Space Positioning of the 5-DOF Robotic Excavator

2011 ◽  
Vol 130-134 ◽  
pp. 3531-3535
Author(s):  
Xi Hua Xie ◽  
Liang Zhou ◽  
Qing Hua He
Keyword(s):  
Coordinate Transformation ◽  
Dimensional Space ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Transformation Matrix ◽  
The Body ◽  
Three Dimensions ◽  
Angle Sensor ◽  
Robotic Excavator ◽  
Space Angle

The carriage positioning of excavator in three-dimensions (3-D) is the precondition of the robotic excavator starting roboticized works. In order to get the carriage position of excavator in three-dimensional space, angle sensors of such joints as bucket, arm, boom, and boom deflection are brought to bear. At the same time, a 2D-inclination sensor is introduced to check the list and pitch angles of the platform, and a rotatory angle sensor is introduced to check swing angle of the platform. And a laser receiver was mounted on the arm to measure the relative height of the arm to the laser beam from ground sender. Then the kinematic model is established, the coordinate transformation matrix of carriage positioning is formulated, and the height of the body relative to the ground is gotten. As a result, the coordinate transformation matrix of the bucket relative to the ground and the digging depth are formulated. That makes the excavator orient bucket precisely and set excavation depth exactly, and make automotive elaborate excavation come true.

Distributed Formation Control of UAVs for Circumnavigating a Moving Target in Three-Dimensional Space

2021 ◽  
Vol 01 (03) ◽  
Author(s):  
Yanhong Luo ◽  
Ao Bai ◽  
Huaguang Zhang
Keyword(s):  
Feedback Linearization ◽  
Formation Control ◽  
Control Method ◽  
Dimensional Space ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Moving Target ◽  
Dynamic Feedback ◽  
Space Angle ◽  
Three Dimensional Space

In this paper, a novel formation control strategy is proposed to address the target tracking and circumnavigating problem of multi-UAV formation. First, two sets of definitions, space angle definition and space vector definition, are presented in order to describe the flight state and construct the desired relative velocity. Then, the relative kinematic model between the UAV and the moving target is established. The distributed control law is constructed by using dynamic feedback linearization so as to realize the tracking and circumnavigating control with the desired velocity, circling radius and relative angular spacing. Next, the exponential stability of the closed-loop system is further guaranteed by properly choosing some corresponding parameters based on the Lyapunov method. Finally, the numerical simulation is carried out to verify the effectiveness of the proposed control method.

scholarly journals Determination of load distribution in a given medium according to the values of the loads at certain points

2021 ◽  
pp. 167-175
Author(s):  
Oleksandr Mostovenko ◽  
Serhii Kovalov ◽  
Svitlana Botvinovska
Keyword(s):  
Boundary Conditions ◽  
Load Distribution ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Geometric Model ◽  
Three Dimensional ◽  
The Body ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

Taking into account force, temperature and other loads, the stress and strain state calculations methods of spatial structures involve determining the distribution of the loads in the three-dimensional body of the structure [1, 2]. In many cases the output data for this distribution can be the values of loadings in separate points of the structure. The problem of load distribution in the body of the structure can be solved by three-dimensional discrete interpolation in four-dimensional space based on the method of finite differences, which has been widely used in solving various engineering problems in different fields. A discrete conception of the load distribution at points in the body or in the environment is also required for solving problems by the finite elements method [3-7]. From a geometrical point of view, the result of three-dimensional interpolation is a multivariate of the four-dimensional space [8], where the three dimensions are the coordinates of a three-dimensional body point, and the fourth is the loading at this point. Such interpolation provides for setting of the three coordinates of the point and determining the load at that point. The simplest three-dimensional grid in the three-dimensional space is the grid based on a single sided hypercube. The coordinates of the nodes of such a grid correspond to the numbering of nodes along the coordinate axes. Discrete interpolation of points by the finite difference method is directly related to the numerical solutions of differential equations with given boundary conditions and also requires the setting of boundary conditions. If we consider a three-dimensional grid included into a parallelepiped, the boundary conditions are divided into three types: 1) zero-dimensional (loads at points), where the three edges of the grid converge; 2) one-dimensional (loads at points of lines), where the four edges of the grid converge; 3) two-dimensional (loads at the points of faces), where the five edges of the grid converge. The zero-dimensional conditions are boundary conditions for one-dimensional interpolation of the one-dimensional conditions, which, in turn, are boundary conditions for two-dimensional conditions, and the two-dimensional conditions are boundary conditions for determining the load on the inner points of the grid. If a load is specified only at certain points of boundary conditions, then the interpolation problem is divided into three stages: one-dimensional load interpolation onto the line nodes, two-dimensional load interpolation onto the surface nodes and three-dimensional load interpolation onto internal grid nodes. The proposed method of discrete three-dimensional interpolation allows, according to the specified values of force, temperature or other loads at individual points of the three-dimensional body, to interpolate such loads on all nodes of a given regular three-dimensional grid with cubic cells. As a result of interpolation, a discrete point framework of the multivariate is obtained, which is a geometric model of the distribution of physical characteristics in a given medium according to the values of these characteristics at individual points.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

