R-FLEX: Ultra-Dense Fiber-Positioning Robots

• R-FLEX is a class of high-precision fiber-positioning mechanisms designed for ultra-dense multi-object spectrographs using both concentric-tube and flexure-based approaches.
• It achieves large patrol radii with minimized telecentric error and repeatable micron-level positioning through innovative actuation and mechanical design.
• The technology supports scalability to 30,000+ units, ensuring low optical degradation and high manufacturability for next-generation spectroscopic facilities.

R-FLEX denotes a class of compact fiber-positioning concepts developed for massively multiplexed astronomical spectroscopy. In the focal-plane architecture described as FLEX in “High multiplex and precision: the design and development of FLEX, a grid-based fiber positioner with large patrol radius and minimized telecentric error,” the prompt’s R-FLEX corresponds to a grid-based positioner intended for facilities such as the Wide-Field Spectroscopic Telescope (WST), where tens of thousands of fibers must be packed onto a curved focal surface while preserving patrol reach, telecentricity, and optical throughput (Omadutt et al., 19 Jun 2026). The same designation also appears explicitly in “Design and performance of ‘R-FLEX’, a flexure-based fiber positioning robot for spectroscopic cosmology,” where it denotes a flexure-based radial fiber-positioning robot optimized for 6.2 mm pitch and large-scale manufacture (Wenner et al., 1 Aug 2025). Together, these usages place R-FLEX within the broader development of ultra-dense, high-precision fiber robotics for next-generation multi-object spectrographs.

1. Nomenclature and technical scope

In the cited literature, the name is used in two closely related but mechanically distinct ways. The first is the FLEX architecture in (Omadutt et al., 19 Jun 2026), which the prompt identifies as R-FLEX. The second is the explicitly named R-FLEX mechanism in (Wenner et al., 1 Aug 2025).

Usage	Description	Representative parameters
FLEX in (Omadutt et al., 19 Jun 2026)	Compact grid-based fiber positioner using three concentric Nitinol tubes	patrol radius up to $\sim 22.5$ mm; telecentric error $< 0.39^\circ$; 30,240 positioners
R-FLEX in (Wenner et al., 1 Aug 2025)	Flexure-based radial fiber-positioning robot for spectroscopic cosmology	6.2 mm pitch; 4 mm travel; repeatable positioning accuracy $\leq 5\ \mu$m

The common technical domain is dense focal-plane robotics for fiber-fed spectroscopy. Both mechanisms respond to the same scaling pressure: future instruments require much higher packing density than earlier systems, while still needing repeatability, low angular error, mechanical durability, and compatibility with deployment at the $\sim 30{,}000$-unit scale.

2. Instrumental context and design objectives

The primary astronomical driver is the next generation of high-multiplex spectroscopic facilities. The FLEX paper frames the problem through the WST requirement of 30,000+ fibers across a 1.4-meter surface, with the further constraint that the focal surface is curved and tightly packed (Omadutt et al., 19 Jun 2026). The architecture is therefore designed to combine a very large patrol area with unusually low telecentric error and a small mechanical footprint, so that many fibers can reach nearby targets without imposing excessive collision complexity.

The paper defines three geometric quantities central to the design. Pitch is the center-to-center spacing between neighboring positioners; patrol radius is the maximum radial reach from a home position; and telecentric error is the angular misalignment between the fiber face and the optical axis. The explicit design criteria are

$R_{\text{patrol}} \ge 2.5\,p$

and

$\theta_{\text{telecentric}} \le 0.5^\circ.$

For the two pitch values discussed in the FLEX design, $p = 6.2$ mm and $p = 6.86$ mm, the target patrol radii are about 15.5 mm and 17.15 mm, while the simulated maximum patrol radius reaches $\sim 22.5$ mm in the mechanical model context (Omadutt et al., 19 Jun 2026). At the patrol limit, the abstract reports a telecentric error of less than $0.39^\circ$, and the performance summary gives approximately $< 0.39^\circ$0 at 6.2 mm pitch and $< 0.39^\circ$1 at 6.86 mm pitch. The comparison table lists FLEX’s maximum telecentric error as $< 0.39^\circ$2, in contrast to a tilting-spine architecture such as Echidna, which exceeds $< 0.39^\circ$3 (Omadutt et al., 19 Jun 2026).

The separately named R-FLEX paper formulates a similar density challenge from the perspective of DESI. DESI uses 5000 robotic fiber positioners at 10.4 mm pitch, and the paper projects that future instruments will require 2.5–3× smaller fiber robots by area (Wenner et al., 1 Aug 2025). Its design goals are correspondingly explicit: 6.2 mm target pitch, 4 mm travel range, $< 0.39^\circ$4m repeatable positioning accuracy, parasitic motion < 30 $< 0.39^\circ$5m, angular misalignment < 0.3°, ~1 million cycles, and ~30,000 units of production scale.

