Earth-fixed Reference Frame Research Articles

Collision-free output-feedback super-twisting control of robotic surface vehicles for coordinated path following with experiments

This paper addresses the coordinated path following (CPF) control of robotic surface vehicles (RSVs) in the presence of multiple obstacles and lumped disturbances over a resource-constrained wireless network. A collision-free output-feedback super-twisting control architecture is proposed for CPF without using velocity measurements. Specifically, robust exact differentiator observers are designed at first to recover the unmeasured velocities, and estimate the lumped disturbances, simultaneously. Next, anti-disturbance output-feedback super-twisting control laws are proposed to achieve individual path following in earth-fixed reference frame, and an adaptive potential field with a user-defined collision hazard degree is introduced to avoid the collisions with obstacles. To reduce the network traffic, self-triggered path updating laws are then designed for avoiding the continuous transmitting and listening of neighboring RSVs. The stability analysis shows that the closed-loop system is input-to-state stable outside the collision avoidance region, and Zeno behavior will not happen. Experiments are finally conducted to validate the efficacy of the proposed collision-free output-feedback super-twisting control method for the self-triggered CPF of RSVs.

Safety-Critical Containment Maneuvering of Underactuated Autonomous Surface Vehicles Based on Neurodynamic Optimization With Control Barrier Functions.

This article addresses the safety-critical containment maneuvering of multiple underactuated autonomous surface vehicles (ASVs) in the presence of multiple stationary/moving obstacles. In a complex marine environment, every ASV suffers from model uncertainties, external disturbances, and input constraints. A safety-critical control method is proposed for achieving a collision-free containment formation. Specifically, a fixed-time extended state observer is employed for estimating the model uncertainties and external disturbances. By estimating lumped disturbances in fixed time, nominal containment maneuvering control laws are designed in an Earth-fixed reference frame. Input-to-state safe control barrier functions (ISSf-CBFs) are constructed for mapping safety constraints on states to constraints on control inputs. A distributed quadratic optimization problem with the norm of control inputs as the objective function and ISSf-CBFs as constraints is formulated. A recurrent neural network-based neurodynamic optimization approach is adopted to solve the quadratic optimization problem for computing the forces and moments within the safety and input constraints in real time. It is proven that the error signals in the closed-loop control system are uniformly ultimately bounded and the multi-ASVs system is guaranteed for input-to-state safety. Simulation results are elaborated to substantiate the effectiveness of the proposed safety-critical control method for ASVs based on neurodynamic optimization with control barrier functions.

A new vessel motion based method for parametric estimation of the waves encountered by the ship in a seaway

Inference of sea wave spectrum based on vessel motions records is a relatively cheap monitoring strategy that has potential to improve the vessel’s day-to-day operational efficiency and the safety of its crew. For this reason, several different approaches have been considered in recent years for turning this technique into practical tools. The methods available in the literature for implementing this strategy may be broadly categorized into parametric and non-parametric approaches. Apart from other aspects, they share the characteristics of generally performing the wave inference in the earth fixed reference frame and not in the ship’s own referential. This procedure has the obvious advantage of providing the absolute wave spectrum as the output, but it comes at the expense of a greater complexity of the estimation algorithm when dealing with the motions of a vessel with forward speed. In a large part, this complexity arises from the uncertainties in the sea state estimation associated with the well-known triple-value problem when dealing with waves reaching the ship from the stern. The present article proposes a new parametric approach for vessel motion-based wave estimation. In this approach, a parametric description of the encounter wave spectrum is presented, thus enabling the algorithm to execute the wave inference in the ship’s reference frame. For dealing with the large shape variability that is inherent to the encounter wave spectra, the proposed parametrization is based on the Weibull’s distribution mathematical function. A first verification of performance of the method is also provided for the case-study of an oceanographic vessel. At this point, such verification is restricted to model-scale tests comprising conditions with and without forward speed. The results obtained are promising and indicate that the methodology is indeed capable of providing good estimates of the waves encountered by the ship under different operating conditions.

