OmniSens: A 6-DoF Inertial Isolation Sensor

• OmniSens is a 6-DoF inertial isolation sensing system that uses a softly suspended reference mass combined with a 6-DoF interferometric readout to capture both translational and rotational motion.
• It integrates into active seismic isolation platforms via a multi-scale optimal control framework, reducing platform motion by up to two orders of magnitude near the microseism.
• Its co-optimized design and simplified rotational blending filter establish OmniSens as a benchmark architecture for advanced inertial sensor systems in gravitational wave observatories.

OmniSens is a six-degree-of-freedom inertial isolation sensing system developed in the context of active seismic isolation for the Einstein Telescope (ET). In the formulation reported for ET, it consists of a single softly suspended reference mass from a silica fibre together with a 6-DoF interferometric readout of that test mass, so that one mechanically symmetric inertial reference object senses both translational and rotational motion (Saffarieh et al., 21 Jul 2025). Its significance arises from the fact that low-frequency seismic isolation is strongly limited by tilt-to-translation coupling, especially below a few hertz near the microseism; within the reported multi-scale optimal control framework, OmniSens is evaluated as a sensor architecture that can be co-optimized with feedback and blending filters, and it achieves substantially better low-frequency isolation than the alternative BRS-T360 configuration, with up to two orders of magnitude lower platform motion near the microseism (Saffarieh et al., 21 Jul 2025).

1. Definition and sensing principle

OmniSens is presented as a 6-DoF inertial isolation sensing system built around two defining elements: a softly suspended reference mass from a silica fibre, and a 6-DoF interferometric sensor reading of that test mass (Saffarieh et al., 21 Jul 2025). Rather than separating tilt sensing and translation sensing into different instruments, the design uses one decoupled and symmetric suspended inertial reference object to sense both. In the ET study, this is the principal conceptual distinction between OmniSens and BRS-T360.

Because the suspension is designed to be decoupled and symmetric, the sensor dynamics can be decomposed into two orthogonal 2-dimensional harmonic oscillators, and the reduced model is stated to capture “almost all the complexity of the 6 DoF platform” (Saffarieh et al., 21 Jul 2025). This decomposition is not merely a modeling convenience; it is the basis for computing equivalent inertial sensor noise and for embedding the sensor in the controller synthesis workflow.

The sensing model is derived from the motion of a pendulum-like reference mass relative to its cage or platform. In the simplified derivation, the key transfer functions are

$\frac{x_m}{x_t(s)} = \frac{g}{g + p_l s^2}$

and

$$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$

These relations connect platform motion to the translational and rotational response of the suspended mass and are then used to build the equivalent inertial sensor noise (Saffarieh et al., 21 Jul 2025).

The parameterization reported for the reference-mass model is specific. The paper gives $g = 9.834\,\mathrm{m/s^2}$, pendulum length $p_l = 0.7\,\mathrm{m}$, second part length $p_d = -1.8\times10^{-4}\,\mathrm{m}$, bottom spring coefficient $k_{el_b}=0.019\,\mathrm{kg\,m^2/s^2}$, mass $m=3.8\,\mathrm{kg}$, moment of inertia $I_m=0.95\,\mathrm{kg\,m^2}$, and effective loss angle $\phi_{eff}=10^{-6}$ (Saffarieh et al., 21 Jul 2025). The thermal-noise contribution of the reference mass is modeled through

$$S_{torq}(\omega) = 4K_B T \phi_{eff} k_{el}/\omega,$$

which is quadrature-summed with sensor readout noise to form the effective inertial sensor noise.

A common misunderstanding is to treat OmniSens as a conventional pair of tilt and translation sensors packaged together. The ET formulation does not describe it that way. It is instead a single suspended reference mass with a 6-DoF interferometric readout, intended to exploit mechanical symmetry and to preserve rotational sensitivity down to zero frequency (Saffarieh et al., 21 Jul 2025).

2. Role within the ET active isolation platform

In the ET study, OmniSens is not analyzed in isolation but as part of a standard active isolation table. The platform is modeled as an adapted LIGO HAM-ISI style single-stage active/passive isolation table with a rigid hexagonal aluminum structure and optical bench, passive isolation via blade springs and flexures, and active isolation using six actuators (Saffarieh et al., 21 Jul 2025). The moving mass is $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$0, the payload mass is $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$1, and the total mass with payload is $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$2 (Saffarieh et al., 21 Jul 2025).

