scholarly journals Numerical Quantification of Controllability in the Null Space for Redundant Manipulators

2021 ◽  
Vol 11 (13) ◽  
pp. 6190
Author(s):  
Seonwoo Kim ◽  
Seongseop Yun ◽  
Dongjun Shin
Keyword(s):  
Root Mean Square ◽  
Null Space ◽  
Robotic Manipulators ◽  
Robotic Arm ◽  
Redundant Manipulators ◽  
Mean Square ◽  
Wide Range ◽  
Sinusoidal Input ◽  
Space Projection ◽  
Rms Error

Redundant motion, which is possible when robotic manipulators are over-actuated, can be used to control robot arms for a wide range of tasks. One of the best known methods for controlling redundancy is the null space projection, which assigns a priority while executing desired tasks. However, when the manipulator is projected into null space, its motion would be limited, since the motion is only permitted in the direction that does not interfere with the primary task. In this study, we have analyzed the null space projector matrix to derive the appropriate direction of the redundant motion by quantifying the allowed motion in each direction. As a result, we have found an ellipsoidal boundary, in which the redundant motion is permitted to move. We have named this ellipsoidal boundary as ’null space quality’ in directions. The proposed null space quality shows similar aspects with that of the robot manipulability, but it reveals a decisively different value when the manipulator operates within the null space. The experimental results showed that the robotic manipulator tracked the sinusoidal input trajectory with reduced root mean square (RMS) error by 33.84%. Furthermore, we have demonstrated the obstacle avoidance of a robotic arm utilizing the null space projector while considering the null space quality.

Seasonal glacier surface velocity fluctuation and contribution of the Eastern and Western Tributary Glaciers in Amery Ice Shelf, East Antarctica

2019 ◽  
Vol 9 (1) ◽  
pp. 49-60
Author(s):  
Shridhar Digambar Jawak ◽  
Shubhang Kumar ◽  
Alvarinho Joaozinho Luis ◽  
Prashant Hemendra Pandit ◽  
Sagar Filipe Wankhede
Keyword(s):  
Remote Sensing ◽  
Root Mean Square ◽  
Winter Season ◽  
Maximum Velocity ◽  
Surface Velocity ◽  
Mean Square ◽  
Ice Shelf ◽  
Amery Ice Shelf ◽  
Rms Error ◽  
Western Side

Glaciers play a crucial role in the study of the climate change pattern of the Earth. Remote sensing with access to large archives of data has the ability to monitor glaciers frequently throughout the year. Therefore, remote sensing is the most beneficial tool for the study of glacier dynamics. Fed by many tributaries from different sides, the Amery Ice Shelf (AIS) is one of the largest ice shelves that drains ice from the Antarctic ice sheet into the Southern Ocean. This study focuses on the eastern and the western tributaries of the AIS. The primary objective of the study was to derive the velocity of the tributary glaciers and the secondary objective was to compare variations in their velocities between the summer and winter season. This study was carried on using the European Space Agency’s (ESA) Sentinel-1 satellite’s Synthetic Aperture Radar (SAR) data acquired from the Sentinel data portal. Offset tracking method was applied to the Ground Range Detected (GRD) product of the Sentinel-1 interferometric wide (IW) swath acquisition mode. The maximum velocity in summer was observed to be around 610 m/yr in the eastern tributary glacier meeting the ice shelf near the Pickering Nunatak, and around 345 m/yr in the Charybdis Glacier Basin from the western side. The maximum velocity in the winter was observed to be 553 m/yr in the eastern side near the Pickering Nunatak whereas 323 m/yr from the western side in the Charybdis Glacier Basin. The accuracy of the derived glacier velocities was computed using bias and root mean square (RMS) error. For the analysis, the publicly available velocity datasets were used. The accuracy based on RMS error was observed to be 85-90% for both seasons with bias values up to 25 m/yr and root mean square error values up to 30 m/yr.

