robots in a numerically stable form amenable to real-time implementation. The dynamic equations of continuum robots under various assumptions have been derived in the planar case (Gravagne et al 2003;Tatlicioglu et al 2007) and derivations based on an energy-work relationship (Ivanescu et al 2007), conservation laws (Chirikjian 1995), and a Newtonian formulation of Cosserat rods (Trivedi et al 2008a) exist. We note that some of the earliest, yet most advanced work in terms of practical implementation is that of Chirikjian (1995), where a variable geometry truss provided a means of computing planar continuum robot dynamics rapidly.…”

“…To accurately define the pose of points of interest on the robot (including its end-effector), one must characterize forces and moments applied to the robot by both its own actuators and the external environment. The most general models available for this (see, e.g., Ivanescu et al (2007), Gravagne et al (2003), Trivedi et al (2008a), Rucker et al (2010a), Rucker et al (2010b), Dupont et al (2010), Chirikjian (1995), and Jones et al (2009)) do not do so in closed form. Instead, they are evaluated numerically to compute statics or dynamics in lieu of forward kinematics.…”

Soft Robots Modeling: A Structured Overview

“…In one other work by the same authors [7], variational approaches are presented in order to compute the optimal curve shapes that comply with both joint and task constraints. The same kinematic model was also employed in [96] and extended to the dynamical modeling of coiling continuum robots. Another possible function that can be used to represent the robot geometry consists in the pythagorean hodograph curves [97].…”