Nanometer Precision With a Planar Parallel Continuum Robot

Abstract

In many cases, soft and continuum robots represent an interesting alternative to articulated robots because they have the advantages of miniaturization capability, safer interactions with humans and often simpler fabricating and integration. However, these benefits are usually considered to arise at the expense of accuracy and precision because of the soft or flexible limbs. This paper demonstrates that, with a proper design, a planar parallel continuum robot is capable of great precision. Indeed, the proposed 3-Degrees-of-Freedom planar parallel continuum robot exhibits a precision of 9.13 nm in position and 1.2 µrad in orientation. In addition, the novel robotic design leverages the effect of the actuators' defects, making the robot more precise than its own actuators. Finally, the workspace of the proposed robot (62.3 mm 2 , 0.6452 rad) is significantly larger than most compliant mechanisms, which is particularly interesting when both very high precision and relatively large displacements are required.

Robust Phase-Based Decoding for Absolute (X, Y, Θ) Positioning by Vision

“…This measurement method has already been used in our laboratory to control the planar displacements of a serial robot in the frame of an automatized assembly task. The method is readily applicable to the characterization of , , Θ manipulators, either at a calibration stage or when used within visual servoing loops [14]. This characterization function is important, especially at the micro-scale where stage sensors are not representative of the actual position of the end-effector of the robot.…”

“…On the other hand, over the last decades computer vision emerged as a very convenient way to control multi degrees of freedom positions and displacements at different size scales. The combination of computer vision with optical microscopy allows accuracy to enter the sub-micrometer range and constitutes a relevant alternative to interferometers in a proportion of applications [10]- [14]. A major advantage of computer vision is to be intrinsically contactless and accuracies in the nanometer range can be demonstrated for in-plane ( , , ) positioning [15], [16].…”

On the Mathematical Modeling of Slender Biomedical Continuum Robots

“…Solutions can then be provided by numerical codes which automatically determine the degrees of freedom used to approximate the function for each discrete value of . For continuum robots these methods have been demonstrated via collocation ( Webster and Rucker, 2009 ) and shooting methods ( Till et al, 2015 ; Mauzé et al, 2020 ) using numerical tools that approximate via piecewise polynomials. It has also been shown recently that the dynamics problem for a wide variety of architectures based on single or multiple Cosserat rod sub-models can be cast as a shooting problem on an ODE once the time derivatives have been discretized using finite differences ( Till et al, 2019 ).…”

Micrometer Positioning Accuracy With a Planar Parallel Continuum Robot

“…Due to the coupling between the rods, there is no analytical solution of those equations considering the previous boundary and equilibrium conditions, thus, a numeral resolution is performed using a shooting method. This shooting method is based on a optimization problem where Eqs 2, 4 constitute its residual vector (Till and Rucker, 2017;Mauzé et al, 2020).…”

“…The first one consists in using a repeatable PCR. The robot recently introduced in (Mauzé et al, 2020) was able to provide an outstanding repeatability of 9.13 nm in position and 1.2 µrad in orientation. Choosing a planar architecture allows using a very resolute and long range multidimensional measurement system which facilitates the understating of the proposed methodology.…”