Measurements of diapycnal diffusivities in stratified fluids

2001 ◽  
Vol 442 ◽  
pp. 267-291 ◽  
Author(s):  
MICHAEL E. BARRY ◽  
GREGORY N. IVEY ◽  
KRAIG B. WINTERS ◽  
JÖRG IMBERGER
Keyword(s):  
Root Mean Square ◽  
Buoyancy Frequency ◽  
Data Sets ◽  
Laboratory System ◽  
Mean Square ◽  
Wide Range ◽  
Vertical Grid ◽  
Order Of Magnitude ◽  
Set Up ◽  
Rate Of Dissipation

Linearly stratified salt solutions of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental set-up allowed the independent direct measurement of a root mean square turbulent lengthscale Lt, turbulent diffusivity for mass Kρ, rate of dissipation of turbulent kinetic energy ε, buoyancy frequency N and viscosity v, as time and volume averaged quantities. The behaviour of both Lt and Kρ was characterized over a wide range of the turbulence intensity measure, ε/vN2, and two regimes were identified.In the more energetic of these regimes (Regime E, where 300 < ε/vN2 < 105), Lt was found to be a function of v, κ and N, whilst Kρ was a function of v, κ and (ε/vN2)1/3. From these expressions for Lt and Kρ, a scaling relation for the root mean square turbulent velocity scale Ut was derived, and this relationship showed good agreement with direct measurements from other data sets.In the weaker turbulence regime (Regime W, where 10 < ε/vN2 < 300) Kρ was a function of v, κ and ε/vN2.For 10 < ε/vN2 < 1000, our directly measured diffusivities, Kρ, are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For ε/vN2 > 1000, our measured diffusivities diverge from the model prediction. For example, at ε/vN2 ≈ 104 there is at least an order of magnitude difference between the measured and predicted diffusivities.

Obstacle avoidance for kinematically redundant manipulators using polyhedral approximations

2003 ◽  
Vol 217 (5) ◽  
pp. 533-542 ◽  
Author(s):  
X Zhu ◽  
H Qiao
Keyword(s):  
Obstacle Avoidance ◽  
Null Space ◽  
Convex Polyhedra ◽  
Redundant Manipulators ◽  
Essential Requirement ◽  
Joint Configuration ◽  
Projection Scheme ◽  
Almost Everywhere ◽  
Space Projection ◽  
Polyhedral Approximations

Collision avoidance is an essential requirement for a manipulator to complete a task in an environment with obstacles. In this paper, a pseudo-distance function is presented for a pair of convex polyhedra, along with the algorithm for calculating its derivative. On this basis, a potential field-based approach for obstacle avoidance of kinematically redundant manipulators is developed, with the manipulator links and the environmental obstacles being geometrically modelled as a set of convex polyhedra. The potential function is differentiable almost everywhere with respect to the joint configuration variables of the manipulator. It is incorporated in the ‘null space projection scheme’ in order to achieve obstacle avoidance. Simulation examples are presented to show the effectiveness of the proposed method.

scholarly journals Minimum Local Emissivity Variance Retrieval of Cloud Altitude and Effective Spectral Emissivity—Simulation and Initial Verification

2004 ◽  
Vol 43 (5) ◽  
pp. 795-809 ◽  
Author(s):  
Hung-Lung Huang ◽  
William L. Smith ◽  
Jun Li ◽  
Paolo Antonelli ◽  
Xiangqian Wu ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Spectral Resolution ◽  
Single Layer ◽  
Spectral Emissivity ◽  
Pressure Level ◽  
High Spectral Resolution ◽  
Mean Square ◽  
Atmospheric Conditions ◽  
Wide Range ◽  
Mean Square Errors

Abstract This paper describes the theory and application of the minimum local emissivity variance (MLEV) technique for simultaneous retrieval of cloud pressure level and effective spectral emissivity from high-spectral-resolution radiances, for the case of single-layer clouds. This technique, which has become feasible only with the recent development of high-spectral-resolution satellite and airborne instruments, is shown to provide reliable cloud spectral emissivity and pressure level under a wide range of atmospheric conditions. The MLEV algorithm uses a physical approach in which the local variances of spectral cloud emissivity are calculated for a number of assumed or first-guess cloud pressure levels. The optimal solution for the single-layer cloud emissivity spectrum is that having the “minimum local emissivity variance” among the retrieved emissivity spectra associated with different first-guess cloud pressure levels. This is due to the fact that the absorption, reflection, and scattering processes of clouds exhibit relatively limited localized spectral emissivity structure in the infrared 10–15-μm longwave region. In this simulation study it is shown that the MLEV cloud pressure root-mean-square errors for a single level with effective cloud emissivity greater than 0.1 are ∼30, ∼10, and ∼50 hPa, for high (200– 300 hPa), middle (500 hPa), and low (850 hPa) clouds, respectively. The associated cloud emissivity root-mean-square errors in the 900 cm−1 spectral channel are less than 0.05, 0.04, and 0.25 for high, middle, and low clouds, respectively.

