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25 pages, 4664 KiB  
Article
Research on the Influence of Radial Variation of Centroid on the Motion of Spherical Robot
by Long Ma, Minggang Li, Rui Chang and Hanxu Sun
Machines 2024, 12(6), 422; https://doi.org/10.3390/machines12060422 - 19 Jun 2024
Viewed by 758
Abstract
Through the pendulum mechanism inside the spherical shell, the centroid can be varied circumferentially, enabling the spherical robot to achieve omnidirectional flexible movement. Additionally, the radial variation ability of the centroid enables spherical robots to adopt two distinct driving modes: the traditional lower [...] Read more.
Through the pendulum mechanism inside the spherical shell, the centroid can be varied circumferentially, enabling the spherical robot to achieve omnidirectional flexible movement. Additionally, the radial variation ability of the centroid enables spherical robots to adopt two distinct driving modes: the traditional lower pendulum driving mode and the inverted pendulum driving mode. There are two manifestations of radial variation in the centroid: having different radial positions of the centroid and achieving radial movement of the centroid. Focusing on these two manifestations, experimental data are obtained through different motion velocities and different motion slopes to conduct research on the influence of radial variation in the centroid on the motion of spherical robots. Based on the experimental data, multiple indicators are analyzed, including response speed, convergence speed, stability, and overshoot, as well as steering ability, climbing ability, and output power. The impact of the radial variation ability of the centroid on the control performance, locomotion capability, and energy consumption of spherical robots is summarized, and the correlation model relating the motion requirements to the radial position of the centroid is established, providing a theoretical basis for the selection of driving modes and centroid positions for spherical robots facing complex task requirements. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Different driving mechanisms of spherical robots: (<b>a</b>) a spherical robot utilizing a wheeled eccentric torque driving mechanism; (<b>b</b>) a spherical robot utilizing a multi-wheel friction internal driving mechanisms; (<b>c</b>) a spherical robot utilizing a pendulum eccentric torque driving mechanisms; (<b>d</b>) a spherical robot utilizing a wind-driving mechanisms; (<b>e</b>) a spherical robot utilizing a localized deformation of the spherical shell; (<b>f</b>) a spherical robot utilizing a leg-driving mechanisms.</p>
Full article ">Figure 2
<p>Two driving modes of spherical robot.</p>
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<p>Prototype of spherical robot BYQ-GS: (<b>a</b>) design model; (<b>b</b>) physical model with half of the spherical shell removed; (<b>c</b>) physical model of internal structure in lower pendulum driving mode; (<b>d</b>) physical model of internal structure in inverted pendulum driving mode.</p>
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<p>Simplified model for the omnidirectional multi-body motion of the radial variable centroid spherical robot.</p>
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<p>The setting of control evaluation indicators and the method for obtaining data.</p>
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<p>Parameter settings for experiment.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>τ</mi> <mo>−</mo> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>τ</mi> <mo>−</mo> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>r</mi> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
Full article ">Figure 10
<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>r</mi> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
Full article ">Figure 11
<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>x</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>α</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
Full article ">Figure 11 Cont.
<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>x</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>α</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>x</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>α</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
Full article ">Figure 12 Cont.
<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>x</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mrow> <mi>α</mi> <mo>−</mo> <mi>rmse</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>x</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>α</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
Full article ">Figure 13 Cont.
<p>Experimental data of <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>x</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>α</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>x</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>|</mo> <msub> <mi>e</mi> <mi>α</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </semantics></math> oobtained from experiments with different radial positions of the centroid. (<b>a</b>) Route 1, (<b>b</b>) Route 2.</p>
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<p>Experimental data of climbing ability obtained from experiments: (<b>a</b>) Different radial positions of the centroid; (<b>b</b>) Radial movement of the centroid during motion.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with different radial positions of the centroid.</p>
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<p>Experimental data of <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> obtained from experiments with radial movement of the centroid.</p>
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18 pages, 7970 KiB  
Article
Defining the Consistent Velocity of Omnidirectional Mobile Platforms
by Elena Rubies and Jordi Palacín
Machines 2024, 12(6), 397; https://doi.org/10.3390/machines12060397 - 11 Jun 2024
Cited by 1 | Viewed by 949
Abstract
The maximum linear (or translational) velocity achievable by an omnidirectional platform is not uniform as it depends on the angular orientation of the motion. This velocity is limited by the maximum angular velocity of the motors driving the wheels and also depends on [...] Read more.
The maximum linear (or translational) velocity achievable by an omnidirectional platform is not uniform as it depends on the angular orientation of the motion. This velocity is limited by the maximum angular velocity of the motors driving the wheels and also depends on the mechanical configuration and orientation of the wheels. This paper proposes a procedure to compute an upper bound for the translational velocity, named the consistent velocity of the omnidirectional platform, which is defined as the minimum of the maximum translational velocities achievable by the platform in any angular orientation with no wheel slippage. The consistent velocity is then a uniform translational velocity always achievable by the omnidirectional platform regardless of the angular orientation of the motion. This paper reports the consistent velocity for a set of omnidirectional platforms with three omni wheels that have the same radius and angular distribution but different angular orientations. Results have shown that these platforms can achieve different maximum velocities in different angular orientations although the consistent velocity is the same for all of them. Results have also shown that the consistent velocity has a linear relation with the angular velocity of the motion. The consistent velocity of a mobile platform can be used by its path-planning algorithm as an upper bound that guarantees the execution of any omnidirectional motion at a uniform and maximum translational velocity. Full article
