Results for “Sensor systems” — Page 84

NASA NTRS1987

Flexible system model reduction and control system design based upon actuator and sensor influence functions

A model reduction technique based on aggregation with respect to sensor and actuator influence functions rather than modes is presented for large systems of coupled second-order differential equations. Perturbation expressions which can predict the effects of spillover on both the reduced-order plant model and the neglected plant model are derived. For the special case of collocated actuators and sensors, these expressions lead to the derivation of constraints on the controller gains that are, given the validity of the perturbation technique, sufficient to guarantee the stability of the closed-loop system. A case study demonstrates the derivation of stabilizing controllers based on the present technique. The use of control and observation synthesis in modifying the dimension of the reduced-order plant model is also discussed. A numerical example is provided for illustration.

Yam, Yeung↗

NASA NTRS2011

Nanosensors-Cellphone Integration for Extended Chemical Sensing Network

This poster is to present the development of a cellphone sensor network for extended chemical sensing. The nanosensors using carbon nanotubes and other nanostructures are used with low power and high sensitivity for chemical detection. The sensing module has been miniaturized to a small size that can plug in or clip on to a smartphone. The chemical information detected by the nanosensors are acquired by a smartphone and transmitted via cellphone 3g or WiFi network to an internet server. The whole integrated sensing system from sensor to cellphone to a cloud will provide an extended chemical sensing network that can cover nation wide and even cover global wide for early warning of a hazardous event.

Li, Jing↗

DOE OSTI2024

Sensor assemblies and methods for emulating interaction of entities within water systems

Methods for emulating interaction of entities within water systems are provided. The methods can include introducing a sensor assembly into a water system. The sensor assembly can include: a circuit board supporting processing circuitry components on either or both of opposing component support surfaces of the circuit board; a housing about the circuit board and the components, the housing being circular about the circuit board in at least one cross section; and wherein the support surfaces of the circuit board are substantially parallel with the plane of the housing in the one cross section.

Deng, Z. Daniel↗

NASA NTRS2016

Carbon Nanofiber Nanoelectrodes for Neural Stimulation and Chemical Detection: The Era of "Smart" Deep Brain Stimulation

A sensor platform based on vertically aligned carbon nanofibers (CNFs) has been developed. Their inherent nanometer scale, high conductivity, wide potential window, good biocompatibility and well-defined surface chemistry make them ideal candidates as biosensor electrodes. Here, we report two studies using vertically aligned CNF nanoelectrodes for biomedical applications. CNF arrays are investigated as neural stimulation and neurotransmitter recording electrodes for application in deep brain stimulation (DBS). Polypyrrole coated CNF nanoelectrodes have shown great promise as stimulating electrodes due to their large surface area, low impedance, biocompatibility and capacity for highly localized stimulation. CNFs embedded in SiO2 have been used as sensing electrodes for neurotransmitter detection. Our approach combines a multiplexed CNF electrode chip, developed at NASA Ames Research Center, with the Wireless Instantaneous Neurotransmitter Concentration Sensor (WINCS) system, developed at the Mayo Clinic. Preliminary results indicate that the CNF nanoelectrode arrays are easily integrated with WINCS for neurotransmitter detection in a multiplexed array format. In the future, combining CNF based stimulating and recording electrodes with WINCS may lay the foundation for an implantable smart therapeutic system that utilizes neurochemical feedback control while likely resulting in increased DBS application in various neuropsychiatric disorders. In total, our goal is to take advantage of the nanostructure of CNF arrays for biosensing studies requiring ultrahigh sensitivity, high-degree of miniaturization, and selective biofunctionalization.