Fixed-Time Resilient Edge-Triggered Estimation and Control of Surface Vehicles for Cooperative Target Tracking Under Attacks

This paper is concerned with the cooperative target tracking of under-actuated unmanned surface vehicles (USVs) with event-triggered communications subject to denial-of-service (DoS) attacks. The target position information can be sensed by a fraction of follower USVs only. A fixed-time resilient cooperative edge-triggered estimation and control architecture is presented for achieving cooperative target tracking under DoS attacks. Specifically, a distributed edge-triggered fixed-time extended state observer (ESO) is designed to recover the position and velocity of the target with a prescribed time regardless of the unreliable communication network subject to DoS attacks. Moreover, the communication burden of the network is reduced by the proposed edge-triggered mechanism. In the control law design, a fixed-time ESO is designed for estimating the model uncertainties and external disturbances in an earth-fixed reference frame. Then, a fixed-time target tracking control law is proposed for each follower USV based on the fixed-time ESO. It is proven that the error signals in the closed-loop control system of USVs are convergent to the origin in a fixed time. An example is provided to substantiate the effectiveness of the proposed fixed-time resilient cooperative edge-triggered estimation and control architecture for USVs.

Statistical validation of ionospheric electron density profiles retrievals from GOES geosynchronous satellites

In this paper, we discuss a novel retrieval of ionospheric electron density profiles using the Radio Occultation (RO) technique applied to measurements captured by the Global Positioning System (GPS) receivers onboard two Geostationary Operational Environmental Satellites (GOES). The GOES satellites operate at ~35,800 km altitude and are primarily weather satellites that operationally contribute continuous remote-sensing data for real-time weather forecasting, as well as near-Earth environment monitoring and Sun observations. The GPS receivers onboard GOES-16 and GOES-17 satellites can track GPS signals propagated through the Earth’s atmosphere, and although the receivers are primarily designed for navigation and station-keeping maneuvers, these GPS measurements that traverse the Earth’s atmosphere can be used to retrieve the ionospheric electron density profiles. This process poses a range of technical challenges. GOES RO links are different from the traditional low Earth orbit (LEO) RO geometry since the receiver is located in an orbit that is higher in altitude than the GPS constellation of transmitters. Additionally, the GPS receivers onboard GOES satellites provide only single-frequency GPS L1 observations and have clocks much less stable than those typically used for RO measurements. The geographical distribution of the retrieved GEO-based RO profiles was found to be uniquely constrained and repeatable based on the relative geostationary fixed positions in the Earth-Centered Earth Fixed reference frame with respect to the GPS constellation orbiting at lower altitude, and significantly different from the coverage patterns of LEO-based RO missions. We demonstrate the successful application of the proposed RO profiling technique with a statistically significant set of GPS observations from GOES-16 and GOES-17 satellites over several years of data collection. This enabled us to retrieve more than 10,000 ionospheric electron density profiles with a maximum altitude of up to 1000–2000 km, much higher than any existing LEO-based RO mission. We demonstrate good performance of GEO-based RO measurements for properly specifying the vertical distribution of ionospheric plasma density by comparing the profiles dataset from the GOES RO experiment with independent reference observations – ground-based ionosondes and LEO-based RO missions, as well as model simulation results provided by the empirical International Reference Ionosphere model. Over multiple years of observations, statistical analysis of discrepancies between the ionospheric F2 layer peak parameters (peak density and height) derived from geosynchronous GOES observations and reference measurements was conducted. This analysis reveals a very good agreement between GOES RO electron density profiles and independent types of measurements in both the F2 peak and the profile shape.