(This article belongs to the Special Issue Recent Advances in Mobile Robots)
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Figure 1

Figure 1
<p>Representation of (<b>a</b>) the parameters of a three-wheeled omnidirectional mobile platform, and detail of <math display="inline"><semantics> <mrow> <msub> <mi>γ</mi> <mi>k</mi> </msub> </mrow> </semantics></math> for (<b>b</b>) an omni wheel and (<b>c</b>) a mecanum wheel.</p>
Full article ">Figure 2
<p>Example of a mobile robot with the 3A omnidirectional platform [<a href="#B21-machines-12-00397" class="html-bibr">21</a>]: (<b>a</b>) the entire structure of the robot; (<b>b</b>) detail of its omni wheels.</p>
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<p>Top-view trajectory of the robot implementing a motion command <math display="inline"><semantics> <mi>M</mi> </semantics></math> for 2 s: expected trajectory (cyan, solid line) and ground truth trajectory (red, dashed line) caused by the maximum angular velocity reachable by its motors.</p>
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<p>Representation of the evolution of the angular velocity of wheel 1 (<math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>) of the 3A mobile platform [<a href="#B21-machines-12-00397" class="html-bibr">21</a>,<a href="#B25-machines-12-00397" class="html-bibr">25</a>] relative to the angular orientation of the motion <math display="inline"><semantics> <mi>α</mi> </semantics></math>. The solid line depicts the evolution obtained when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> rad/s, while the dashed line depicts the evolution when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> rad/s.</p>
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<p>Flowchart detailing the computation of the consistent velocity.</p>
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<p>Top-view of the schematic representation of the 3A platform and polar representation of the maximum translational velocity in each direction (blue) and of the consistent velocity (red) when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Representation of the evolution of the angular velocities of the wheels (<math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1...3</mn> </mrow> </msub> </mrow> </semantics></math>) as a function of the direction <math display="inline"><semantics> <mi>α</mi> </semantics></math> of the linear velocity of the 3A mobile platform when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>: (<b>a</b>) angular velocities required to move at the maximum linear velocities; (<b>b</b>) angular velocities required to move at the consistent velocity.</p>
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<p>Representation of the evolution of the angular velocities of the wheels (<math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1...3</mn> </mrow> </msub> </mrow> </semantics></math>) as a function of the direction <math display="inline"><semantics> <mi>α</mi> </semantics></math> of the linear velocity of the 3A mobile platform when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>: (<b>a</b>) angular velocities required to move at the maximum linear velocity; (<b>b</b>) angular velocities required to move at the consistent velocity; and (<b>c</b>) polar representation of the maximum translational velocity in each direction (blue) and of the consistent velocity (red).</p>
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<p>Polar charts showing the maximum linear velocity <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> (blue) in each direction <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, for different values of <math display="inline"><semantics> <mi>ω</mi> </semantics></math> for the 3A platform: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>2</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>3</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. The red circle represents the value of the consistent velocity.</p>
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<p>Representation of the mobile platforms assessed, their polar charts showing the maximum linear velocity (blue arrow) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> in each direction <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi>rad</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>, and their consistent velocity (red circle).</p>
Full article ">Figure 11
<p>Relationship between the consistent velocity and the angular velocity <math display="inline"><semantics> <mi>ω</mi> </semantics></math> of the assessed mobile platforms.</p>
Full article ">
22 pages, 10952 KiB  
Article
Surface Acoustic Waves (SAW) Sensors: Tone-Burst Sensing for Lab-on-a-Chip Devices
by Debdyuti Mandal, Tally Bovender, Robert D. Geil and Sourav Banerjee
Sensors 2024, 24(2), 644; https://doi.org/10.3390/s24020644 - 19 Jan 2024
Cited by 1 | Viewed by 1634
Abstract
The article presents the design concept of a surface acoustic wave (SAW)-based lab-on-a-chip sensor with multifrequency and multidirectional sensitivity. The conventional SAW sensors use delay lines that suffer from multiple signal losses such as insertion, reflection, transmission losses, etc. Most delay lines are [...] Read more.
The article presents the design concept of a surface acoustic wave (SAW)-based lab-on-a-chip sensor with multifrequency and multidirectional sensitivity. The conventional SAW sensors use delay lines that suffer from multiple signal losses such as insertion, reflection, transmission losses, etc. Most delay lines are designed to transmit and receive continuous signal at a fixed frequency. Thus, the delay lines are limited to only a few features, like frequency shift and change in wave velocity, during the signal analysis. These facts lead to limited sensitivity and a lack of opportunity to utilize the multi-directional variability of the sensing platform at different frequencies. Motivated by these facts, a guided wave sensing platform that utilizes simultaneous tone burst-based excitation in multiple directions is proposed in this article. The design incorporates a five-count tone burst signal for the omnidirectional actuation. This helps the acquisition of sensitive long part of the coda wave (CW) signals from multiple directions, which is hypothesized to enhance sensitivity through improved signal analysis. In this article, the design methodology and implementation of unique tone burst interdigitated electrodes (TB-IDT) are presented. Sensing using TB-IDT enables accessing multiple frequencies simultaneously. This results in a wider frequency spectrum and allows better scope for the detection of different target analytes. The novel design process utilized guided wave analysis of the substrate, and selective directional focused interdigitated electrodes (F-IDT) were implemented. The article demonstrates computational simulation along with experimental results with validation of multifrequency and multidirectional sensing capability. Full article
(This article belongs to the Special Issue MEMS Sensors and Applications)
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Figure 1

Figure 1
<p>Three-dimensional view of the velocity profile of quasi fast shear wave mode in a 36° YX cut-lithium tantalate.</p>