human body↗

NASA NTRS2014

Carbon Nanofiber Nanoelectrodes for Biosensing Applications

A sensor platform based on vertically aligned carbon nanofibers (CNFs) has been developed. Their inherent nanometer scale, high conductivity, wide potential window, good biocompatibility and well-defined surface chemistry make them ideal candidates as biosensor electrodes. Here, we report two studies using vertically aligned CNF nanoelectrodes for biomedical applications. CNF arrays are investigated as neural stimulation and neurotransmitter recording electrodes for application in deep brain stimulation (DBS). Polypyrrole coated CNF nanoelectrodes have shown great promise as stimulating electrodes due to their large surface area, low impedance, biocompatibility and capacity for highly localized stimulation. CNFs embedded in SiO2 have been used as sensing electrodes for neurotransmitter detection. Our approach combines a multiplexed CNF electrode chip, developed at NASA Ames Research Center, with the Wireless Instantaneous Neurotransmitter Concentration Sensor (WINCS) system, developed at the Mayo Clinic. Preliminary results indicate that the CNF nanoelectrode arrays are easily integrated with WINCS for neurotransmitter detection in a multiplexed array format. In the future, combining CNF based stimulating and recording electrodes with WINCS may lay the foundation for an implantable smart therapeutic system that utilizes neurochemical feedback control while likely resulting in increased DBS application in various neuropsychiatric disorders. In total, our goal is to take advantage of the nanostructure of CNF arrays for biosensing studies requiring ultrahigh sensitivity, high-degree of miniaturization, and selective biofunctionalization.

bioinstrumentation↗

DOE OSTI2021

Field Validation of a Smart Energy Recovery Ventilation System Using Low-Cost Indoor Air Quality Sensors

This project is a field validation, using low-cost indoor air quality (IAQ) sensors, of a smart ventilation system that can help low-load homes in humid environments maintain acceptable indoor humidity conditions while providing adequate ventilation according to ASHRAE 62.2. The objectives of this research were to (1) address builders’ concerns with mechanical ventilation in humid environments and (2) answer the question of whether smart control logic helps with occupant comfort and the creation of a more acceptable indoor environment. To address the objectives of the study, the Southface team collected field data for one year in four Charleston, South Carolina, new construction homes in order to determine the differences in occupant comfort; comfort metrics; IAQ; and heating, ventilating, and air-conditioning (HVAC) energy consumption when toggling biweekly between an energy recovery ventilator (ERV) operating continuously and an ERV operating with smart, time-varying humidity control logic. The smart ventilation algorithm under consideration in this field test did create a less humid indoor environment on an annual basis as quantitatively measured through temperature and relative humidity (T/RH) readings, expressed most discernably as “percentage of time above 60% RH” and “percentage of time above 55°F dewpoint.” However, the difference it made was inconsistent during the spring, summer, and fall months, and it was only directionally consistent during the winter months. We suspect that this is primarily due to the long runtimes and concomitant dehumidification activity of the air-conditioning (A/C) units in response to the high sensible loads in Charleston. The effect of the smart ventilation algorithm was not discernable to the occupants in this study, as recorded through seasonal surveys.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2004

Autonomous In-Situ Resources Prospector

This presentation will describe the concept of an autonomous, intelligent, rover-based rapid surveying system to identify and map several key lunar resources to optimize their ISRU (In Situ Resource Utilization) extraction potential. Prior to an extraction phase for any target resource, ground-based surveys are needed to provide confirmation of remote observation, to quantify and map their 3-D distribution, and to locate optimal extraction sites (e.g. ore bodies) with precision to maximize their economic benefit. The system will search for and quantify optimal minerals for oxygen production feedstock, water ice, and high glass-content regolith that can be used for building materials. These are targeted because of their utility and because they are, or are likely to be, variable in quantity over spatial scales accessible to a rover (i.e., few km). Oxygen has benefits for life support systems and as an oxidizer for propellants. Water is a key resource for sustainable exploration, with utility for life support, propellants, and other industrial processes. High glass-content regolith has utility as a feedstock for building materials as it readily sinters upon heating into a cohesive matrix more readily than other regolith materials or crystalline basalts. Lunar glasses are also a potential feedstock for oxygen production, as many are rich in iron and titanium oxides that are optimal for oxygen extraction. To accomplish this task, a system of sensors and decision-making algorithms for an autonomous prospecting rover is described. One set of sensors will be located in the wheel tread of the robotic search vehicle providing contact sensor data on regolith composition. Another set of instruments will be housed on the platform of the rover, including VIS-NIR imagers and spectrometers, both for far-field context and near-field characterization of the regolith in the immediate vicinity of the rover. Also included in the sensor suite are a neutron spectrometer, ground-penetrating radar, and an instrumented cone penetrometer for subsurface assessment. Output from these sensors will be evaluated autonomously in real-time by decision-making software to evaluate if any of the targeted resources has been detected, and if so, to quantify their abundance. Algorithms for optimizing the mapping strategy based on target resource abundance and distribution are also included in the autonomous software. This approach emphasizes on-the-fly survey measurements to enable efficient and rapid prospecting of large areas, which will improve the economics of ISRU system approaches. The mature technology will enable autonomous rovers to create in-situ resource maps of lunar or other planetary surfaces, which will facilitate human and robotic exploration.

