Gravity-induced Errors Research Articles

Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems.

The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs.

Design and development of a freeform active mirror for an astronomy application

The advent of extremely large telescopes will bring unprecedented light-collecting power and spatial resolution, but it will also lead to a significant increase in the size and complexity of focal-plane instruments. The use of freeform mirrors could drastically reduce the number of components in optical systems. Currently, manufacturing issues limit the common use of freeform mirrors at short wavelengths. This article outlines the use of freeform mirrors in astronomical instruments with a description of two efficient freeform optical systems. A new manufacturing method is presented which seeks to overcome the manufacturing issues through hydroforming of thin polished substrates. A specific design of an active array is detailed, which will compensate for residual manufacturing errors, thermoelastic deformation, and gravity-induced errors during observations. The combined hydroformed mirror and the active array comprise the Freeform Active Mirror Experiment, which will produce an accurate, compact, and stable freeform optics dedicated to visible and near-infrared observations.

Gravity modeling in aerospace applications

The science of inertial navigation has evolved to the point that the traditional gravity model is a principal error source in advanced, precise systems. Specifically, the unmodeled vertical deflections of the earth's gravitational field are a major contributor to CEP (circular error probable) divergence in precise terrestrial inertial navigation systems (INS). Over the years, several studies have been undertaken to the development of advanced techniques for accurate, real-time compensation of gravity disturbance vectors. More complex on-board gravity models which compute vertical deflection components will reduce the CEP divergence rate, but imperfect modeling due to on-board processing limitations will still cause residual vertical deflection errors. In order to eliminate or reduce gravity-induced errors in the INS requires measurement of gravity disturbance values and in-flight compensation to the inertial navigator. It is assumed in this paper that gravity disturbance values have been measured prior to the airborne mission and various techniques for compensation are to be considered. As part of a screening process in this study, several gravity compensation techniques (both deterministic and stochastic models) were investigated. The screening process involved identification of gravity models and algorithms, and developments of selection criteria for subsequent screening of the candidates.

1321 Hexapod型パラレルメカニズム工作機械の重力の影響を考慮したキャリブレーション法(GS-13,14 生産加工・生産システム(2),研究発表講演)

1321 Hexapod型パラレルメカニズム工作機械の重力の影響を考慮したキャリブレーション法(GS-13,14 生産加工・生産システム(2),研究発表講演)

Compensation of Gravity-Induced Errors on a Hexapod-Type Parallel Kinematic Machine Tool

This paper presents a methodology to compensate contouring errors introduced by the gravity on a Hexapod-type parallel kinematic machine tool with the Stewart platform. Unlike conventional serial kinematic feed drives, the gravity imposes a critical effect on the positioning accuracy of a parallel kinematic feed drive, and its effect significantly varies depending on the position and the orientation of the spindle. We first present a kinematic model to predict the elastic deformation of struts caused by the gravity. The positioning error at the tool tip is given as the superposition of the deformation of each strut. It is experimentally verified for a commercial parallel kinematic machine tool that the machine's contouring error is significantly reduced by compensating gravity-induced errors on a reference trajectory.

パラレルメカニズム型工作機械における重力に起因する運動誤差の補正法(パラレルメカニズム)

パラレルメカニズム型工作機械における重力に起因する運動誤差の補正法(パラレルメカニズム)

337 Compensation of Gravity-induced Errors on Hexapod-type Parallel Mechanism Machine Tools

337 Compensation of Gravity-induced Errors on Hexapod-type Parallel Mechanism Machine Tools

Gravity-induced errors in airborne inertial navigation

This paper describes a simple yet powerful statistical technique for calculating the effects of errors in a detailed navigation gravity model on an inertial navigation system (INS) traveling a great circle flight path. Error variances in the horizontal position and velocity of an aircraft are computed from the time-dependent frequency response of the inertial navigation system and the power spectral densities of errors in the along- and cross-track gravity disturbance components derived from the navigation gravity model. The power spectra are obtained by first computing the spectrum of the vertical gravity disturbance errors using available degree spectrum models and results of mean gravity value estimation error analyses, then using fundamental equations of gravitational potential theory to relate this vertical disturbance error spectrum to the desired along- and cross-track disturbance error spectra. These spectra have dramatically different shapes with the cross-track component having much greater power at low frequencies. Since the response of a lightly damped INS is sharply peaked at low frequencies, nearly all of the navigation error is initially induced in the cross-track direction and accumulates in the along-track direction primarily through Coriolis coupling.