Dynamics of highly elastic mechanisms using the generalized multiple shooting method: Simulations and experiments

Lan, Chao-Chieh; Lee, Kok Meng; Liou, Jian Hao

doi:10.1016/j.mechmachtheory.2009.06.006

Cited by 10 publications

(3 citation statements)

References 30 publications

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“…This creates a continuous ordinary differential equation (ODE) in the spatial dimension and a boundary value problem (BVP) that we can solve using any numerical integration scheme in the spatial dimension and a shooting method to obtain the solution for the rod/robot state at each timestep. Variants of this approach have been explored in Gatti-Bono and Perkins (2002) and Lan and Lee (2006); Lan et al (2009) for planar dynamics of fly-fishing lines and compliant mechanisms, but not rods or continuum robots in three dimensions. It is a commonly held view that Cosserat-rod-based models for continuum and soft robots are overly complex and too costly for real-time implementation.…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Till

Aloi

Rucker

2019

The International Journal of Robotics Research

228

185

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The dynamic equations of many continuum and soft robot designs can be succinctly formulated as a set of partial differential equations (PDEs) based on classical Cosserat rod theory, which includes bending, torsion, shear, and extension. In this work we present a numerical approach for forward dynamics simulation of Cosserat-based robot models in real time. The approach implicitly discretizes the time derivatives in the PDEs and then solves the resulting ordinary differential equation (ODE) boundary value problem (BVP) in arc length at each timestep. We show that this strategy can encompass a wide variety of robot models and numerical schemes in both time and space, with minimal symbolic manipulation required. Computational efficiency is gained owing to the stability of implicit methods at large timesteps, and implementation is relatively simple, which we demonstrate by providing a short MATLAB-coded example. We investigate and quantify the tradeoffs associated with several numerical subroutines, and we validate accuracy compared with dynamic rod data gathered with a high-speed camera system. To demonstrate the method’s application to continuum and soft robots, we derive several Cosserat-based dynamic models for robots using various actuation schemes (extensible rods, tendons, and fluidic chambers) and apply our approach to achieve real-time simulation in each case, with additional experimental validation on a tendon robot. Results show that these models capture several important phenomena, such as stability transitions and the effect of a compressible working fluid.

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Section: Introductionmentioning

confidence: 99%

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Till

Aloi

Rucker

2019

The International Journal of Robotics Research

228

185

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show abstract

“…As instance, the Pseudo-Rigid Body (PRB) models introduce lumped springs and rigid bodies in order to recur to the existing theory of rigid body mechanisms, [6,7,8]. Other papers are focused on the well-established FEA theory, [9,10], while some authors recurred to other techniques as the generalized multiple shooting method (GMSM) in which dynamic equations with joint boundary conditions are derived by using Hamilton's principle and are solved by treating a boundary value problem as an initial value problem, [11]. In [12] the authors used Hamilton's principle combined with Newmark scheme to describe the dynamic model of a cantilever, which accounts for bending, shear and axial deformations with no geometric approximation.…”

Section: Introductionmentioning

confidence: 99%

Coupled fluid-dynamical and structural analysis of a mono-axial mems accelerometer

Cammarata¹,

Petrone²

2013

The International Journal of Multiphysics

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“…For example, the mechanism with an additional eccentric link between coupler and crank pin was considered in [12]; the authors pointed out that under the same operational condition, the model that they proposed had higher output torque than that of the conventional mechanism. In [13], the dynamics of elastic mechanisms with different boundary conditions by the use of shooting method was studied; it showed that the accuracy of the model was determined by the order of space marching schemes.…”

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confidence: 99%