Dissly, R. W.↗

NASA NTRS1992

Development of a machine vision system for automated structural assembly

Research is being conducted at the LaRC to develop a telerobotic assembly system designed to construct large space truss structures. This research program was initiated within the past several years, and a ground-based test-bed was developed to evaluate and expand the state of the art. Test-bed operations currently use predetermined ('taught') points for truss structural assembly. Total dependence on the use of taught points for joint receptacle capture and strut installation is neither robust nor reliable enough for space operations. Therefore, a machine vision sensor guidance system is being developed to locate and guide the robot to a passive target mounted on the truss joint receptacle. The vision system hardware includes a miniature video camera, passive targets mounted on the joint receptacles, target illumination hardware, and an image processing system. Discrimination of the target from background clutter is accomplished through standard digital processing techniques. Once the target is identified, a pose estimation algorithm is invoked to determine the location, in three-dimensional space, of the target relative to the robots end-effector. Preliminary test results of the vision system in the Automated Structural Assembly Laboratory with a range of lighting and background conditions indicate that it is fully capable of successfully identifying joint receptacle targets throughout the required operational range. Controlled optical bench test results indicate that the system can also provide the pose estimation accuracy to define the target position.

Sydow, P. Daniel↗

NASA NTRSDate not supplied

Enabling Interoperability in Earth System Digital Twins (ESDT): Integrating Observations, Models, and AI for Actionable Insights Through NASA'S Intelligent Systems Technology Program

NASA’s Intelligent Systems Technology Program (IST) is driving a paradigm shift in Earth science through the development of Earth System Digital Twins (ESDT). These integrated information systems create a dynamic "digital replica" of the Earth by harmonizing continuous, multi-source observations with high-fidelity models and state-of-the-art artificial intelligence (AI) that enable “What now?”, “What next?”, and “What if?” scenario building. These scenarios are reflected in NASA IST’s series of ESDTs, from the Coastal Zone Digital Twin that integrates complex data on the current state of the Chesapeake Bay to the Terrestrial Environmental Rapid-Replication and Assimilation Hydrometeorological (TerraHydro) AI-based ESDT that forecasts water movement across Earth’s surface, to the Agriculture Land Information System (AgLIS) which can be used to assess optimal planting dates and crop yield estimates. By bridging the gap between vast data archives and actionable insights, these projects enable a system-of-systems approach to understanding complex, interacting Earth processes. This poster will highlight recent innovations and future directions from NASA’s ESDT initiatives: Continuous Data Assimilation & Multi-Source Fusion. A core requirement of the ESDT work is the transition from static models to dynamic "living" replicas. This involves creating frameworks for the continual assimilation of near-real-time data from uncoordinated, heterogeneous sources, including satellite observations and airborne assets, and ground-based Internet of Things (IoT) sensors. These systems link design, operational status, and environmental data, ensuring the digital twin accurately reflects the current state of the physical Earth system. High-Fidelity Hybrid Modeling & Computational Acceleration to enable interactive "what-if" explorations, programs are moving beyond traditional, slow physical solvers by developing fast surrogate machine learning models and Deep Generative Models (DGMs). These hybrid approaches use neural networks to emulate complex physics, such as cloud feedback or ocean dynamics, at a fraction of the original computing cost, often leveraging advanced hardware like Graphics Processing Units (GPUs) to achieve the necessary scale. Federated Ecosystems & Interoperable Frameworks rather than building isolated tools, NASA IST is moving toward federated ESDTs and reusable analytic collaborative frameworks. This theme focuses on interoperability standards and common ontologies that allow specialized digital twins to interact and share data. This system-of-systems architecture supports multi-discipline investigations, such as analyzing how upstream watershed changes impact downstream urban flooding or how wildfire emissions affect regional air quality. By leveraging these advancements, ESDTs empower researchers and decision-makers to conduct real-time analysis and run complex hypothetical scenarios, ultimately improving our understanding of Earth’s evolving systems and informing critical real-world applications.