Earth rotation parameters from GPS and BDS: Contributions from MEO and IGSO satellites

The Earth Rotation Parameters (ERPs) are fundamental transformation parameters to link the celestial reference frame and Earth-fixed reference frame. Global Navigation Satellite System (GNSS) is one of the key technologies to determine the ERPs and BeiDou Navigation Satellite System (BDS) has been constructed completely in 2020. In this study, we present a 2.5-years (01/2020–06/2022) results of the ERPs determination based on the GPS, global BDS (BDS-3), the regional BDS (BDS-2) combined BDS-3 (as BDS solution), Medium Earth Orbit (MEO)-only BDS (BDS-M) and the GPS combined BDS (GC). We take the IERS 14C04 products as reference to evaluate the accuracy of the ERPs estimates. The results of 3-day arc solution show that (1) compared to the estimates based on GPS solution, the GC combined solution achieves an improvement of 1 %, 7 %, 12 %, 3 % and 5 % for X and Y pole coordinates, X and Y pole coordinate rates and LOD, respectively. In detail, for GC solution, the standard deviation (STD) is 62.9 and 57.4 μas for X and Y pole coordinates, 81.3 and 85.7 μas/d for X and Y pole coordinate rates, 7.8 μs/d for LOD. (2) the STD of BDS solution is 86.2 μas, 79.9 μas, 118.9 μas/d , 111.5 μas/d , and 11.8 μs/d for pole coordinates, their rates and LOD, which has an improvement of 10 %, 3 % for pole coordinates, 5 %, 5 % for pole coordinate rates than BDS-3 and BDS-M solutions, respectively. In terms of the STD for LOD, the BDS solution leads to a decrease about 5 % comparing with BDS-3 solution but has little difference with BDS-M solution. (3) From the point view of spectrum analysis, comparing with those from BDS-3 and BDS-M, the spurious signals in the ERPs estimates derived from BDS can be reduced, demonstrating the superior contribution of BDS-2 and IGSO satellites. The GC combination and 3-day arc solution are proved to further mitigate the artificial signals.

Visually Induced Motion Sickness on the Horizon

Visually induced motion sickness is an unpleasant but common side-effect of many simulations and VR-applications. We investigated whether an earth-fixed reference frame provided in the simulation is able to reduce motion sickness. To do so, we created a moving starfield that did not contain any indicators of the spatial orientation of the observer. As the observer was simulated to move through the randomly oscillating starfield, a time-to-contact task had to be carried out. Two colored stars on collision course with each other had to be spotted, then they disappeared and the time of their collision had to be judged. Eye-movements, task performance, and motion sickness were recorded. This condition without visual reference to the observer's upright was supplemented with three conditions containing either an earth-fixed fixation cross, an earth-fixed horizon line, or a line that was yoked to the head. Results show that only the earth-fixed horizon was able to significantly reduce visually induced motion sickness. Thus, a mere earth-stationary anchor does not suffice, a clear indication of earth horizontal seems necessary to reap a modest benefit.

DESMEX: A novel system development for semi-airborne electromagnetic exploration

There is a clear demand to increase detection depths in the context of raw material exploration programs. Semi-airborne electromagnetic (semi-AEM) methods can address these demands by combining the advantages of powerful transmitters deployed on the ground with efficient helicopter-borne mapping of the magnetic field response in the air. The penetration depth can exceed those of classic airborne EM systems because low frequencies and large transmitter-receiver offsets can be realized in practice. A novel system has been developed that combines high-moment horizontal electric bipole transmitters on the ground with low-noise three-axis induction coil magnetometers, a three-axis fluxgate magnetometer, and a laser gyro inertial measurement unit integrated within a helicopter-towed airborne platform. The attitude data are used to correct the time series for motional noise and subsequently to rotate into an earth-fixed reference frame. In a second processing step, and as opposed to existing semi-AEM systems, we transform the data into the frequency domain and estimate the complex-valued transfer functions between the received magnetic field components and the synchronously recorded injection current by regression analysis. This approach is similar to the procedure used in controlled-source EM. For typical source bipole moments of 20–40 kAm and for rectangular current waveforms with a fundamental frequency of approximately 10 Hz, we can estimate reliable three-component (3C) transfer functions in the frequency range from 10 to 5000 Hz over a measurement area of [Formula: see text] for a single source installation. The system has the potential to be used for focused exploration of deep targets.