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<p>Velocity profiles of the 36°YX lithium tantalate with different modes, qL (<b>left</b>), qFS (<b>middle</b>), and qSS (<b>right</b>).</p>
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<p>Guided wave mode shapes with real eigenvalues in frequency domain around 10 MHz.</p>
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<p>Guided wave mode shapes with eigenvalues in frequency domain around 10 MHz vary with small imaginary parts smaller than 1 × 10<sup>−9</sup>.</p>
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<p>Schematic design of the concentric circular IDT (actuator) for the sensing platform.</p>
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<p>(<b>a</b>) 2D-Schematic of the sensing platform, and (<b>b</b>) 3D isometric view of the whole sensor.</p>
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<p>Computation simulation of concentric circular IDT on top of 36°YX lithium tantalate wafer at time t = 0.9927 µs.</p>
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<p>Concentric circular IDT on top of 36°YX lithium tantalate wafer at t = 0.99 µs generating SH waves at the bottom of the wafer (backside). The non-decaying nature of the shear horizontal waves allows waves to transmit along the thickness of the substrate.</p>
Full article ">Figure 9
<p>Simulation of the shear horizontal waves generated by the concentric circular IDT and waves propagating along the direction at 90° at time: (<b>a</b>) 0 μs, (<b>b</b>) 0.8 μs, (<b>c</b>) 2.012 μs, and (<b>d</b>) 3.312 μs.</p>
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<p>Simulated sensing voltage recorded over time by interdigitated electrodes (Focused and Tone Burst) at 0°,45°, 90°,135°, and 180°, corresponding to the concentric circular actuator using the input tone burst signal.</p>
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<p>Five-count tone burst signal at 2.5 MHz central frequency (<b>left</b>), and frequency transformation of the signal (<b>Right</b>).</p>
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<p>Schematic of the tone burst interdigitated electrodes.</p>
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<p>Block diagram of the fabrication process of the sensor (<b>top</b>), and actual image of the sensor (<b>bottom</b>).</p>
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<p>Experimental setup of the sensor and its different components. The image displays the signal response from 135° configuration excited at 12.5 MHz actuation.</p>
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<p>Direction-dependent frequency tuning curves of the F-IDTs at different configurations.</p>
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<p>Experimental time domain signals of the different sensing electrodes at their tuned frequency.</p>
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<p>Frequency-transformed plots of the time domain signals of different sensory interdigitated electrodes at their tuned frequency.</p>
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<p>Hilbert Transformation of the signals in frequency domain of the MC-LR antigens vs. antibodies for the detection recorded over the time (0–55 min).</p>
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<p>Zoomed peak frequency shifts of MC-LR antigens vs. antibodies at time interval (<b>a</b>) 30 min-near 9.75 MHz zone, (<b>b</b>) 20 min-near 10.9 MHz zone, and (<b>c</b>) 50 min-near 9 MHz zone.</p>
Full article ">
17 pages, 20339 KiB  
Article
An Extended Vector Polar Histogram Method Using Omni-Directional LiDAR Information
by Byunguk Lee, Wonho Kim and Seunghwan Lee
Symmetry 2023, 15(8), 1545; https://doi.org/10.3390/sym15081545 - 5 Aug 2023
Cited by 1 | Viewed by 1283
Abstract
This study presents an extended vector polar histogram (EVPH) method for efficient robot navigation using omni-directional LiDAR data. Although the conventional vector polar histogram (VPH) method is a powerful technique suitable for LiDAR sensors, it is limited in its sensing range by the [...] Read more.
This study presents an extended vector polar histogram (EVPH) method for efficient robot navigation using omni-directional LiDAR data. Although the conventional vector polar histogram (VPH) method is a powerful technique suitable for LiDAR sensors, it is limited in its sensing range by the single LiDAR sensor to a semicircle. To address this limitation, the EVPH method incorporates multiple LiDAR sensor’s data for omni-directional sensing. First off, in the EVPH method, the LiDAR sensor coordinate systems are directly transformed into the robot coordinate system to obtain an omni-directional polar histogram. Several techniques are also employed in this process, such as minimum value selection and linear interpolation, to generate a uniform omni-directional polar histogram. The resulting histogram is modified to represent the robot as a single point. Subsequently, consecutive points in the histogram are grouped to construct a symbol function for excluding concave blocks and a threshold function for safety. These functions are combined to determine the maximum cost value that generates the robot’s next heading angle. Robot backward motion is made feasible based on the determined heading angle, enabling the calculation of the velocity vector for time-efficient and collision-free navigation. To assess the efficacy of the proposed EVPH method, experiments were carried out in two environments where humans and obstacles coexist. The results showed that, compared to the conventional method, the robot traveled safely and efficiently in terms of the accumulated amount of rotations, total traveling distance, and time using the EVPH method. In the future, our plan includes enhancing the robustness of the proposed method in congested environments by integrating parameter adaptation and dynamic object estimation methods. Full article
(This article belongs to the Special Issue Unmanned Vehicles, Automation, and Robotics)
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Figure 1

Figure 1
<p>Flowchart of the proposed method. Multiple LiDAR sensors are used to create a robot-centric omni-directional histogram. During this process, coordinate system transformations are considered. The omni-directional histogram undergoes a modification process to prevent collisions, taking into account the size of the robot. Subsequently, point data are grouped and a threshold function is constructed to enhance stability. The final robot’s moving direction is calculated from the result of the cost function, which generates linear and angular velocities in the direction of stability. Consequently, the robot can move efficiently without colliding at any given moment.</p>
Full article ">Figure 2
<p>An example of the construction process for a robot-centered omni-directional polar histogram. Original LiDAR data in (<b>a</b>) are represented in the Cartesian coordinate system as shown in (<b>b</b>). The coordinates are then transformed using the geometric relation between the sensor and the robot as shown in (<b>c</b>). Finally, the transformed coordinates are represented in the polar coordinate system, resulting in a robot-centered omni-directional polar histogram represented in (<b>d</b>). These processes can be streamlined by employing a direct transformation approach proposed in this study.</p>
Full article ">Figure 3
