Results for “distributed control and optimization” — Page 11

NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗

NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗

NASA NTRS1980

The effect of preparation conditions on the structure and mechanical properties of reaction-sintered silicon nitride

The microstructure of reaction sintered silicon nitride (RSSN) was changed over a wide range by varying the grain density, grain size of the silicon starting powder, nitriding conditions, and by introducing artificial pores. The influence of single microstructural parameters on mechanical properties like room temperature strength, creep behavior, and resistance to thermal shock was investigated. The essential factors influencing these properties were found to be total porosity, pore size distribution, and the fractions of alpha and beta Si3N4. In view of high temperature engineering applications of RSSN, potentials for optimizing the material's properties by controlled processing are discussed.

Heinrich, J.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-11456-DND

NASA’s precision scheduling and spacing research has matured to show the high potential of merging efficient flows in high density operations - Precision scheduling and efficient delay distribution minimizes early descent from enroute altitude and low-altitude vectoring - Precision merging and spacing control improves throughput - Enables the extended use of flight path optimization based procedures FAA/NASA/Industry collaboration is needed to accelerate implementation of ADS-B applications in a way that achieves the full benefit of NextGen operations to those that equip in high density airspace Integrated precision scheduling and spacing will to offer immediate and systematic benefits to airlines in many environments, even with different equipage levels and traffic densities

Harry Swenson↗

NASA NTRSDate not supplied

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗

NASA NTRS1995

Artificial neural network application for space station power system fault diagnosis

This study presents a methodology for fault diagnosis using a Two-Stage Artificial Neural Network Clustering Algorithm. Previously, SPICE models of a 5-bus DC power distribution system with assumed constant output power during contingencies from the DDCU were used to evaluate the ANN's fault diagnosis capabilities. This on-going study uses EMTP models of the components (distribution lines, SPDU, TPDU, loads) and power sources (DDCU) of Space Station Alpha's electrical Power Distribution System as a basis for the ANN fault diagnostic tool. The results from the two studies are contrasted. In the event of a major fault, ground controllers need the ability to identify the type of fault, isolate the fault to the orbital replaceable unit level and provide the necessary information for the power management expert system to optimally determine a degraded-mode load schedule. To accomplish these goals, the electrical power distribution system's architecture can be subdivided into three major classes: DC-DC converter to loads, DC Switching Unit (DCSU) to Main bus Switching Unit (MBSU), and Power Sources to DCSU. Each class which has its own electrical characteristics and operations, requires a unique fault analysis philosophy. This study identifies these philosophies as Riddles 1, 2 and 3 respectively. The results of the on-going study addresses Riddle-1. It is concluded in this study that the combination of the EMTP models of the DDCU, distribution cables and electrical loads yields a more accurate model of the behavior and in addition yielded more accurate fault diagnosis using ANN versus the results obtained with the SPICE models.

Momoh, James A.↗

NASA NTRS2004

Product Distribution Theory for Control of Multi-Agent Systems

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Lee, Chia Fan↗

NASA NTRSDate not supplied

Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports

A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.

multidisciplinary optimization↗

NASA NTRS1985

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

Gibson, J. S.↗

NASA NTRS1987

Processor tradeoffs in distributed real-time systems

The problem of the optimization of the design of real-time distributed systems is examined with reference to a class of computer architectures similar to the continuously reconfigurable multiprocessor flight control system structure, CM2FCS. Particular attention is given to the impact of processor replacement and the burn-in time on the probability of dynamic failure and mean cost. The solution is obtained numerically and interpreted in the context of real-time applications.