2D Necklace Flower Constellations applied to Earth observation missions

This work focuses on the nominal design and later maintenance of satellite constellations based on the 2D Necklace Flower Constellations for their application in Earth observation missions. To that end, we introduce a generalization of the 2D Necklace Flower Constellations formulation to adapt the methodology to constellations whose satellites have different mission requirements, while still allowing to reduce the searching space in satellite constellation design. Moreover, this design is combined with its dual distribution in the Earth Centered–Earth Fixed reference frame to obtain additional information about the dynamic of the system, including the sub-satellite point revisiting time, or the relative to Earth distribution. This is used to optimize the constellation in terms of maximum uniformity of the distribution with respect to the Earth. Finally, a detailed example of application of this design methodology is presented, where a constellation based on satellites with different mission requirements is considered.

A sliding grid based method for the roll decay simulation

The paper describes a novel technique meant to support the numerical prediction of the roll decay for a ship hull equipped with bilge keels in an attempt of establishing a methodology for accurate prediction of the damping forces which occur during the oscillation. The numerical simulation is achieved by making use of the ISIS-CFD solver, part of the FineTM/Marine package available in the NUMECA suite. The solver is based on finite volume method to build the spatial discretization for the governing equation to solve the incompressible unsteady RANSE in a global approach. Closure to the turbulence is achieved by making use of the detached eddy simulation model which has been found as being enough accurate. All the computations are performed in respect to an earth-fixed Cartesian reference frame with only one degree of freedom i.e. roll motion. The validation of the computed solution is done through the comparisons with the experimental data.

Estimation of free core resonance parameters based on long-term strain observations in the diurnal frequency band

The free core nutation (FCN) is one of the Earth’s rotational eigenmodes, which is caused by the retrograde motion of the liquid core relative to the mantle. The FCN period and Q-factor are determined by the elastic properties of the core/mantle boundary (CMB) and their electromagnetic interaction. In the celestial coordinate system, the FCN period is about 430 days; in the Earth-fixed reference frame this effect manifests itself in the form of the free core resonance (FCR) whose frequency falls in the diurnal tidal band. FCR observation requires highly accurate measurement of the amplitudes and phases of the near-diurnal tidal waves. In particular, the parameter estimates for minor waves K1, P1, Ψ1, and Φ1 are critically important for evaluating the FCR effect, i.e., the period and decay of this resonant mode. The progress in the experimental study of FCR is mainly due to the accumulation of the data from superconducting gravimeters and VLBI; at the same time, also the data of the precision laser strainmeters were used. In this work, the FCR effect is studied based on the long-term strain precision records by two European stations: Baksan, Russia (laser interferometer–strainmeter with a measuring armlength of 75 m [Milyukov et al., 2005; 2007] and Gran Sasso, Italy (two perpendicular laser interferometer–strainmeters, BA and BC, each with a measuring armlength of 90 m [Amoruso and Crescentini, 2009]).

Estimation of Free Core Resonance Parameters Based on Long-Term Strain Observations in the Diurnal Frequency Band

The free core nutation (FCN) is one of the Earth’s rotational eigenmodes, which is caused by the retrograde motion of the liquid core relative to the mantle. The FCN period and Q-factor are determined by the elastic properties of the core/mantle boundary (CMB) and their electromagnetic interaction. In the celestial coordinate system, the FCN period is about 430 days; in the Earth-fixed reference frame this effect manifests itself in the form of the free core resonance (FCR) whose frequency falls in the diurnal tidal band. FCR observation requires highly accurate measurement of the amplitudes and phases of the near-diurnal tidal waves. In particular, the parameter estimates for minor waves K1, P1, Ψ1, and Φ1 are critically important for evaluating the FCR effect, i.e., the period and decay of this resonant mode. The progress in the experimental study of FCR is mainly due to the accumulation of the data from superconducting gravimeters and VLBI; at the same time, also the data of the precision laser strainmeters were used. In this work, the FCR effect is studied based on the long-term strain precision records by two European stations: Baksan, Russia (laser interferometer–strainmeter with a measuring armlength of 75 m [Milyukov et al., 2005; 2007] and Gran Sasso, Italy (two perpendicular laser interferometer–strainmeters, BA and BC, each with a measuring armlength of 90 m [Amoruso and Crescentini, 2009]).