The Brain Stem Saccadic Burst Generator Encodes Gaze in Three-Dimensional Space

2008 ◽  
Vol 99 (5) ◽  
pp. 2602-2616 ◽  
Author(s):  
Marion R. Van Horn ◽  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Brain Stem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Saccadic Eye Movements ◽  
Three Dimensions ◽  
Related Information ◽  
Computer Based ◽  
Different Depths ◽  
The Brain

When we look between objects located at different depths the horizontal movement of each eye is different from that of the other, yet temporally synchronized. Traditionally, a vergence-specific neuronal subsystem, independent from other oculomotor subsystems, has been thought to generate all eye movements in depth. However, recent studies have challenged this view by unmasking interactions between vergence and saccadic eye movements during disconjugate saccades. Here, we combined experimental and modeling approaches to address whether the premotor command to generate disconjugate saccades originates exclusively in “vergence centers.” We found that the brain stem burst generator, which is commonly assumed to drive only the conjugate component of eye movements, carries substantial vergence-related information during disconjugate saccades. Notably, facilitated vergence velocities during disconjugate saccades were synchronized with the burst onset of excitatory and inhibitory brain stem saccadic burst neurons (SBNs). Furthermore, the time-varying discharge properties of the majority of SBNs (>70%) preferentially encoded the dynamics of an individual eye during disconjugate saccades. When these experimental results were implemented into a computer-based simulation, to further evaluate the contribution of the saccadic burst generator in generating disconjugate saccades, we found that it carries all the vergence drive that is necessary to shape the activity of the abducens motoneurons to which it projects. Taken together, our results provide evidence that the premotor commands from the brain stem saccadic circuitry, to the target motoneurons, are sufficient to ensure the accurate control shifts of gaze in three dimensions.

Cutaneous Receptive Field Organization in the Ventral Posterior Nucleus of the Thalamus in the Common Marmoset

1999 ◽  
Vol 82 (4) ◽  
pp. 1865-1875 ◽  
Author(s):  
P. Wilson ◽  
P. D. Kitchener ◽  
P. J. Snow
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Receptive Fields ◽  
Common Marmoset ◽  
The Body ◽  
Common Marmosets ◽  
Body Regions ◽  
Low Threshold ◽  
The Common ◽  
Receptive Field Organization

The organization of cutaneous receptive fields in the ventroposterior (VP) thalamus of the common marmosets ( Callithrix jacchus) was determined from single-unit recordings, and these data were correlated with the cytochrome oxidase (CO) histochemistry of the thalamus in the same animals. Under continuously maintained ketamine anesthesia, the receptive fields of a total of 192 single units were recorded from the right VP thalamus using 2 MΩ glass microelectrodes. After the receptive fields were mapped, the brains were reacted for CO histochemistry on 50-μm coronal frozen sections through the entire VP thalamus. The majority of units were localized to the CO-reactive regions that define the medial and lateral divisions of VP (VPm and VPl). Apart from the expected finding of the face being represented in VPm and the body in VPl, reconstructing the electrode tracks and unit locations in the histological sections revealed a general association between discrete regions of CO reactivity and the representation of specific body regions. Some low-threshold cutaneous units were apparently localized to VPi (the CO weak regions dorsal, ventral, and interdigitating with, the CO regions of VP). These VPi units were clearly part of the same representational map as the VPl and VPm units. We conclude that the low-threshold cutaneous receptive fields of the marmoset are organized in a single continuous representation of the contralateral body surface, and that this representation can most simply be interpreted as being folded or crumpled into the three-dimensional space of VP thalamus. The folded nature of the body map in VP may be related to the folded nature of VP as revealed by CO histochemistry.

Estimating Three-Dimensional Space from Multiple Two-Dimensional Views

1993 ◽  
Vol 2 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Kristinn R. Thorisson
Keyword(s):  
Visual Search ◽  
Eye Movement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Three Dimensions ◽  
Limiting Factor ◽  
Single Subject ◽  
Search Performance ◽  
Two Dimensional

The most common visual feedback technique in teleoperation is in the form of monoscopic video displays. As robotic autonomy increases and the human operator takes on the role of a supervisor, three-dimensional information is effectively presented by multiple, televised, two-dimensional (2-D) projections showing the same scene from different angles. To analyze how people go about using such segmented information for estimations about three-dimensional (3-D) space, 18 subjects were asked to determine the position of a stationary pointer in space; eye movements and reaction times (RTs) were recorded during a period when either two or three 2-D views were presented simultaneously, each showing the same scene from a different angle. The results revealed that subjects estimated 3-D space by using a simple algorithm of feature search. Eye movement analysis supported the conclusion that people can efficiently use multiple 2-D projections to make estimations about 3-D space without reconstructing the scene mentally in three dimensions. The major limiting factor on RT in such situations is the subjects' visual search performance, giving in this experiment a mean of 2270 msec (SD = 468; N = 18). This conclusion was supported by predictions of the Model Human Processor (Card, Moran, & Newell, 1983), which predicted a mean RT of 1820 msec given the general eye movement patterns observed. Single-subject analysis of the experimental data suggested further that in some cases people may base their judgments on a more elaborate 3-D mental model reconstructed from the available 2-D views. In such situations, RTs and visual search patterns closely resemble those found in the mental rotation paradigm (Just & Carpenter, 1976), giving RTs in the range of 5-10 sec.