3. Concentric-tube FLEX mechanism

The defining mechanical feature of FLEX is a positioner built from three concentric, laser-cut Nitinol tubes: an outer tube (OT), a middle tube (MT), and an inner tube (IT) (Omadutt et al., 19 Jun 2026). Nitinol is described as a superelastic nickel-titanium alloy, nominally 50.8 at.% Ni, processed so that its austenite finish temperature satisfies

$< 0.39^\circ$6

ensuring superelastic behavior over the operating range. In that regime, the tubes can accommodate up to about 8% recoverable strain through stress-induced martensitic transformation.

The tubes are not simple cylinders. Each layer uses a different laser-cut lattice pattern, optimized by finite element analysis to limit stress concentrations and avoid buckling while keeping peak von Mises stress below the transformation plateau, around $< 0.39^\circ$7 MPa at $< 0.39^\circ$8C (Omadutt et al., 19 Jun 2026). This architecture is central to the optical behavior: the concentric-tube deformation keeps the fiber tip inherently parallel to its base as the structure deflects.

That feature differentiates FLEX from traditional tilting-spine positioners. In a tilting spine, the shaft rotates, so the fiber face tilts relative to the focal surface and telescope pupil, producing both defocus and telecentric error. FLEX instead generates radial reach while preserving near-parallel tip orientation, so the fiber remains much better aligned with the optical axis (Omadutt et al., 19 Jun 2026). The low telecentric error is therefore not incidental but a consequence of the nested-tube kinematics.

Fiber routing is equally important. Because the interior of the concentric-tube assembly is hollow, the fiber can run freely along the positioner axis rather than undergoing tight bends. The paper explicitly states that this free internal passage reduces focal ratio degradation risk and protects the fiber bundle during repeated patrol motions, especially near the outer edge of the patrol field (Omadutt et al., 19 Jun 2026). In this design, mechanical reach and optical preservation are co-designed rather than treated as separate subsystems.

4. Actuation, control, and structural verification

FLEX uses three piezoelectric stick-slip motors in a compact, single-plane push-pull configuration, providing tip, tilt, and piston (focus) degrees of freedom (Omadutt et al., 19 Jun 2026). The control strategy is coarse/fine: high voltage produces larger steps for rapid acquisition, then reduced voltage and controlled frequency provide fine positioning with micron-level adjustment. The drive signal is a sawtooth waveform, with a slow voltage ramp during stick and a rapid drop during slip.

The actuator parameters reported are a 0–24 V operating range, 0.3 $< 0.39^\circ$9m minimum step size, 2.5 N maximum force output, and an envelope of $\leq 5\ \mu$0 mm by 67 mm length (Omadutt et al., 19 Jun 2026). Simulation-derived force requirements are lower, about 1.17 N at 6.2 mm pitch and 1.32 N at 6.86 mm pitch, so the specified force provides roughly a factor-of-two safety margin.

Finite element analysis is used to validate the mechanism. Under a simulated 0.4 mm axial differential stroke, the structure reaches large patrol radii while remaining below the transformation stress plateau. Peak equivalent stresses at maximum actuation are 360.9 MPa in the OT, 355.9 MPa in the MT, and 311.2 MPa in the IT for the full-stroke model. The pitch-specific stress table gives 258.14/252.71/229.85 MPa at 6.2 mm pitch and 283.94/279.10/250.59 MPa at 6.86 mm pitch (Omadutt et al., 19 Jun 2026).

Fatigue is assessed using the Pelton superelastic fatigue framework with mean strain and strain amplitude

$\leq 5\ \mu$1

The design points fall within the conservative $\leq 5\ \mu$2-cycle limit, with fatigue margins of $\leq 5\ \mu$3 at 6.2 mm pitch and $\leq 5\ \mu$4 at 6.86 mm pitch. Since WST requires more than 500,000 reconfiguration cycles, the simulated lifetime margin is reported as comfortably sufficient (Omadutt et al., 19 Jun 2026).

5. Focal-surface architecture and multiplexing strategy

FLEX is not only a single-positioner concept but also a full focal-surface tiling architecture. The proposed layout uses 90 identical curvilinear modules arranged in a modified triskele-like geometry around a central integral-field-spectrograph pickoff mirror (Omadutt et al., 19 Jun 2026). The full system contains 30,240 positioners across a 2-degree hexagonal field of view, with a focal-surface diameter of 1406.2 mm and a central cutout diameter of 184.4 mm.

The field is broken into trients, each containing 26 right-handed and 4 left-handed modules, so that the modules remain mostly identical while accommodating the central obstruction. Only 3 support struts are required, obscuring just 0.8% of the field of view, and the large patrol radius allows full positioner coverage even across those struts (Omadutt et al., 19 Jun 2026). The module geometry is slightly tapered, with width tapering by 0.7%, and irregularities at the struts are reported as $\leq 5\ \mu$5m, small enough to fit within the $\leq 5\ \mu$6 mm strut width.