<p>Constructed omni−directional polar histogram based on the direct transformation. In (<b>a</b>), <math display="inline"><semantics><mrow><mi>O</mi><msub><mi>d</mi><mi>i</mi></msub></mrow></semantics></math> and <math display="inline"><semantics><msub><mi>d</mi><mi>i</mi></msub></semantics></math> are compared in the polar coordinate system. In (<b>b</b>), <math display="inline"><semantics><mrow><mi>O</mi><msub><mi>d</mi><mi>i</mi></msub></mrow></semantics></math> shows its strength based on linear interpolation and uniform representation.</p>
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<p>Modification of the omni−directional polar histogram. In (<b>a</b>,<b>b</b>), <math display="inline"><semantics><mrow><mi>O</mi><msub><mi>d</mi><mi>i</mi></msub></mrow></semantics></math> and <math display="inline"><semantics><mrow><mi>O</mi><msub><mi>D</mi><mi>i</mi></msub></mrow></semantics></math> are compared.</p>
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<p>An example problem involving grouping obstacles according to <math display="inline"><semantics><msub><mi>d</mi><mrow><mi>t</mi><mi>h</mi><mi>r</mi></mrow></msub></semantics></math>. In (<b>a</b>), the result is for <math display="inline"><semantics><msub><mi>d</mi><mrow><mi>t</mi><mi>h</mi><mi>r</mi></mrow></msub></semantics></math> = 1.2, which is a large value, causing the entire area to be represented as a single block. In (<b>b</b>), the result is for <math display="inline"><semantics><msub><mi>d</mi><mrow><mi>t</mi><mi>h</mi><mi>r</mi></mrow></msub></semantics></math> = 0.1. By examining the size of the cluster represented by the red straight line, it can be observed that the entire area is appropriately clustered.</p>
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<p>The result of grouped blocks. The proposed method checks the polar histogram circularly while grouping obstacles seamlessly.</p>
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<p>Visualization of the symbol function. The function has zeros in concave blocks (red). In non-concave blocks, ones are assigned (black). As a binary function, it plays a crucial role in influencing the cost function, prompting the robot to move towards non-concave blocks.</p>
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<p>The geometric meaning of <math display="inline"><semantics><msub><mi>h</mi><mi>g</mi></msub></semantics></math>, <math display="inline"><semantics><msub><mi>h</mi><mi>o</mi></msub></semantics></math>, and <math display="inline"><semantics><msub><mi>h</mi><mi>r</mi></msub></semantics></math>. <math display="inline"><semantics><msub><mi>h</mi><mi>r</mi></msub></semantics></math> represents the robot’s heading angle in the global coordinate system, <math display="inline"><semantics><msub><mi>h</mi><mi>o</mi></msub></semantics></math> denotes the angle between the obstacle and the robot, and <math display="inline"><semantics><msub><mi>h</mi><mi>g</mi></msub></semantics></math> represents the angle between the obstacle and the target point. To influence the cost function, <math display="inline"><semantics><msub><mi>h</mi><mi>g</mi></msub></semantics></math> and <math display="inline"><semantics><msub><mi>h</mi><mi>o</mi></msub></semantics></math> are multiplied by <math display="inline"><semantics><msub><mi>k</mi><mn>1</mn></msub></semantics></math> and <math display="inline"><semantics><msub><mi>k</mi><mn>2</mn></msub></semantics></math>, respectively.</p>
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<p>Visualization of the cost function and target direction. The target direction (indicated in red) is properly determined as a result of the cost function.</p>
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<p>Illustration of the designed robot and equipped sensors. The robot is equipped with two RPLiDAR A3 modeled sensors as shown in (<b>a</b>). In (<b>b</b>), the red semicircle indicates the area scanned by the front LiDAR sensor, while the blue semicircle indicates the area scanned by the rear LiDAR sensor.</p>
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<p>The first scenario. The red arrows indicate the paths of a crowd. The solid red circles and dotted red circles represent their current positions, and previous positions, respectively.</p>
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<p>The trajectory comparison of two methods in the first experiment. The blue line represents the result of the conventional method, while the orange line shows the result of the proposed method. The red arrows indicate the paths of a crowd. The solid red circles and dotted red circles represent their current positions, and previous positions, respectively. Unlike the conventional method that involves multiple rotations during avoidance, the proposed method rapidly maneuvers to avoid obstacles by moving backward. (<b>a</b>) t = 6, (<b>b</b>) t = 10, (<b>c</b>) t = 30.</p>
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<p>The scenario of the second experiment. The blue blocks represent static obstacles. The red arrow indicates the path of the human. The solid red circle and dotted red circle represent the current position, and the previous position of human, respectively.</p>
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<p>The trajectory comparison of the two methods in the second experiment. The blue line represents the conventional method, while the orange line represents the proposed method. The red arrow indicates the path of the human. The solid red circle and dotted red circle represent the current position, and the previous position of human, respectively. When the path between two static obstacles, which the robot can typically pass through, is obstructed by a human, conventional methods result in the robot taking a wide turn to avoid the obstacle. However, the proposed method offers a more efficient solution by quickly navigating backward to effectively avoid the obstruction. (<b>a</b>) t = 6, (<b>b</b>) t = 19, (<b>c</b>) t = 30.</p>
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<p>The target direction comparison of the two methods in the first experiment. The blue arrow represents the conventional method, while the orange arrow represents the proposed method. The red arrows indicate the paths of a crowd. The solid red circles and dotted red circles represent their current positions, and previous positions, respectively. The distinct decisions and motions of the two methods at the above time points result in noteworthy differences in the overall outcomes. (<b>a</b>) t = 6, (<b>b</b>) t = 10.</p>
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<p>The target direction comparison of the two methods in the second experiment. The blue arrow represents the conventional method, while the orange arrow represents the proposed method. The red arrow indicates the path of the human. The solid red circle and dotted red circle represent the current position, and the previous position of human, respectively. The distinct decisions and motions of the two methods at the above time points result in noteworthy differences in the overall outcomes. (<b>a</b>) t = 6, (<b>b</b>) t = 9.</p>
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25 pages, 14592 KiB  
Article
Phasor-Like Interpretation of the Angular Velocity of the Wheels of Omnidirectional Mobile Robots
by Jordi Palacín, Elena Rubies, Ricard Bitriá and Eduard Clotet
Machines 2023, 11(7), 698; https://doi.org/10.3390/machines11070698 - 1 Jul 2023
Cited by 2 | Viewed by 2484
Abstract
Omnidirectionality is a feature that allows motion in any direction without orientation maneuvers. Omnidirectional mobile robots are usually based on omni or mecanum wheels. The motion of an omnidirectional mobile robot is defined by a target motion command [...] Read more.