Vision algorithms for fixed-wing unmanned aerial vehicle landing system

Autonomous landing has become a core technology of unmanned aerial vehicle (UAV) guidance, navigation and control system in recent years. As a novel autonomous landing approach, computer vision has been studied and applied in rotary-wing UAV landing successfully. This paper aims to fixed-wing UAV and focus on two problems: how to find runway only depending on airborne front-looking camera and how to align UAV with the designated landing runway. The paper can be divided into two parts to solve above two problems respectively. In the first part, the paper firstly presents an algorithm of region of interest (ROI) detection, which is based on spectral residual saliency map, and then an algorithm of feature vector extraction based on sparse coding and spatial pyramid matching (SPM) is proposed, finally, ROI including designated landing runway is recognized by a linear support vector machine. In the second part, the paper presents an approach of relative position and pose estimation between UAV and landing runway. Estimation algorithm firstly selects five feature points on the runway surface, and then establishes a new earth-fixed reference frame, finally uses orthogonal iteration to estimate landing parameters including three parameters of distance, height and offset, and three pose parameters of roll, yaw, pitch. The experimental results verify the effectiveness of the algorithms proposed in this paper.

Framing visual roll-motion affects postural sway and the subjective visual vertical.

Effects of visual roll-motion on postural sway and the subjective visual vertical (SVV) often is studied using mechanical devices, whereas electronic displays offer cheaper and more flexible alternatives. These devices typically emit and reflect light scattered by the edges of the screen, providing Earth-fixed cues of verticality. These cues may decrease the effects of rotating stimuli, a possibility that has not been studied explicitly before in one experimental design. We exposed 16 participants to a visual dot pattern, either stationary, or rotating in roll, that was or was not surrounded by a visible Earth-fixed reference frame. To eliminate unintended visual cues, the experiment was performed in complete darkness and participants wore neutral density goggles passing only 1% of light. Postural sway was measured using a force platform. SVV measurements were obtained from a visible rod. To monitor the participants, motion sickness severity was obtained with an 11-point rating scale. Results showed that the presence of an Earth-fixed frame significantly decreased the effect of the rotating pattern on postural sway and SVV deviations. Therefore, when studying subjective verticality related effects of visual stimuli, it is imperative that all visual Earth-fixed cues are not just minimized but completely eliminated. The observation that an Earth-fixed frame significantly decreased the effect of the rotating pattern on both postural sway and the SVV points towards a common neural origin, possibly involving a neural representation of verticality. Finally, we showed that an electronic screen can yield similar effect sizes as those taken from the literature using mechanical devices.Electronic supplementary materialThe online version of this article (doi:10.3758/s13414-016-1150-3) contains supplementary material, which is available to authorized users.

The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations

The precise ionosphere modeling is crucial and remains a challenge for GPS positioning and navigation, as well as many other Earth observation systems. In this research, two approaches have been proposed to model the vertical total electron content (VTEC) of the ionosphere using spherical slepian function. For the two-dimensional case, VTEC has been modeled in a sun-fixed reference frame and the three-dimensional approach based on the system of the three-dimensional base functions has been defined as the tensor product of the spherical slepian function for the longitude and latitude in an Earth-fixed reference frame, and the polynomial B-spline function for time. Rather than the spherical harmonics, the spherical slepian functions can be employed to produce the locally and globally orthogonal bases to optimally represent the data in any arbitrary region up to a given degree. The spherical slepian functions have been applied to the real data obtained from the ground-based GPS observation across the western part of the USA.