Fiber allocation is stratified by spectral resolution. One in 16 positioners is designated for high-resolution spectroscopy, while the remainder feed three low-resolution spectrograph sets. The resulting counts are 1,890 HR fibers and 28,350 LR fibers, for 30,240 total (Omadutt et al., 19 Jun 2026). Each module is 4 rows wide and 84 positioners long, giving 336 fibers per module. The paper reports 99.17% HR internal coverage, and states that all four spectrograph sets achieve virtually full coverage of the field. The LR fibers are grouped into slitlets for three spectrographs, which the paper emphasizes as a way to sort targets by magnitude into spectrographs, reducing cross-talk and improving packing efficiency.

6. The separate flexure-based R-FLEX robot

A distinct but related development appears in “Design and performance of ‘R-FLEX’, a flexure-based fiber positioning robot for spectroscopic cosmology” (Wenner et al., 1 Aug 2025). Here, R-FLEX is a flexure-based radial fiber-positioning robot rather than a concentric-tube grid positioner. Its purpose is to provide precision radial motion for fiber robots mountable at 6.2 mm pitch, while keeping the mechanism inside a package of about $\leq 5\ \mu$7 mm and allowing the travel to extend outside that envelope.

The mechanism converts small rotational motion at the base into larger linear radial motion at the fiber end. It uses a $\leq 5\ \mu$8 mm brushless DC gearmotor, a roller cam, a drive spool / cam system, a 19 mm arm, a 60 mm parallel-arm flexure, and pairs of symmetric thin leaf flexures at the arm ends (Wenner et al., 1 Aug 2025). The paper describes the resulting kinematics as backlash-free and polar, with a slim package and low part count.

Its development workflow proceeded through four phases: kinematic and stress calculations in a spreadsheet, conversion to a Python parameter sweep with 100,000 iterations, selection of the best design with confirmation by finite element analysis, and prototype fabrication and testing (Wenner et al., 1 Aug 2025). Candidate materials included Ti 6Al-4V, 17-7PH (TH1050), 7075-T6, and BeCu C17200 (TH04); titanium was selected because of its high fatigue-strength-to-elastic-modulus ratio and because it does not require heat treatment. Fabrication used wire EDM, with remaining parts from commercial procurement or traditional CNC machining.

The paper gives the position-calibration relation

$\leq 5\ \mu$9

with fitted values $\sim 30{,}000$0 mm, $\sim 30{,}000$1, and $\sim 30{,}000$2 mm (Wenner et al., 1 Aug 2025). Testing used optical CMM measurements for tip, tilt, and focus; a custom optical-centroiding station for blind and correction moves; and high-speed video for natural frequency measurement. The reported measured performance includes 4.2 $\sim 30{,}000$3m rms $\sim 30{,}000$4-$\sim 30{,}000$5 error, 37.3 Hz natural frequency, 0.020° $\sim 30{,}000$6 angular error, 0.086° $\sim 30{,}000$7 angular error, 50 $\sim 30{,}000$8m defocus, and 4.171 mm travel range (Wenner et al., 1 Aug 2025). The assembly met the $\sim 30{,}000$9m rms requirement in extension-direction operation and in high-speed retraction, while larger errors during slow retraction were attributed to asymmetries in static friction.

7. Significance and technical distinctions

The significance of R-FLEX, in the sense used for the FLEX architecture, lies in the combination of very high target density, large patrol area, low telecentric error, active focus control, and scalable manufacturing within a single focal-plane concept (Omadutt et al., 19 Jun 2026). Its optical alignment strategy differs fundamentally from tilting-spine approaches, and its internal fiber routing addresses focal ratio degradation as part of the mechanical design rather than as a downstream packaging issue.

The separately named flexure-based R-FLEX mechanism demonstrates a different route to the same systems problem: dense packing, long travel relative to package size, and manufacturability at the $R_{\text{patrol}} \ge 2.5\,p$0-unit scale (Wenner et al., 1 Aug 2025). The two papers therefore describe distinct mechanisms operating in the same design space. One relies on a superelastic concentric-tube assembly with piezoelectric stick-slip actuation; the other on a motor-driven cam, lever, and parallel-arm flexure chain.

A common misconception would be to treat R-FLEX as a single standardized hardware design. The literature supplied here does not support that reading. Instead, it documents two related astronomical instrumentation concepts sharing the same naming neighborhood: a grid-based, large-patrol FLEX positioner architecture for WST-like facilities, and a flexure-based radial R-FLEX robot for spectroscopic cosmology. What unifies them is not identical mechanism topology, but a common engineering objective: enabling future massively multiplexed spectroscopic instruments to place far more fibers, at far smaller pitch, without surrendering precision, durability, or focal-plane coverage.