Evaluation of the APSIM-Wheat model in terms of different cultivars, management regimes and environmental conditions

2012 ◽  
Vol 92 (5) ◽  
pp. 937-949 ◽  
Author(s):  
Yi Zhang ◽  
Liping Feng ◽  
Enli Wang ◽  
Jing Wang ◽  
Baoguo Li
Keyword(s):  
Root Mean Square ◽  
Environmental Conditions ◽  
Field Experiments ◽  
Growth And Yield ◽  
Planting Density ◽  
Mean Square ◽  
Sowing Dates ◽  
Wide Range ◽  
Management Regimes ◽  
Mean Square Errors

Zhang, Y., Feng, L., Wang, E., Wang, J. and Li, B. 2012. Evaluation of the APSIM-Wheat model in terms of different cultivars, management regimes and environmental conditions. Can. J. Plant Sci. 92: 937–949. Wheat is one of the most important crops in the world, and wheat models have been widely used to study yield responses to changes in management and climate. However, less information is available on how a wheat model performs in simulation of wheat response to changes in varieties, sowing dates and planting densities across space. This study presents an evaluation of the APSIM-Wheat model using data from field experiments consisting of three sowing dates, two and three crop varieties and three planting densities in a split-split plot design at three ecological sites from 2008 to 2010 in the North China Plain. The results show that the APSIM-Wheat model could capture a large part of the variation in phenology, biomass and yield for the same variety across sites. However, errors of simulation in phenology and yield were increased with delay in sowing date, with the average absolute root mean square errors of 2 d, 3 d, and 3–4 d in phenology, and the normalized root mean square error (RMSEn) of 7–12%, 11–16%, 16–22% in yield at early, medium, and late sowing dates, respectively. Simulation of yield achieved poor results with decreased planting density, with average RMSEn of 9–12%, 11–12%, and 16–19% at high, medium, and low density, respectively. Additionally, the simulation behaved in a complex manner, and the errors varied greatly with different combinations of sowing dates and planting densities. These alerted us that the model should be used cautiously to simulate growth and yield over a wide range of sowing dates and planting densities. Improved modeling of the responses of wheat growth to extreme temperatures during winter and spring periods, and to varying planting densities is needed for better future prediction. Other areas of model improvements are also discussed.

The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer

1964 ◽  
Vol 18 (1) ◽  
pp. 117-143 ◽  
Author(s):  
D. B. Spalding ◽  
S. W. Chi
Keyword(s):  
Experimental Data ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mixing Length ◽  
Mean Square ◽  
Temperature Ratio ◽  
Wide Range ◽  
Mixing Length Theory ◽  
Meansquare Error

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).A new calculation procedure is developed from the postulate that a unique relation exists betweencfFcandRFRwherecfis the drag coefficient,Ris the Reynolds number, andFcandFRare functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for bothFcandFRto be deduced empirically, soFcis calculated by means of mixing-length theory andFRis found semi-empirically. Tables and charts of values ofFcandFRare presented for a wide range ofMGandTS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

scholarly journals ANALISIS KALIBRASI MODEL HSS CLARK DENGAN MENGGUNAKAN PROGRAM HEC-HMS

2018 ◽  
Vol 6 (2) ◽  
pp. 15-22
Author(s):  
Syahrul Ramadhani ◽  
Yohanna Lilis Handayani ◽  
Sigit Sutikno
Keyword(s):  
Objective Function ◽  
Root Mean Square ◽  
Mean Square ◽  
Loss Model ◽  
Percent Error ◽  
Rms Error

Penerapan Hidrograf Satuan Sintetik (HSS) Clark pada DAS Lubuk Bendahara membutuhkan analisis yanglebih detail. Data curah hujan dan pencatatan muka air otomatis (AWLR) lapangan diperlukan sebagai bahankalibrasi. Parameter kehilangan air (loss model), aliran dasar (baseflow) dan transformasi aliran (transformmethod) dalam hidrograf satuan sintetik Clark dikalibrasi dengan menggunakan program HEC-HMS. Proseskalibrasi ini menggunakan tiga metode objective function yaitu Peak Weighted Root Mean Square (RMS) Error,Percent Error Peak dan Percent Error Volume. Hasil kalibrasi menunjukkan nilai yang dihasilkanmenggunakan metode Peak-Weighted RMS Error sebesar 2,57, selisih volume -0,09% dan selisih debit puncak1,1%.

scholarly journals Development of observation-based global multilayer soil moisture products for 1970 to 2016