Omnidirectionality is a feature that allows motion in any direction without orientation maneuvers. Omnidirectional mobile robots are usually based on omni or mecanum wheels. The motion of an omnidirectional mobile robot is defined by a target motion command M=v,α,ω, where v is the module of the translational velocity; α is the angular orientation of the translational velocity, and ω is the angular velocity of the mobile robot. The motion is achieved by converting the target motion command into the target angular velocities that must be applied to the active wheels of the robot. This work proposes a simplified phasor-like interpretation of the relationship between the parameters of a specific motion command and the angular velocities of the wheels. The concept of phasor-like notation is validated from the analysis of the kinematics of omnidirectional mobile robots using omni wheels and mecanum wheels. This simplified phasor-like notation fosters unconstrained conceptual design of single-type and hybrid multi-wheeled omnidirectional mobile robots without the distribution or type of wheels being a design constraint. Full article
(This article belongs to the Special Issue Mobile Robotics: Mathematics, Models and Methods)
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<p>Wheels frequently used in omnidirectional mobile robots: (<b>a</b>) single omni wheel; (<b>b</b>) optimal omni wheel; (<b>c</b>) mecanum wheel.</p>
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<p>Representation of the motion command, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math>, defined in the mobile robot frame <math display="inline"><semantics> <mrow> <mfenced close="}" open="{"> <mi>b</mi> </mfenced> </mrow> </semantics></math> of a mobile platform: (<b>a</b>) top-view of a robot using three optimal omni wheels; (<b>b</b>) top-view of a robot using four mecanum wheels. The free rollers of the wheels that are in contact with the floor are represented with wider lines.</p>
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<p>APR-02 mobile robot: (<b>a</b>) complete robot; (<b>b</b>) top-view of its internal motion system based on three omni wheels.</p>
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<p>Top-view representation of the parameters of a three-wheeled omni mobile robot: (<b>a</b>) motion parameters and system frames; (<b>b</b>) wheel parameters.</p>
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<p>OSOYOO mecanum mobile robot: (<b>a</b>) complete robot; (<b>b</b>) top-view of its motion system based on four mecanum wheels.</p>
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<p>Top-view representation of the parameters of a four-wheeled mecanum mobile robot: (<b>a</b>) motion parameters and wheel frames; (<b>b</b>) wheel parameters.</p>
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<p>Simulation of the trajectories of the APR mobile robot obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">α</mi> <mrow> <mi mathvariant="normal">i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>16</mn> </mrow> </msub> <mo>=</mo> <mn>22.5</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s in the case of a displacement during <math display="inline"><semantics> <mi>t</mi> </semantics></math> = 16.0 s.</p>
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<p>Representation of the angular velocity of the omni wheels obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>360</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Simulation of the trajectories of the APR mobile robot obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">α</mi> <mrow> <mi mathvariant="normal">i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>16</mn> </mrow> </msub> <mo>=</mo> <mn>22.5</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0.1 rad/s in the case of a displacement during <math display="inline"><semantics> <mi>t</mi> </semantics></math> = 15.7 s.</p>
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<p>Representation of the angular velocity of the omni wheels obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>360</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0.5 rad/s (used instead of <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0.1 rad/s in order to visually enhance the effect of the average shift caused by <math display="inline"><semantics> <mi>ω</mi> </semantics></math>).</p>
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<p>Simulation of the trajectories of the mecanum mobile robot obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">α</mi> <mrow> <mi mathvariant="normal">i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>16</mn> </mrow> </msub> <mo>=</mo> <mn>22.5</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s in the case of a displacement during <math display="inline"><semantics> <mi>t</mi> </semantics></math> = 16.0 s.</p>
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<p>Representation of the angular velocity of the mecanum wheels obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>360</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Simulation of the trajectories of the mecanum mobile robot obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">α</mi> <mrow> <mi mathvariant="normal">i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>16</mn> </mrow> </msub> <mo>=</mo> <mn>22.5</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0.1 rad/s in the case of a displacement during <math display="inline"><semantics> <mi>t</mi> </semantics></math> = 15.7 s.</p>
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<p>Representation of the angular velocity of the mecanum wheels obtained with a motion command <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mfenced> <mrow> <mi>v</mi> <mo>,</mo> <msub> <mi>α</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>ω</mi> </mrow> </mfenced> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>…</mo> <mn>360</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>°</mo> <mo>·</mo> <mfenced> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> when <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0.5 rad/s.</p>
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<p>Asymmetric three-wheeled omni mobile robot: (<b>a</b>) schematic top-view representation; (<b>b</b>) profile of the angular velocities of the wheels for <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Symmetric four-wheeled omni mobile robot: (<b>a</b>) schematic top-view representation; (<b>b</b>) profile of the angular velocities of the wheels for <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Asymmetric four-wheeled mecanum mobile robot: (<b>a</b>) schematic top-view representation; (<b>b</b>) profile of the angular velocities of the wheels for <math display="inline"><semantics> <mi>v</mi> </semantics></math> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Symmetric eight-wheeled mecanum mobile robot: (<b>a</b>) schematic top-view representation; (<b>b</b>) profile of the angular velocities of the wheels for <span class="html-italic">v</span> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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<p>Hybrid six-wheeled omnidirectional mobile robot: (<b>a</b>) schematic top-view representation; (<b>b</b>) profile of the angular velocities of the wheels for <span class="html-italic">v</span> = 0.3 m/s and <math display="inline"><semantics> <mi>ω</mi> </semantics></math> = 0 rad/s.</p>
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16 pages, 4960 KiB  
Article
Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure
by Xiangting Xu, Zhichao Fan, Xuedong Chen, Jingwei Cheng and Yangguang Bu
Sensors 2023, 23(4), 1777; https://doi.org/10.3390/s23041777 - 4 Feb 2023
Cited by 1 | Viewed by 2212
Abstract
The ultrasonic detectability of buried defects within composite materials is dependent on the anisotropy of the composite material by which the propagation property of acoustic wave in each direction is variably affected. In this study, the characteristics of acoustic waves propagating in different [...] Read more.
