Elastic Stability of Cosserat Rods and Parallel Continuum Robots

Till, John; Rucker, D. Caleb

doi:10.1109/tro.2017.2664879

Cited by 86 publications

(66 citation statements)

References 35 publications

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“…Even for tasks where desired task accelerations are slow compared with robot dynamics, dynamic models are sometimes valuable. In some robots, elastic instability due to robot structure (Webster et al, 2009) or loading conditions (Till and Rucker, 2017b) can result in a sudden, dynamic movement of the robot even when actuator commands are slowly changing. Further, discontinuous changes in loading associated with tasks such as cutting, grabbing, and releasing objects may result in dynamic motion even for robots that behave quasi-statically in free space.…”

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

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255

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

Self Cite

255

185

View full text Add to dashboard Cite

show abstract

“…It is also possible to modify the existing operators, e.g. multiplication, to incorporate a normalizing term to deal with a non-unit quaternion, as in (Tunay 2013;Till and Rucker 2017;Rucker 2018). We use the former in this paper and implemented in the software package.…”

Section: Resultsmentioning

confidence: 99%

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

Sadati

Naghibi

Shiva

et al. 2020

The International Journal of Robotics Research

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A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

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“…21 This method is mathematically concise and minimally affected by discretization issues compared with the lumped-parameter and finite element approaches. 23 In this paper, an optimal control method based on the principle of minimal total potential energy is utilized to solve the improved Kirchhoff rod model.…”

Section: Optimal Control Methodsmentioning

confidence: 99%

A hybrid continuum robot based on pneumatic muscles with embedded elastic rods

Sun

Chen

Liu

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Continuum robots have attracted increasing attention in recent years due to their intrinsic compliance and safety. Nevertheless, the use of structure compliance may lead to reduction of stiffness and positioning precision. This paper presents a novel design of a hybrid continuum robot whose actuators are composed of pneumatic muscles and embedded elastic rods. Such robot can switch drive modes between large-scale movement and fine adjustment of position by employing a locking mechanism to change its stiffness. A three-dimensional static model of the robot is presented using an improved Kirchhoff rod theory, where elastic deformation of the robot is accounted for from an optimal control point of view via minimal total potential energy principle. Experiments were carried out to validate the static model and to test the stiffness and precision of the robot. This work provides a possible way to strengthen the control precision of a continuum robot with compliant structure.

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Elastic Stability of Cosserat Rods and Parallel Continuum Robots

Cited by 86 publications

References 35 publications

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

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

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

A hybrid continuum robot based on pneumatic muscles with embedded elastic rods

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