2021 ◽  
Vol 13 (9) ◽  
pp. 4385-4405
Author(s):  
Yaoping Wang ◽  
Jiafu Mao ◽  
Mingzhou Jin ◽  
Forrest M. Hoffman ◽  
Xiaoying Shi ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Root Mean Square ◽  
Land Surface ◽  
Soil Layer ◽  
Added Value ◽  
Surface Model ◽  
Mean Square ◽  
Wide Range ◽  
Mean Square Errors

Abstract. Soil moisture (SM) datasets are critical to understanding the global water, energy, and biogeochemical cycles and benefit extensive societal applications. However, individual sources of SM data (e.g., in situ and satellite observations, reanalysis, offline land surface model simulations, Earth system model – ESM – simulations) have source-specific limitations and biases related to the spatiotemporal continuity, resolutions, and modeling and retrieval assumptions. Here, we developed seven global, gap-free, long-term (1970–2016), multilayer (0–10, 10–30, 30–50, and 50–100 cm) SM products at monthly 0.5∘ resolution (available at https://doi.org/10.6084/m9.figshare.13661312.v1; Wang and Mao, 2021) by synthesizing a wide range of SM datasets using three statistical methods (unweighted averaging, optimal linear combination, and emergent constraint). The merged products outperformed their source datasets when evaluated with in situ observations (mean bias from −0.044 to 0.033 m3 m−3, root mean square errors from 0.076 to 0.104 m3 m−3, Pearson correlations from 0.35 to 0.67) and multiple gridded datasets that did not enter merging because of insufficient spatial, temporal, or soil layer coverage. Three of the new SM products, which were produced by applying any of the three merging methods to the source datasets excluding the ESMs, had lower bias and root mean square errors and higher correlations than the ESM-dependent merged products. The ESM-independent products also showed a better ability to capture historical large-scale drought events than the ESM-dependent products. The merged products generally showed reasonable temporal homogeneity and physically plausible global sensitivities to observed meteorological factors, except that the ESM-dependent products underestimated the low-frequency temporal variability in SM and overestimated the high-frequency variability for the 50–100 cm depth. Based on these evaluation results, the three ESM-independent products were finally recommended for future applications because of their better performances than the ESM-dependent ones. Despite uncertainties in the raw SM datasets and fusion methods, these hybrid products create added value over existing SM datasets because of the performance improvement and harmonized spatial, temporal, and vertical coverages, and they provide a new foundation for scientific investigation and resource management.

Effective secondary task execution of redundant manipulators

Robotica ◽  
1998 ◽  
Vol 16 (4) ◽  
pp. 457-462 ◽  
Author(s):  
Jadran Lenarčič
Keyword(s):  
Projection Operator ◽  
Secondary Task ◽  
Numerical Experiments ◽  
Null Space ◽  
Numerical Procedure ◽  
Redundant Manipulators ◽  
Space Operator ◽  
Task Execution ◽  
Weighting Matrix ◽  
Space Projection

In standard pseudoinverse-based approaches to treat redundant manipulators, the vector of joint increments that corresponds to a desired motion in the space of the secondary task is projected in the Jacobian null space associated with the primary task. In general, this projection may distort the projected vector, so that the secondary task may not adequately be executed. A usual remedy is to rotate the null space projection operator by using a special-purpose weighting matrix. The problem, however, is that this rotation cannot be enforced arbitrarily since it influences the manipulator's performance. In our work we propose an algorithm that is independent on the chosen null space operator and always provides the best attainable motion in the space of the secondary task. Hence, the secondary task is executed more efficiently and the numerical procedure is more robust. A series of numerical experiments confirmed these results.

scholarly journals Maximum Likelihood Position Location with a Limited Number of

2011 ◽  
Vol 9 (01) ◽  
Author(s):  
D. Munoz-Rodriguez ◽  
L. Suarez-Robles ◽  
C. Vargas-Rosales ◽  
J. R. Rodriguez-Cruz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Root Mean Square ◽  
Likelihood Estimation ◽  
Error Distribution ◽  
Location Information ◽  
Mean Square ◽  
Position Location ◽  
Rms Error ◽  
Simulation Results

A Position Location (PL) scheme for mobile users on the outskirts of coverage areas is presented. The proposed methodology makes it possible to obtain location information with only two land-fixed references. We introduce a¨general formulation and show that maximum-likelihood estimation can provide adequate PL information in this scenario. The Root Mean Square (RMS) error and error-distribution characterization are obtained for different propagation scenarios. In addition, simulation results and comparisons to another method are provided showing the accuracy and the robustness of the method proposed. We study accuracy limits of the proposed methodology for different propagation environments and show that even in the case of mismatch in the error variances, good PL estimation is feasible.

Sign in / Sign up

Export Citation Format

Share Document