The ultrasonic detectability of buried defects within composite materials is dependent on the anisotropy of the composite material by which the propagation property of acoustic wave in each direction is variably affected. In this study, the characteristics of acoustic waves propagating in different directions for composite materials are explored based on the full matrix capture (FMC) data using an ultrasonic phased array. The elastic constant of multidirectional carbon fiber reinforced plastic (CFRP) laminate is first derived based on the genetic algorithm. The characteristics of transmitted and reflected waves in higher angles are predicted by implementing the Christoffel equation, and the focal law used in post-processing of FMC data can be optimized accordingly. The imaging results of the total focusing method (TFM) using the improved focal law are compared with the results of the conventional TFM. The results suggest that the optimized TFM can effectively characterize the defect by reducing the background noise. Furthermore, since it is impractical to theoretically correct angle-dependent velocity for in situ inspection, a linear extrapolation method based on the experimentally measurable velocity at low angles is proposed to estimate the velocity profile at higher angles. The imaging results using the fast extrapolated velocity profile is then compared with the theoretical, and it has been demonstrated that while the difference between the images using the theoretical focal law and the linearly extrapolated one is barely visible, the later one is overwhelmingly advantageous to be realiszd for engineering practices. Full article
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<p>The diagram of (<b>a</b>) the three-dimensional matrix of <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>T</mi> </msub> <mo>×</mo> <msub> <mi>M</mi> <mi>R</mi> </msub> <mo>×</mo> <mi>n</mi> </mrow> </semantics></math> and (<b>b</b>) the transformed two-dimensional matrix of <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mo>Δ</mo> </msub> <mo>×</mo> <mi>n</mi> </mrow> </semantics></math>.</p>
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<p>Normalized time domain waveform with different transmit-receiving intervals ∆, ∆ = 0 (<b>a</b>) and ∆ = 29 (<b>b</b>).</p>
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<p>Flow chart of the velocity measurement for CFRP multidirectional plate.</p>
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<p>Schematic diagram of TFM imaging.</p>
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<p>The diagram of the CFRP specimen containing delamination defects at different locations.</p>
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<p>Experimental setup of the phased array detection (<b>a</b>) and a cross-section of the test block (<b>b</b>).</p>
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<p>The cubic polynomial fitting curve from experimentally measured discrete points.</p>
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<p>The diagrams of (<b>a</b>) measured discrete velocities at the angles from 0° to 45.8° and (<b>b</b>) the theoretical fitting curve from 0° to 90°.</p>
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<p>The predicted high-angle velocities using four different approaches.</p>
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<p>TFM imaging results for the 3 mm deep delamination defect using delay law of (<b>a</b>) constant velocity, (<b>b</b>) piecewise constant velocity, (<b>c</b>) linear velocity and (<b>d</b>) theoretical velocity as well as the 5 mm deep delamination defect using delay law of (<b>e</b>) constant velocity, (<b>f</b>) piecewise constant velocity, (<b>g</b>) linear velocity, and (<b>h</b>) theoretical velocity.</p>
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<p>TFM imaging intensities for 3 mm deep defects along lines at (<b>a</b>) <span class="html-italic">x</span> = 1.1 mm and (<b>b</b>) <span class="html-italic">z</span> = 3 mm, as well as the 5 mm deep defects along lines at (<b>c</b>) <span class="html-italic">x</span> = 1.1 mm and (<b>d</b>) <span class="html-italic">z</span> = 5 mm.</p>
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17 pages, 3443 KiB  
Article
Omni Wheel Arrangement Evaluation Method Using Velocity Moments
by Masaaki Hijikata, Renato Miyagusuku and Koichi Ozaki
Appl. Sci. 2023, 13(3), 1584; https://doi.org/10.3390/app13031584 - 26 Jan 2023
Cited by 6 | Viewed by 7772
Abstract
Wheeled omnidirectional mobile robots have been developed for industrial and service applications. Conventional research on Omni wheel robots has mainly been directed toward point-symmetric wheel arrangements. However, more flexible asymmetric arrangements may be beneficial to prevent tipping over or to make the robot [...] Read more.
Wheeled omnidirectional mobile robots have been developed for industrial and service applications. Conventional research on Omni wheel robots has mainly been directed toward point-symmetric wheel arrangements. However, more flexible asymmetric arrangements may be beneficial to prevent tipping over or to make the robot more compact. Asymmetry can also be the result of a motor/wheel failure in a robot with a redundant configuration; in this case, it may be possible to continue operations, but with an asymmetrical arrangement. For controlling such asymmetric arrangements, it is necessary to consider the moment of propulsive force generated by the wheels. Since it is difficult to measure the propulsive force accurately, in this work we model propulsive forces as being proportional to the ground speed of the wheels. Under this assumption, we estimated the robot’s behavior in an asymmetric wheel configuration by considering the balance of the velocity moment, which is the moment of the wheel’s ground speed. By verifying the robot’s behavior with various wheel configurations, we confirmed experimentally that the sum of the velocity moments affects the straightness of the robot and allows us to improve the design of asymmetric wheel arrangements and control during wheel failures. Full article
(This article belongs to the Section Robotics and Automation)
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<p>Practical omnidirectional robot. (<b>a</b>) “AiTran” developed by DAIHEN Corporation, can be used not only for loading but also for towing cage carts and substituting for forks and can be widely applied to various objects and scenes in factories <math display="inline"><semantics> <msup> <mrow/> <mn>1</mn> </msup> </semantics></math>. (<b>b</b>) Robot under development by Sony Corporation and Shimizu Corporation to improve the efficiency of construction management tasks such as patrolling and monitoring at construction sites <math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math>. (<b>c</b>) “Display Robot” developed by THK Corporation and Yoshityu Mannequin Corporation for customer service and advertising activities in commercial facilities, hotels, and airports <math display="inline"><semantics> <msup> <mrow/> <mn>3</mn> </msup> </semantics></math>. (<math display="inline"><semantics> <msup> <mrow/> <mn>1</mn> </msup> </semantics></math> <a href="https://www.youtube.com/watch?v=IPszY3uGrt8" target="_blank">https://www.youtube.com/watch?v=IPszY3uGrt8</a>, accessed on 19 January 2023. <math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> <a href="https://www.sony.com/ja/SonyInfo/News/Press/202112/21-1214/" target="_blank">https://www.sony.com/ja/SonyInfo/News/Press/202112/21-1214/</a>, accessed on 19 January 2023. <math display="inline"><semantics> <msup> <mrow/> <mn>3</mn> </msup> </semantics></math> <a href="https://products.thk.com/jp/ja/news/products/article-01102020-1.html" target="_blank">https://products.thk.com/jp/ja/news/products/article-01102020-1.html</a>, accessed on 19 January 2023).</p>
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<p>The example of omnidirectional wheels. (<math display="inline"><semantics> <msup> <mrow/> <mn>1</mn> </msup> </semantics></math> <a href="https://www.nexusrobot.com/product/4-inch100mm-double-aluminum-omni-wheel-bearing-rollers-14054.html" target="_blank">https://www.nexusrobot.com/product/4-inch100mm-double-aluminum-omni-wheel-bearing-rollers-14054.html</a>, accessed on 18 January 2023. <math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> <a href="https://www.nexusrobot.com/product/4-inch-100mm-mecanum-wheel-rightbearing-rollers-14094r.html" target="_blank">https://www.nexusrobot.com/product/4-inch-100mm-mecanum-wheel-rightbearing-rollers-14094r.html</a>, accessed on 18 January 2023).</p>