Krishna, C. M.↗

NASA NTRS1999

A Survey of Collective Intelligence

This chapter presents the science of "COllective INtelligence" (COIN). A COIN is a large multi-agent systems where: i) the agents each run reinforcement learning (RL) algorithms; ii) there is little to no centralized communication or control; iii) there is a provided world utility function that, rates the possible histories of tile full system. Tile conventional approach to designing large distributed systems to optimize a world utility does not use agents running RL algorithms. Rather that approach begins with explicit modeling of the overall system's dynamics, followed by detailed hand-tuning of the interactions between the components to ensure that they "cooperate" as far as the world utility is concerned. This approach is labor-intensive, often results in highly non-robust systems, and usually results in design techniques that, have limited applicability. In contrast, with COINs we wish to solve the system design problems implicitly, via the 'adaptive' character of the RL algorithms of each of the agents. This COIN approach introduces an entirely new, profound design problem: Assuming the RL algorithms are able to achieve high rewards, what reward functions for the individual agents will, when pursued by those agents, result in high world utility? In other words, what reward functions will best ensure that we do not have phenomena like the tragedy of the commons, or Braess's paradox? Although still very young, the science of COINs has already resulted in successes in artificial domains, in particular in packet-routing, the leader-follower problem, and in variants of Arthur's "El Farol bar problem". It is expected that as it matures not only will COIN science expand greatly the range of tasks addressable by human engineers, but it will also provide much insight into already established scientific fields, such as economics, game theory, or population biology.

Wolpert, David H.↗

NASA NTRS2013

Silent and Efficient Supersonic Bi-Directional Flying Wing

The supersonic bi-directional (SBiDir) flying wing (FW) concept has a great potential to achieve low sonic boom with high supersonic aerodynamic performance due to removal of performance conflict between high speed and low speed by rotating goo in flight. This NIAC Phase 1 research has achieved three objectives: 2) prove the concept based on simulation that it can achieve very low boom with smooth Sine wave ground over-pressure signature and excellent aerodynamic efficiency; 3) conduct trade study to correlate the geometric parameters with sonic boom and aerodynamic performance for further automated design optimization in Phase II. The design methodology developed in Phase I includes three parts: 1) an advanced geometry model, which can vary airfoil meanline angle distribution to control the expansion and shock waves on the airplane surface to mitigate sonic boom and improve aerodynamic efficiency. 2) a validated CFD procedure to resolve near field flow with accurate shock strength. The sonic boom propagation from near field to far field ground is simulated by NASA NF Boom code. The surface friction drag prediction is based on fiat plate correlation adopted by Seebass and supported by the experimental study of Winter and Smith, which is on the conservative side and is more reliable than CFD RANS simulation. 3) a mission analysis tool based on Corke's model that provides design requirements and constraints of supersonic airplanes for range, payload, volume, size, weight, etc. The design mission target is a supersonic transport with cruise Mach number 1.6, 100 passengers, and 4000nm range. The trade study has several very important findings: 1) The far field ground sonic boom signature is directly related to the smoothness of the flow on the airplane surface. The meanline angle distribution is a very effective control methodology to mitigate surface shock and expansion wave strength, and mitigating compression wave coalescing by achieving smooth loading distribution chord-wise. Compared with a linear meanline angle distribution, a design using nonlinear and non-monotonic meanline angle distribution is able to reduce the sonic boom ground loudness by over 20dBP1. The design achieves sonic boom ground loudness less than 70dBP1 and aerodynamic dynamic efficiency 1/D of 8.4. 2) Decreasing sweep angle within the Mach cone will increase 1/D as well as sonic boom. A design with variable sweep from 84° at the very leading edge to 68° at the tip achieves an extraordinarily high 1/D of 10.4 at Mach number 1.6 due to the low wave drag. If no sonic boom constraint is attached, SBiDir-FW concept still has a lot of room to increase the 1/D. 3) The round leading edge and trailing edge under high sweep angle are beneficial to improve aerodynamic performance, sonic boom, and to increase volume of the airplane. 4) Subsonic performance is benefited greatly from the high slenderness of supersonic configuration after rotating goo. A design with excellent supersonic aspect ratio of 0.44, 1/D of 8.g, gives an extraordinary subsonic aspect ration of 10 and 1/D of 1g.7. Two configurations are designed in details to install internal seats, landing gears, and engine installation to demonstrate the feasibility of SBiDir-FW configuration to accommodate all the required volume for realistic airplane. Here we emphasize that the qualitative findings in Phase I are very encouraging, more important than the quantitative results. Qualitative findings give the understanding of physics and provide the path to achieve the ultimate high performance design. The promising quantitative results achieved in Phase I need to be confirmed by wind tunnel testing in Phase II and ultimately proved by flight test. The other important step forward will be made to study the rotation transition from both CFD unsteady simulation and wind tunnel testing.

