Dynamics for variable length multisection continuum arms

Abstract

Variable length multisection continuum arms are a class of continuum robotic manipulators that generate motion by structural mechanical deformation. Unlike most continuum robots, the sections of these arms do not have (central) supporting flexible backbone, and are actuated by multiple variable length actuators. Because of the constraining nature of actuators, the continuum sections can bend and/or elongate (compress) depending on the elongation/contraction characteristics of the actuators being used. Continuum arms have a number of distinctive differences with respect to traditional rigid arms namely: smooth bending, high inherent compliance, and adaptive whole arm grasping. However, due to numerical instability and the complexity of curve parametric models, there are no spatial dynamic models for multisection continuum arms. This paper introduces novel spatial dynamics and applies these to variable length multisection continuum arms with any number of sections. An efficient recursive computational scheme for deriving the equations of motion is presented. This is applied in a general form based on structurally accurate and numerically well posed modal kinematics that assumes circular arc deformation of continuum sections without torsion. It is shown that the proposed modal dynamics are highly scalable, producing efficient and accurate numerical results. The spatial dynamic simulation results are experimentally validated using a pneumatic muscle actuated multisection prototype continuum arm. For the first time this enables investigation of spatial dynamic effects in this class of continuum arms.

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz–Galerkin Methods

“…due to structure swallow. Similar design is used in recent research [5], [6], [17]. The measured and identified structural parameters are presented in Table I with an experimental setup similar to the one in [14], [15] (Fig.…”

“…Based on the experimental observations, a modified Lagrange polynomial, as a differentiable polynomial of finite order, is chosen to drive a weak-form series-solution for the mechanics of a continuum manipulator using continues Ritz and Ritz-Galerkin methods. To the best of our knowledge and compared to the most recent similar research in the field [17], this is the first time that the infinite modeling state space of such problem minimizes to the geometrical positions of two points at the tip and in the middle of the manipulator. As a result, different dynamic impedance and configuration control scenarios are formulated using traditional nonlinear control theories in a unified and easy to implement vector formalism.…”

“…3) Continuum form of Lagrange dynamics [8], [13] or the Principle of Virtual Work (PVW) [14], [15] using CC, continuous VC or series-solutions as kinematic maps, where the kinematic map parameters are the dynamic model states. 4) Cosserat rod model [6], [16] and beam theory method, as a simplified version of that [9], which result in a boundary value problem (BVP) to be solved using numerical optimization methods [6], [17]. 5) approximate identification based series-solutions where coefficients of a simple [18] or complex [19] series are identified using experimental results to construct a hardware-specific model.…”

Center-of-Gravity-Based Approach for Modeling Dynamics of Multisection Continuum Arms

“…1a. Beyond our prior work reported in [37], [42], [41], the proposed dynamic model; (1) accommodates variable-length multisection continuum arms with arbitrary number of sections and a wide range of length and radii combinations, (2) considers both linear and angular kinetic energies of the continuum arm at the CoG for better system energy accuracy, (3) achieves energy matching via a series of energy shaping coefficients that are constant for any variable-length multisection continuum arms, (4) employs the results from [37] to systematically derive the EoM terms recursively, (5) demonstrates O n 2 complexity for the first time for a dynamic model based on continuous (non-discretized) deformation representation, and for a threesection continuum arm, (6) runs at 9.5 kHz (step execution rate), and (7) achieves sub real-time dynamic simulation in Matlab Simulink environment. Therefore the proposed model unifies the ideas of lumped parametric approaches of discrete rigid-bodied robotics and continuous (integral) approaches of continuum robotics and is expected to lay a strong numerical and algorithmic foundation for implementing dynamic control schemes.…”

“…In this work, we extend and generalize our CoG-based spatial dynamic model derived for a single continuum section [42], evaluate against the integral dynamics proposed in [37] to verify the numerical accuracy and computational efficiency, and validate the model against spatial dynamic responses of the prototype arm shown in Fig. 1a.…”