The platform dynamics are summarized by

$$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$3

with

$$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$4

The stiffness matrix includes translational and rotational coupling terms derived from the platform geometry and from flexure and blade-spring parameters. The reported parameter set includes $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$5, $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$6, $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$7, blade spring stiffness $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$8, flexure stiffnesses $$\frac{\phi_m}{x_t(s)} = - \frac{s^2 \left(\kappa_{el_b} + p_d g m\right)}{\left(g + p_l s^2\right)\left(I_m s^2 + \kappa_{el_b} + p_d g m\right)}.$$9, and torsional stiffness $g = 9.834\,\mathrm{m/s^2}$0 (Saffarieh et al., 21 Jul 2025).

This platform-level embedding is central to the meaning of OmniSens in the ET literature. The sensor choice determines which frequencies can be effectively controlled, how soon the inertial loop must roll off, and how severely tilt-to-translation coupling contaminates horizontal isolation. OmniSens is therefore treated as a system-level sensing architecture rather than as an interchangeable component.

3. Multi-scale optimal control architecture

The ET paper formulates the design problem as multi-scale optimal control because the feedback controller and the sensor blending filters are nested and frequency-coupled (Saffarieh et al., 21 Jul 2025). The full set of filters is optimized jointly as

$g = 9.834\,\mathrm{m/s^2}$1

where $g = 9.834\,\mathrm{m/s^2}$2 and $g = 9.834\,\mathrm{m/s^2}$3 are the feedback filters for horizontal translation and rotation, and $g = 9.834\,\mathrm{m/s^2}$4 and $g = 9.834\,\mathrm{m/s^2}$5 are blending filters. The blending relation is

$g = 9.834\,\mathrm{m/s^2}$6

The two “scales” are explicitly the outer feedback loop acting on platform motion and the inner blending between inertial sensing and displacement sensing within the controller architecture. Because blending occurs inside the loop, its effect cannot be separated cleanly from controller synthesis; this is why the problem is framed as joint optimization rather than sequential filter design.

The optimization is encoded through a generalized plant

$g = 9.834\,\mathrm{m/s^2}$7

with $g = 9.834\,\mathrm{m/s^2}$8 denoting elementwise multiplication (Saffarieh et al., 21 Jul 2025). The generalized plant includes noise-coloring transfer functions, weighting functions, physical plant transfer functions, and controller/blending blocks. For OmniSens, the relevant noise channels include ground disturbance, displacement-sensor noise, inertial sensing noise, and, in the rotational channel, thermal noise of the suspended reference mass.

This architecture matters because OmniSens is evaluated not by a single open-loop sensitivity curve but by its place in a closed-loop co-design problem. The paper’s emphasis is that sensing, blending, and feedback must be optimized together when the platform exhibits cross-coupling between horizontal and rotational degrees of freedom (Saffarieh et al., 21 Jul 2025).

4. Acausal optimum and sensor-limited performance metrics

The key analytical object in the ET treatment of OmniSens is the “acausal optimum” $g = 9.834\,\mathrm{m/s^2}$9, defined as

$p_l = 0.7\,\mathrm{m}$0

This quantity is described as the best possible noise floor achievable at each frequency if one could perfectly select the smallest contributing noise source there (Saffarieh et al., 21 Jul 2025). It is “acausal” because it is an unattainable ideal, but it provides a benchmark for what the sensor set makes possible.

Its inverse becomes the weighting function,

$p_l = 0.7\,\mathrm{m}$1

which forces the optimizer to emphasize bands where the sensor signal-to-noise ratio is intrinsically favorable and to avoid over-controlling bands in which the sensing architecture is poor (Saffarieh et al., 21 Jul 2025). The paper explicitly interprets $p_l = 0.7\,\mathrm{m}$2 as quantifying sensor SNR across frequencies. Where SNR is high, the inertial readout can be trusted; where SNR drops below 1, loop gain is attenuated and the platform tends toward free-running behavior.

The optimization itself is posed as

$p_l = 0.7\,\mathrm{m}$3

subject to

$p_l = 0.7\,\mathrm{m}$4

The interpretation given in the paper is that the $p_l = 0.7\,\mathrm{m}$5-type objective minimizes RMS residual motion, while the $p_l = 0.7\,\mathrm{m}$6 constraint maintains feasibility relative to a prescribed performance envelope (Saffarieh et al., 21 Jul 2025). This is an important correction to a common simplification: the ET study does not optimize only raw residual platform motion. It optimizes motion relative to the best performance implied by the sensor set.

For the rotational loop, the reported sensitivity function is

$p_l = 0.7\,\mathrm{m}$7

and a simplified weighted closed-loop output is written as

$p_l = 0.7\,\mathrm{m}$8

This expression makes explicit how disturbance noise, displacement-sensor noise, and inertial-sensor noise are combined through blending and loop sensitivity.