Earth System↗

DOE OSTI2026

Supervised Learning-Based Spatial Position Estimation with Vertical Displacement for Hovering UAV Wireless Power Transfer

This study presents a supervised learning-based spatial position estimation approach for wireless power transfer (WPT) systems supporting hovering unmanned aerial vehicle (UAV) charging. Unlike stationary charging scenarios, hovering UAVs introduce continuous lateral misalignment and vertical displacement, leading to variations in magnetic coupling and reduced power transfer efficiency. To address this challenge, the proposed method estimates the relative spatial position of the receiver coil using only electrical measurements obtained at the secondary side. A supervised learning model is trained to map output voltage and current features to spatial coordinates, enabling position awareness without requiring external sensors, vision systems, or communication links. The sensing functionality is inherently integrated into the WPT system, allowing simultaneous power transfer and localization through the same magnetic interface. Experimental validation is conducted on a laboratory-scale prototype under varying lateral offsets and air-gap conditions. In addition, spline-based interpolation is employed to increase spatial data density for training. The results demonstrate that the proposed framework can capture spatial variations associated with both lateral and vertical displacement, providing reliable position estimation under hovering conditions. This work establishes a hardware-efficient, sensorless solution for UAV wireless charging and serves as a baseline for advanced data-driven position estimation methods in dynamic WPT systems.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗

DOE OSTI2025

Leveraging FPGA Advantages for Quicker Data Processing for LBNF

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, Jacob↗

DOE OSTI2025

Real-Time FPGA Implementation For Frequency Sweep Interferometry In The LBNF Complex

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, A. Jacob [Fermilab; Unlisted]↗

NASA NTRS2009

Resonance-induced sensitivity enhancement method for conductivity sensors

Methods and systems for improving the sensitivity of a variety of conductivity sensing devices, in particular capacitively-coupled contactless conductivity detectors. A parallel inductor is added to the conductivity sensor. The sensor with the parallel inductor is operated at a resonant frequency of the equivalent circuit model. At the resonant frequency, parasitic capacitances that are either in series or in parallel with the conductance (and possibly a series resistance) is substantially removed from the equivalent circuit, leaving a purely resistive impedance. An appreciably higher sensor sensitivity results. Experimental verification shows that sensitivity improvements of the order of 10,000-fold are possible. Examples of detecting particulates with high precision by application of the apparatus and methods of operation are described.

Tai, Yu-Chong↗

DOE OSTI2025

Secure State Estimation with Asynchronous Measurements for Coordinated Cyber Attack Detection in Active Distribution Systems

Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data.

asynchronous measurements↗

NASA NTRS2003

The Inertial Stellar Compass (ISC): A Multifunction, Low Power, Attitude Determination Technology Breakthrough

The Inertial Stellar Compass (ISC) is a miniature, low power, stellar inertial attitude determination system with an accuracy of better than 0.1 degree (1 sigma) in three axes. The ISC consumes only 3.5 Watts of power and is contained in a 2.5 kg package. With its embedded on-board processor, the ISC provides attitude quaternion information and has Lost-in-Space (LIS) initialization capability. The attitude accuracy and LIS capability are provided by combining a wide field of view Active Pixel Sensor (APS) star camera and Micro- ElectroMechanical System (MEMS) inertial sensor information in an integrated sensor system. The performance and small form factor make the ISC a useful sensor for a wide range of missions. In particular, the ISC represents an enabling, fully integrated, micro-satellite attitude determination system. Other applications include using the ISC as a single sensor solution for attitude determination on medium performance spacecraft and as a bolt on independent safe-hold sensor or coarse acquisition sensor for many other spacecraft. NASA's New Millennium Program (NMP) has selected the ISC technology for a Space Technology 6 (ST6) flight validation experiment scheduled for 2004. NMP missions, such a s ST6, are intended to validate advanced technologies that have not flown in space in order to reduce the risk associated with their infusion into future NASA missions. This paper describes the design, operation, and performance of the ISC and outlines the technology validation plan. A number of mission applications for the ISC technology are highlighted, both for the baseline ST6 ISC configuration and more ambitious applications where ISC hardware and software modifications would be required. These applications demonstrate the wide range of Space and Earth Science missions that would benefit from infusion of the ISC technology.

