Modal kinematics for multisection continuum arms

Abstract

This paper presents a novel spatial kinematic model for multisection continuum arms based on mode shape functions (MSF). Modal methods have been used in many disciplines from finite element methods to structural analysis to approximate complex and nonlinear parametric variations with simple mathematical functions. Given certain constraints and required accuracy, this helps to simplify complex phenomena with numerically efficient implementations leading to fast computations. A successful application of the modal approximation techniques to develop a new modal kinematic model for general variable length multisection continuum arms is discussed. The proposed method solves the limitations associated with previous models and introduces a new approach for readily deriving exact, singularity-free and unique MSF's that simplifies the approach and avoids mode switching. The model is able to simulate spatial bending as well as straight arm motions (i.e., pure elongation/contraction), and introduces inverse position and orientation kinematics for multisection continuum arms. A kinematic decoupling feature, splitting position and orientation inverse kinematics is introduced. This type of decoupling has not been presented for these types of robotic arms before. The model also carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics and impose actuator mechanical limitations onto the kinematics thus generating fully realizable results. The proposed method is easily applicable to a broad spectrum of continuum arm designs.

A novel continuum robotic cable aimed at applications in space

“…There are an infinite number of solutions to the system defined in (11) and (12). Therefore, we empirically determine the relationship between the curve shape variables and the modeled lengths.…”

“…Therefore, we empirically determine the relationship between the curve shape variables and the modeled lengths. Knowing that curve parameters are functions of observed length variables, the mapping given by (11) and (12) can be described by functions of observed length changes as (13) whereq j = l j1 ,l j2 ,l j3 T ∈ R 3 is the observed length change vector of the jth section and f ji is the functional relevant functional mapping. Because the shape parameters can be empirically computed, mappings can be derived for the modeled lengths.…”

“…[9] Many other continuum arms have been inspired by its design. [11][12][13][14][15] However, the profiles of Octarm and other similar robots are quite large, thus resulting in limited penetration in congested spaces.…”

Dual Quaternion based modal kinematics for multisection continuum arms

“…Note that the DQ for a general continuum section, given by (4) and (5)) can be utilized for any continuum section (with varying mechanical parameters such as L 0 and r) simply by substituting these values in the computation of curve parameters (λ i , φ i and θ i listed in [15]). Because of the numerical instabilities associated with the CP kinematics, as detailed in [15], [21], both (4) and (5) suffer from the same numerical problems found in (1) yielding undefined and incorrect solutions within singular neighborhoods. To circumvent these problems, we derive MSF's for each DQ element derived in (4) and (5) as described in [15].…”

Research on Stiffness of Multibackbone Continuum Robot Based on Screw Theory and Euler-Bernoulli Beam

“…Continuum robot does not have its own joints, which can produce flexible deformation in any part, so it has a strong ability to avoid obstacles and better adapt to the complex unstructured environments. Continuum robots offer a number of potential advantages over the traditional rigid-link robots in applications involving disaster relief [1], industrial applications [2], and medical aid [3].…”