5. Comparison with BRS-T360

The ET study compares OmniSens against BRS-T360, a sensing arrangement combining a Beam Rotation Sensor (BRS) for tilt sensing and a T360 seismometer for horizontal translation sensing (Saffarieh et al., 21 Jul 2025). BRS-T360 is treated as a realistic benchmark rather than a strawman: T360 acceleration noise is taken from manufacturer data and converted to amplitude spectral density, and BRS tilt noise is modeled as the quadrature sum of readout noise and thermal flexure noise, with the BRS readout assumed to be upgraded to interferometric readout (Saffarieh et al., 21 Jul 2025).

The principal reported result is that OmniSens significantly outperforms BRS-T360 at low frequency, especially near the microseism, reducing platform motion by at least two orders of magnitude in that region (Saffarieh et al., 21 Jul 2025). The paper attributes this advantage to two properties: sensitivity to inertial rotations down to zero frequency, and lower suspension thermal noise compared with the alternative sensing configuration.

The comparison also appears in the optimized filter sizes:

Configuration	Optimized sizes
OmniSens	$p_l = 0.7\,\mathrm{m}$9; $p_d = -1.8\times10^{-4}\,\mathrm{m}$0; $p_d = -1.8\times10^{-4}\,\mathrm{m}$1; $p_d = -1.8\times10^{-4}\,\mathrm{m}$2; $p_d = -1.8\times10^{-4}\,\mathrm{m}$3
T360+BRS	$p_d = -1.8\times10^{-4}\,\mathrm{m}$4; $p_d = -1.8\times10^{-4}\,\mathrm{m}$5; $p_d = -1.8\times10^{-4}\,\mathrm{m}$6; $p_d = -1.8\times10^{-4}\,\mathrm{m}$7; $p_d = -1.8\times10^{-4}\,\mathrm{m}$8

The significance assigned in the paper is that OmniSens requires a comparatively simpler rotational blending filter, consistent with the claim that its inertial rotational performance is strong enough that the table displacement sensor is less important in that channel (Saffarieh et al., 21 Jul 2025). By contrast, the BRS-T360 configuration requires more filter complexity in the rotational blending path, and a separate SISO optimization of the $p_d = -1.8\times10^{-4}\,\mathrm{m}$9-loop is reported to be less effective than full MIMO optimization when tilt-to-translation coupling is important.

6. Re-optimization, design implications, and broader usage of the label

A major contribution of the ET paper is the optimization workflow built around OmniSens rather than only the sensor result itself. Because the controller is organized through the generalized plant and the acausal optimum, the design can be re-optimized when the environment changes, when the ground-motion spectrum shifts, when the sensor configuration changes, or when plant parameters are updated (Saffarieh et al., 21 Jul 2025). The study explicitly uses real seismic data from LNGS, specifically a high-noise 90th percentile December 2023 spectrum to represent a severe scenario. This makes OmniSens a case study in co-optimizing sensing, control, and mechanics under realistic and time-varying seismic conditions.

In that sense, OmniSens denotes both a specific 6-DoF interferometric inertial sensor and a design philosophy: one integrated inertial reference is evaluated through system-level control synthesis rather than through isolated sensor figures of merit. A plausible implication is that the ET treatment elevates OmniSens from a hardware proposal to a benchmark architecture for early-stage isolation co-design.

Outside ET active isolation, the label appears more loosely in the accompanying literature as a descriptor for omnidirectional or unified sensing paradigms rather than as the name of the ET sensor itself. GelSight360 is described as an “OmniSens-style tactile sensor” because it provides omnidirectional, high-resolution tactile sensing over a curved fingertip-like surface and combines that geometry with a cross-LED photometric-stereo illumination architecture and Poisson-based depth reconstruction (Tippur et al., 2023). Omni-LOS is described as “OmniSens-like” because it fuses LOS and NLOS transient measurements in a unified differentiable model to recover near-$k_{el_b}=0.019\,\mathrm{kg\,m^2/s^2}$0 surrounding geometry from a single scan spot (Huang et al., 2023). LatentOmni is likewise presented as relevant to an “OmniSens-style query” when tightly coupled inference over synchronized sensory streams is required, replacing explicit text-only chain-of-thought with interleaved textual reasoning and continuous latent audio-visual states (Dai et al., 21 May 2026). This suggests that “OmniSens” has developed a broader descriptive resonance around systems that seek all-around or jointly grounded sensing, even though its most concrete technical definition in the provided literature is the ET 6-DoF inertial isolation sensor (Saffarieh et al., 21 Jul 2025).