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<p>Pattern diagram of the Omni wheel robot: The parameters of each wheel of an Omni wheel robot are shown when a wheel of radius <span class="html-italic">r</span> is placed at position (<span class="html-italic">x</span>,<span class="html-italic">y</span>) and direction <math display="inline"><semantics> <mi>θ</mi> </semantics></math>. <math display="inline"><semantics> <mi>ω</mi> </semantics></math> and <span class="html-italic">V</span> are the rotational and ground speeds of the wheel, and <math display="inline"><semantics> <msup> <mi>l</mi> <msup> <mrow/> <mo>′</mo> </msup> </msup> </semantics></math> are the distance to the center of rotation of the robot relative to the velocity vector of each wheel.</p>
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<p>Appearance of the robot.</p>
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<p>Appearance of the robot’s parts: (<b>a</b>) shows the board that serves as the foundation. (<b>b</b>) shows the plate to hold the motor.</p>
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<p>The robot hardware configuration.</p>
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<p>The robot trajectory during each travel direction with 4-wheeled Omni wheel robots.</p>
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<p>The robot trajectory during each travel direction with 4-wheeled Omni wheel robots.</p>
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<p>The robot trajectory during each travel direction with 6-wheeled Omni wheel robots.</p>
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<p>The robot’s actual angular speeds during each travel direction and command speed with 4-wheeled Omni wheel robots.</p>
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<p>The robot’s actual angular speeds during each travel direction and command speed with 4-wheeled Omni wheel robots.</p>
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<p>The robot’s actual angular speeds during each travel direction and command speed with 6-wheeled Omni wheel robots.</p>
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<p>The relationship between the sum of the velocity moments generated by the command velocity and the angular velocity.</p>
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<p>The relationship between the sum of the velocity moments generated by the command velocity and the angular velocity.</p>
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16 pages, 2351 KiB  
Article
Non-Parametric Calibration of the Inverse Kinematic Matrix of a Three-Wheeled Omnidirectional Mobile Robot Based on Genetic Algorithms
by Jordi Palacín, Elena Rubies, Ricard Bitrià and Eduard Clotet
Appl. Sci. 2023, 13(2), 1053; https://doi.org/10.3390/app13021053 - 12 Jan 2023
Cited by 11 | Viewed by 1944
Abstract
Odometry is a computation method that provides a periodic estimation of the relative displacements performed by a mobile robot based on its inverse kinematic matrix, its previous orientation and position, and the estimation of the angular rotational velocity of its driving wheels. Odometry [...] Read more.
Odometry is a computation method that provides a periodic estimation of the relative displacements performed by a mobile robot based on its inverse kinematic matrix, its previous orientation and position, and the estimation of the angular rotational velocity of its driving wheels. Odometry is cumulatively updated from tens to hundreds of times per second, so any inaccuracy in the definition of the inverse kinematic matrix of a robot leads to systematic trajectory errors. This paper proposes a non-parametric calibration of the inverse kinematic (IK) matrix of a three-wheeled omnidirectional mobile robot based on the use of genetic algorithms (GA) to minimize the positioning error registered in a set of calibration trajectories. The application of this non-parametric procedure has provided an average improvement of 82% in the estimation of the final position and orientation of the mobile robot. This is similar to the improvement achieved with analogous parametric methods. The advantage of this non-parametric approach is that it covers a larger search space because it eliminates the need to define feasible physical limits to the search performed to calibrate the inverse kinematic matrix of the mobile robot. Full article
(This article belongs to the Special Issue Advances in Robot Path Planning, Volume II)
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<p>APR-02 mobile robot performing a transversal (or lateral) displacement: (<b>a</b>) starting point; (<b>b</b>,<b>c</b>) intermediate points; and (<b>d</b>) destination point.</p>
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<p>Detail of the omnidirectional motion system of the APR-02 mobile robot. <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mi>R</mi> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mi>R</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> is the mobile robot frame in which <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>R</mi> </msub> </mrow> </semantics></math> represents the front and forward direction of the robot.</p>
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<p>Parametric definition of the omnidirectional motion system of the APR-02 mobile robot. <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mi>R</mi> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mi>R</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> represents the mobile robot frame in which <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>R</mi> </msub> </mrow> </semantics></math> is the front of the mobile robot.</p>
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<p>Diagram of the Genetic Algorithm search performed to calibrate the inverse kinematic matrix of the APR-02 mobile robot.</p>
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<p>Sample trajectory followed by the APR-02 mobile robot for the motion command <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>v</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>ω</mi> <mo>≠</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> = (0.2 m/s, 30°, 0.35 rad/s). The ground truth trajectory was estimated from the information of the LIDAR (red line) while the odometry was estimated with the theoretical value of the inverse kinematic matrix of the mobile robot (blue line).</p>
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<p>Comparison between the ground truth trajectory followed by the mobile robot (red line) and the odometry estimated with: the theoretical IK (green line), the parametric IK (brown line) and the non-parametric IK (magenta line). Trajectories originated by the following motion commands, <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>v</mi> <mo>,</mo> <mi>α</mi> <mo>,</mo> <mi>ω</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>: (<b>a</b>) (0.2 m/s, 30°, 0.35 rad/s); (<b>b</b>) (0.2 m/s, 210°, 0.35 rad/s); (<b>c</b>) (0.2 m/s, 120°, 0.35 rad/s); and (<b>d</b>) (0.2 m/s, 300°, 0.35 rad/s).</p>
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<p>Detail of the final position of the robot corresponding to the full trajectories displayed in <a href="#applsci-13-01053-f006" class="html-fig">Figure 6</a>. Ground truth trajectory of the mobile robot (red) and odometry of the mobile robot computed using the theoretical IK (green), the parametric IK [<a href="#B17-applsci-13-01053" class="html-bibr">17</a>] (brown) and the noon-parametric IK (magenta).</p>
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19 pages, 2612 KiB  
Article
Predefined-Time Fuzzy Neural Network Control for Omnidirectional Mobile Robot
by Peng Qin, Tao Zhao, Nian Liu, Zhen Mei and Wen Yan
Processes 2023, 11(1), 23; https://doi.org/10.3390/pr11010023 - 22 Dec 2022
Cited by 4 | Viewed by 1757
Abstract
In this paper, a fuzzy neural network based predefined-time trajectory tracking control method is proposed for the tracking problem of omnidirectional mobile robots (FM-OMR) with uncertainties. Considering the requirement of tracking error convergence time, a position tracking controller based on predefined-time stability is [...] Read more.