Bauer, Frank H.↗

NASA NTRS2020

An Inter Planetary Network Enabled by SmallSats

This paper describes the implementation of an unparalleled large sensor and communications platform along the solar system that we call the inter planetary network (IPN). The proposed IPN consists of thousands of small spacecraft (e.g. CubeSats) strategically deployed around planetary bodies in the solar system where each spacecraft is furnished with fast communications and sensor systems. The IPN concept is being proposed as an avant-garde science and communications platform that could allow for continuous fast communications and remarkable science returns. The IPN spacecraft, furnished with suitable miniaturized sensors, could form an amazing deep space platform for unique observation of the solar system, stars, galaxies and universe. A key feature of the IPN architecture is the use of swarms of spacecraft as network units. Super-high-speed intra-swarm communications could be achieved via omnidirectional optical links. The swarms act as autonomous network nodes and are capable of forming large synthetic apertures that enable high data rate communications among the IPN nodes. Depending on the sensors they carry, these swarms may also be capable of forming large synthetic sensors by rapidly combining data among the spacecraft. We envision distances between spacecraft forming a swarm to be in the range of 102-104 kilometers, whereas distances of 106-108 kilometers among swarms (IPN nodes) are expected. We provide an example of an initial IPN implementation in the inner solar system where swarms of spacecraft are deployed around the Earth, Moon, Mars, Venus and Mercury. Placing swarms around 3 Lagrange points per planet yield a total of 12 possible IPN network nodes. We present communications link calculations among IPN nodes that allow high data rate communications between Earth and Mars while Mars is in solar conjunction (behind the Sun). A second example of an IPN platforms includes a giant spaceborne radio telescope behind the moon.

Velazco, Jose↗

NASA NTRS2020

An Inter Planetary Network Enabled by SmallSats

This paper describes the implementation of an unparalleled large sensor and communications platform along the solar system that we call the inter planetary network (IPN). The proposed IPN consists of thousands of small spacecraft (e.g. CubeSats) strategically deployed around planetary bodies in the solar system where each spacecraft is furnished with fast communications and sensor systems. The IPN concept is being proposed as an avant-garde science and communications platform that could allow for continuous fast communications and remarkable science returns. The IPN spacecraft, furnished with suitable miniaturized sensors, could form an amazing deep space platform for unique observation of the solar system, stars, galaxies and universe. A key feature of the IPN architecture is the use of swarms of spacecraft as network units. Super-high-speed intra-swarm communications could be achieved via omnidirectional optical links. The swarms act as autonomous network nodes and are capable of forming large synthetic apertures that enable high data rate communications among the IPN nodes. Depending on the sensors they carry, these swarms may also be capable of forming large synthetic sensors by rapidly combining data among the spacecraft. We envision distances between spacecraft forming a swarm to be in the range of 102-104 kilometers, whereas distances of 106-108 kilometers among swarms (IPN nodes) are expected. We provide an example of an initial IPN implementation in the inner solar system where swarms of spacecraft are deployed around the Earth, Moon, Mars, Venus and Mercury. Placing swarms around 3 Lagrange points per planet yield a total of 12 possible IPN network nodes. We present communications link calculations among IPN nodes that allow high data rate communications between Earth and Mars while Mars is in solar conjunction (behind the Sun). A second example of an IPN platforms includes a giant spaceborne radio telescope behind the moon.

Velazco, Jose E↗

NASA NTRS1994

High-Resolution Gamma-Ray Imaging Measurements Using Externally Segmented Germanium Detectors

Fully two-dimensional gamma-ray imaging with simultaneous high-resolution spectroscopy has been demonstrated using an externally segmented germanium sensor. The system employs a single high-purity coaxial detector with its outer electrode segmented into 5 distinct charge collection regions and a lead coded aperture with a uniformly redundant array (URA) pattern. A series of one-dimensional responses was collected around 511 keV while the system was rotated in steps through 180 degrees. A non-negative, linear least-squares algorithm was then employed to reconstruct a 2-dimensional image. Corrections for multiple scattering in the detector, and the finite distance of source and detector are made in the reconstruction process.

spectroscopy gamma ray germanium sensor nucleosynt↗