Zha, Gecheng↗

NASA NTRS2009

Quantifying Parameter Sensitivity, Interaction and Transferability in Hydrologically Enhanced Versions of Noah-LSM over Transition Zones

We use sensitivity analysis to identify the parameters that are most responsible for shaping land surface model (LSM) simulations and to understand the complex interactions in three versions of the Noah LSM: the standard version (STD), a version enhanced with a simple groundwater module (GW), and version augmented by a dynamic phenology module (DV). We use warm season, high-frequency, near-surface states and turbulent fluxes collected over nine sites in the US Southern Great Plains. We quantify changes in the pattern of sensitive parameters, the amount and nature of the interaction between parameters, and the covariance structure of the distribution of behavioral parameter sets. Using Sobol s total and first-order sensitivity indexes, we show that very few parameters directly control the variance of the model output. Significant parameter interaction occurs so that not only the optimal parameter values differ between models, but the relationships between parameters change. GW decreases parameter interaction and appears to improve model realism, especially at wetter sites. DV increases parameter interaction and decreases identifiability, implying it is overparameterized and/or underconstrained. A case study at a wet site shows GW has two functional modes: one that mimics STD and a second in which GW improves model function by decoupling direct evaporation and baseflow. Unsupervised classification of the posterior distributions of behavioral parameter sets cannot group similar sites based solely on soil or vegetation type, helping to explain why transferability between sites and models is not straightforward. This evidence suggests a priori assignment of parameters should also consider climatic differences.

Rosero, Enrique↗

NASA NTRS1994

Optimization of Adaptive Intraply Hybrid Fiber Composites with Reliability Considerations

The reliability with bounded distribution parameters (mean, standard deviation) was maximized and the reliability-based cost was minimized for adaptive intra-ply hybrid fiber composites by using a probabilistic method. The probabilistic method accounts for all naturally occurring uncertainties including those in constituent material properties, fabrication variables, structure geometry, and control-related parameters. Probabilistic sensitivity factors were computed and used in the optimization procedures. For actuated change in the angle of attack of an airfoil-like composite shell structure with an adaptive torque plate, the reliability was maximized to 0.9999 probability, with constraints on the mean and standard deviation of the actuation material volume ratio (percentage of actuation composite material in a ply) and the actuation strain coefficient. The reliability-based cost was minimized for an airfoil-like composite shell structure with an adaptive skin and a mean actuation material volume ratio as the design parameter. At a O.9-mean actuation material volume ratio, the minimum cost was obtained.

Shiao, Michael C.↗

NASA NTRS2005

Physical and hydraulic properties of baked ceramic aggregates used for plant growth medium

Baked ceramic aggregates (fritted clay, arcillite) have been used for plant research both on the ground and in microgravity. Optimal control of water and air within the root zone in any gravity environment depends on physical and hydraulic properties of the aggregate, which were evaluated for 0.25-1-mm and 1-2-mm particle size distributions. The maximum bulk densities obtained by any packing technique were 0.68 and 0.64 g cm-3 for 0.25-1-mm and 1-2-mm particles, respectively. Wettable porosity obtained by infiltration with water was approximately 65%, substantially lower than total porosity of approximately 74%. Aggregate of both particle sizes exhibited a bimodal pore size distribution consisting of inter-aggregate macropores and intra-aggregate micropores, with the transition from macro- to microporosity beginning at volumetric water content of approximately 36% to 39%. For inter-aggregate water contents that support optimal plant growth there is 45% change in water content that occurs over a relatively small matric suction range of 0-20 cm H2O for 0.25-1-mm and 0 to -10 cm H2O for 1-2-mm aggregate. Hysteresis is substantial between draining and wetting aggregate, which results in as much as a approximately 10% to 20% difference in volumetric water content for a given matric potential. Hydraulic conductivity was approximately an order of magnitude higher for 1-2-mm than for 0.25-1-mm aggregate until significant drainage of the inter-aggregate pore space occurred. The large change in water content for a relatively small change in matric potential suggests that significant differences in water retention may be observed in microgravity as compared to earth.