scholarly journals On a set of quartic surfaces in space of four dimensions; and a certain involutory transformation

1926 ◽  
Vol 110 (756) ◽  
pp. 700-708
Keyword(s):  
Present Note ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quartic Surface ◽  
Four Dimensions ◽  
Cubic Surfaces ◽  
Mutual Relations ◽  
Quartic Surfaces ◽  
Three Dimensional Space

There exists in space of four dimensions an interesting figure of 15 lines and 15 points, first considered by Stéphanos (‘Compt. Rendus,’ vol. 93, 1881), though suggested very clearly by Cremona’s discussion of cubic surfaces in three-dimensional space. In connection with the figure of 15 lines there arises a quartic surface, the intersection of two quadrics, which is of importance as giving rise by projection to the Cyclides, as Segre has shown in detail (‘Math. Ann.,’ vol. 24, 1884). The symmetry of the figure suggests, howrever, the consideration of 15 such quartic surfaces; and it is natural to inquire as to the mutual relations of these surfaces, in particular as to their intersections. In general, two surfaces in space of four dimensions meet in a finite number of points. It appears that in this case any two of these 15 surfaces have a curve in common; it is the purpose of the present note to determine the complete intersection of any two of these 15 surfaces. Similar results may be obtained for a system of cubic surfaces in three dimensions, corresponding to those here given for this system of quartic surfaces in four dimensions, since the surfaces have one point in common, which may be taken as the centre of a projection.

Symmetry-adapted digital modeling II. The double-helix B-DNA

2016 ◽  
Vol 72 (3) ◽  
pp. 312-323 ◽  
Author(s):  
A. Janner
Keyword(s):  
Dimensional Space ◽  
Double Helix ◽  
Three Dimensional ◽  
Reduction Factor ◽  
Lattice Points ◽  
Three Dimensions ◽  
Coarse Grained ◽  
Digital Modeling ◽  
Dna Strands ◽  
Dna Double Helix

The positions of phosphorus in B-DNA have the remarkable property of occurring (in axial projection) at well defined points in the three-dimensional space of a projected five-dimensional decagonal lattice, subdividing according to the golden mean ratio τ:1:τ [with τ = (1+\sqrt {5})/2] the edges of an enclosing decagon. The corresponding planar integral indicesn1,n2,n3,n4(which are lattice point coordinates) are extended to include the axial indexn5as well, defined for each P position of the double helix with respect to the single decagonal lattice ΛP(aP,cP) withaP= 2.222 Å andcP= 0.676 Å. A finer decagonal lattice Λ(a,c), witha=aP/6 andc=cP, together with a selection of lattice points for each nucleotide with a given indexed P position (so as to define a discrete set in three dimensions) permits the indexing of the atomic positions of the B-DNA d(AGTCAGTCAG) derived by M. J. P. van Dongen. This is done for both DNA strands and the single lattice Λ. Considered first is the sugar–phosphate subsystem, and then each nucleobase guanine, adenine, cytosine and thymine. One gets in this way a digital modeling of d(AGTCAGTCAG) in a one-to-one correspondence between atomic and indexed positions and a maximal deviation of about 0.6 Å (for the value of the lattice parameters given above). It is shown how to get a digital modeling of the B-DNA double helix for any given code. Finally, a short discussion indicates how this procedure can be extended to derive coarse-grained B-DNA models. An example is given with a reduction factor of about 2 in the number of atomic positions. A few remarks about the wider interest of this investigation and possible future developments conclude the paper.

Analysis on Structure and Morphological of Carton Packaging

2013 ◽  
Vol 442 ◽  
pp. 338-341
Author(s):  
A Qiang Sun
Keyword(s):  
Structural Design ◽  
Body Shape ◽  
Space Form ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Body ◽  
Packaging Materials ◽  
Paper Study ◽  
Structural Morphology ◽  
Three Dimensional Space

The package structure is a three-dimensional space form, so people know the products are in used in the packaging. In packaging materials for paper use is very extensive, paper products are easy to shape the body shape for easy printing and recyclable advantage. This paper study design of the paper packaging structural, combining paper packaging structural design applications to explore the paper packaging structural morphology and environmentalist design consciousness.

scholarly journals Improving Problem-Solving Skills with the Help of Plane-Space Analogies

2013 ◽  
Vol 3 (4) ◽  
pp. 79-98
Author(s):  
László Budai
Keyword(s):  
High School Students ◽  
Problem Solving ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Spatial Thinking ◽  
Great Promise ◽  
School Students ◽  
Problem Solving Skills ◽  
Plane Space

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry programs, GeoGebra and DGS, combined with plane space analogies for the development of spatial thinking and problem-solving skills in the three dimensions of solid geometry.

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