Measuring dynamics of the subjective vertical and tilt using a joystick

Humans are able to estimate the vertical direction of an Earth fixed reference frame, which estimate is known as the subjective vertical (SV). To identify the SV, a distinction must be made between accelerations due to self-motion and gravity. Previous studies on this topic measured the SV using a variety of methods possibly affecting the outcome differently. In this study subjects were sinusoidally moved around their naso-occipital axis and their SV was dynamically measured using a joystick. In half the experimental conditions, the joystick was moved with the motion and was kept vertical on other experimental conditions, thus moving against self-motion. Although physically indicating the same angle, the average perceived angle was larger when moving the joystick with the motion than against. The difference can be explained by assuming an idiotropic vector being at issue when measuring the subjective vertical, and not when measuring subjective tilt.

Estimation of Human Foot Motion During Normal Walking Using Inertial and Magnetic Sensor Measurements

A foot motion filtering algorithm is presented for estimating foot kinematics relative to an earth-fixed reference frame during normal walking motion. Algorithm input data are obtained from a foot-mounted inertial/magnetic measurement unit. The sensor unit contains a three-axis accelerometer, a three-axis angular rate sensor, and a three-axis magnetometer. The algorithm outputs are the foot kinematic parameters, which include foot orientation, position, velocity, acceleration, and gait phase. The foot motion filtering algorithm incorporates novel methods for orientation estimation, gait detection, and position estimation. Accurate foot orientation estimates are obtained during both static and dynamic motion using an adaptive-gain complementary filter. Reliable gait detection is accomplished using a simple finite state machine that transitions between states based on angular rate measurements. Accurate position estimates are obtained by integrating acceleration data, which has been corrected for drift using zero velocity updates. Algorithm performance is examined using both simulations and real-world experiments. The simulations include a simple but effective model of the human gait cycle. The simulation and experimental results indicate that a position estimation error of less than 1% of the total distance traveled is achievable using commonly available commercial sensor modules.

Perceived Surface Slant Is Systematically Biased in the Actively-Generated Optic Flow

Humans make systematic errors in the 3D interpretation of the optic flow in both passive and active vision. These systematic distortions can be predicted by a biologically-inspired model which disregards self-motion information resulting from head movements (Caudek, Fantoni, & Domini 2011). Here, we tested two predictions of this model: (1) A plane that is stationary in an earth-fixed reference frame will be perceived as changing its slant if the movement of the observer's head causes a variation of the optic flow; (2) a surface that rotates in an earth-fixed reference frame will be perceived to be stationary, if the surface rotation is appropriately yoked to the head movement so as to generate a variation of the surface slant but not of the optic flow. Both predictions were corroborated by two experiments in which observers judged the perceived slant of a random-dot planar surface during egomotion. We found qualitatively similar biases for monocular and binocular viewing of the simulated surfaces, although, in principle, the simultaneous presence of disparity and motion cues allows for a veridical recovery of surface slant.

B-spline modeling of VTEC over Turkey using GPS observations

In this study we propose two approaches to model the Vertical Total Electron Content (VTEC) of the ionosphere with quadratic B-spline functions. For the 2-D case, VTEC is modeled in a Sun-fixed reference frame. In the 3-D approach, the 2-D model is extended to represent the temporal variations in an Earth-fixed reference frame. The localizing features of B-splines allow resolving finer structures for the regions with a sufficient number of observations by increasing the level of functions. To reduce the effects of outliers, Iteratively Re-weighted Least Squares (IRLS) with a bi-square weighting function as a robust regression algorithm is applied for parameter estimation. Another iterative method LSQR is performed for the solution of the linear systems providing a regularization effect for ill-conditioned problems. B-spline approaches are applied to real data obtained from the ground-based GPS observations over Turkey. Results are compared with the solutions of the Bernese GPS Software.

Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame

The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various problems of satellite geodesy and celestial mechanics.