NASA Center JSC↗

NASA NTRS2012

Monitoring of International Space Station Telemetry Using Shewhart Control Charts

Shewhart control charts have been established as an expedient method for analyzing dynamic, trending data in order to identify anomalous subsystem performance as soon as such performance would exceed a statistically established baseline. Additionally, this leading indicator tool integrates a selection methodology that reduces false positive indications, optimizes true leading indicator events, minimizes computer processor unit duty cycles, and addresses human factor concerns (i.e., the potential for flight-controller data overload). This innovation leverages statistical process control, and provides a relatively simple way to allow flight controllers to focus their attention on subtle system changes that could lead to dramatic off-nominal system performance. Finally, this capability improves response time to potential hardware damage and/or crew injury, thereby improving space flight safety. Shewhart control charts require normalized data. However, the telemetry from the ISS Early External Thermal Control System (EETCS) was not normally distributed. A method for normalizing the data was implemented, as was a means of selecting data windows, the number of standard deviations (Sigma Level), the number of consecutive points out of limits (Sequence), and direction (increasing or decreasing trend data). By varying these options, and treating them like dial settings, the number of nuisance alerts and leading indicators were optimized. The goal was to capture all leading indicators while minimizing the number of nuisances. Lean Six Sigma (L6S) design of experiment methodologies were employed. To optimize the results, Perl programming language was used to automate the massive amounts of telemetry data, control chart plots, and the data analysis.

Fitch, Jeffery T.↗

NASA NTRS2011

Multi-Parameter Aerosol Scattering Sensor

This work relates to the development of sensors that measure specific aerosol properties. These properties are in the form of integrated moment distributions, i.e., total surface area, total mass, etc., or mathematical combinations of these moment distributions. Specifically, the innovation involves two fundamental features: a computational tool to design and optimize such sensors and the embodiment of these sensors in actual practice. The measurement of aerosol properties is a problem of general interest. Applications include, but are not limited to, environmental monitoring, assessment of human respiratory health, fire detection, emission characterization and control, and pollutant monitoring. The objectives for sensor development include increased accuracy and/or dynamic range, the inclusion in a single sensor of the ability to measure multiple aerosol properties, and developing an overall physical package that is rugged, compact, and low in power consumption, so as to enable deployment in harsh or confined field applications, and as distributed sensor networks. Existing instruments for this purpose include scattering photometers, direct-reading mass instruments, Beta absorption devices, differential mobility analyzers, and gravitational samplers. The family of sensors reported here is predicated on the interaction of light and matter; specifically, the scattering of light from distributions of aerosol particles. The particular arrangement of the sensor, e.g. the wavelength(s) of incident radiation, the number and location of optical detectors, etc., can be derived so as to optimize the sensor response to aerosol properties of practical interest. A key feature of the design is the potential embodiment as an extremely compact, integrated microsensor package. This is of fundamental importance, as it enables numerous previously inaccessible applications. The embodiment of these sensors is inherently low maintenance and high reliability by design. The novel and unique features include the underlying computational underpinning that allows the optimization for specific applications, and the physical embodiment that affords the construction of a compact, durable, and reliable integrated package. The advantage appears in the form of increased accuracy relative to existing instruments, and the applications enabled by the physical attributes of the resulting configuration

Greenberg, Paul S.↗

NASA NTRS1971

A graphite/epoxy compression panel for the space shuttle.

Martin Marietta fabricated a hat-section-stiffened compression panel of graphite/epoxy composite that was analyzed to optimize the structural configuration and material distribution. The fabrication processes developed were modified following the appearance of several problems associated with the unique physical properties of the material. Quality control processes were developed, with emphasis in the areas of ultrasonics and X-ray.

Meredith, O. D.↗