In this paper, a fuzzy neural network based predefined-time trajectory tracking control method is proposed for the tracking problem of omnidirectional mobile robots (FM-OMR) with uncertainties. Considering the requirement of tracking error convergence time, a position tracking controller based on predefined-time stability is proposed. Compared with the traditional position tracking control method, the minimum upper bound of the convergence time can be explicitly set. In order to obtain more accurate angular velocity tracking, the inner loop controller combines Type 1 fuzzy neural network (T1FNN) to estimate the uncertainty. In addition, considering the problem of feedback channel noise, a Kalman filter combining velocity and position information is proposed. Finally, the simulation results verify the effectiveness of this method. Full article
(This article belongs to the Section Automation Control Systems)
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<p>Structure diagram of FM-OMR.</p>
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<p>Mecanum wheel.</p>
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<p>Control structure diagram.</p>
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<p>Tracking error.</p>
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<p>Structure of T1FNN.</p>
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<p>Circular trajectory tracking.</p>
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<p>Tracking error of X component.</p>
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<p>Tracking error of Y component.</p>
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<p>Tracking error of <math display="inline"><semantics> <mi>θ</mi> </semantics></math> component.</p>
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<p>Tracking error of <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Tracking error of angular velocity.</p>
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<p>Error index.</p>
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<p>Signal <span class="html-italic">x</span>.</p>
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<p>Signal <span class="html-italic">y</span>.</p>
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<p>Signal <math display="inline"><semantics> <mi>θ</mi> </semantics></math>.</p>
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9 pages, 3024 KiB  
Communication
Three-Dimensional Acoustic Device for Testing the All-Directional Anisotropic Characteristics of Rock Samples
by Kai Zhang, Shengqing Li, Yuanda Su, Baohai Tan, Wenjie Wu and Shoutao Xin
Sensors 2022, 22(23), 9473; https://doi.org/10.3390/s22239473 - 4 Dec 2022
Cited by 1 | Viewed by 1509
Abstract
Many oil and gas fields, especially non-conventional shale and compacted sand reservoirs, have formation anisotropy. The acoustic anisotropy measurement of cores in these reservoirs can guide drilling, well logging, and exploitation. However, almost all core holders are designed for cylinder cores, which are [...] Read more.
Many oil and gas fields, especially non-conventional shale and compacted sand reservoirs, have formation anisotropy. The acoustic anisotropy measurement of cores in these reservoirs can guide drilling, well logging, and exploitation. However, almost all core holders are designed for cylinder cores, which are not suitable for all-directional measurements. A three-dimensional measurement device was designed on the basis of the cross-hole sonic logging method. This device mainly consisted of two pairs of transducers, a signal generator, an oscillograph, an omnidirectional positioning system, and a computer control system. By adjusting the measurement latitude and longitude circle automatically, this device scanned spherical sample rocks and obtained full-wave waveforms in all directions. Experiments were performed taking granite from the Jiaodong Peninsula, China, as an example, and the arrival times and velocities of the longitudinal and shear waves were calculated based on the full-wave waveforms. Thereafter, anisotropic physical characterizations were carried out on the basis of these velocities. These data play an important role in guiding formation fracturing and analyzing the stability of borehole walls. Full article
(This article belongs to the Special Issue Advanced Technology in Acoustic Signal Processing)
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<p>Traditional measurement methods sample the same core in different directions.</p>
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<p>Actual picture of the three-dimensional anisotropic measurement device: (<b>a</b>) omnidirectional positioning system, (<b>b</b>) signal generator and amplifier, and (<b>c</b>) oscillograph.</p>
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<p>Schematic of measurements conducted by the 3-D measurement device.</p>
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<p>Granite rock sample from Jiaodong Peninsula, China.</p>
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<p>Full-wave received waveforms in different dimensions measured at the longitude of 150°.</p>
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<p>Arrival times of longitudinal waves on the basis of scanning-measurement endings.</p>
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<p>Arrival times of shear waves on the basis of scanning-measurement endings.</p>
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<p>Velocity anisotropies in the longitudinal direction and latitudinal direction.</p>
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<p>Measured velocities of the longitudinal and shear waves of the same testing point (blue dots) and their fit curve (red line).</p>
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<p>Calculated elastic anisotropic parameters: (<b>a</b>) Poisson’s ratio, (<b>b</b>) bulk modulus, (<b>c</b>) shear modulus, and (<b>d</b>) Young’s modulus.</p>
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19 pages, 5600 KiB  
Article
Effect of Stator Blades on the Startup Dynamics of a Vertical Axis Wind Turbine
by Taimoor Asim, Dharminder Singh, M. Salman Siddiqui and Don McGlinchey
Energies 2022, 15(21), 8135; https://doi.org/10.3390/en15218135 - 31 Oct 2022
Cited by 4 | Viewed by 2942
Abstract
Vertical Axis Wind Turbines (VAWTs) are omni-directional, low-cost, low-efficiency wind power extractors. A conventional drag-based VAWT consists of multiple thin rotor blades with a typical peak Tip Speed Ratio (λ) of < 1. Their lower cut-in speed and maintenance cost make them ideal [...] Read more.
Vertical Axis Wind Turbines (VAWTs) are omni-directional, low-cost, low-efficiency wind power extractors. A conventional drag-based VAWT consists of multiple thin rotor blades with a typical peak Tip Speed Ratio (λ) of < 1. Their lower cut-in speed and maintenance cost make them ideal for power generation in urban environments. Numerous studies have been carried out analysing steady operation of VAWTs and quantifying their performance characteristics, however, minimal attention has been paid to their start-up dynamics. There are a few recent studies in which start-up dynamics of lift-based VAWTs have been analysed but such studies for drag-based VAWTs are severely limited. In this study, start-up dynamics of a conventional multi-blade drag-based VAWT have been numerically investigated using a time-dependant Computational Fluid Dynamics (CFD) solver. In order to enhance the start-up characteristics of the drag-based VAWT, a stator has been integrated in the design assembly. The numerical results obtained in this study indicate that an appropriately designed stator can significantly enhance the start-up of a VAWT by directing the flow towards the rotor blades, leading to higher rotational velocity (ω) and λ. With the addition of a stator, the flow fields downstream the VAWT becomes more uniform. Full article
(This article belongs to the Special Issue Modeling and Simulation of Floating Offshore Wind Farms)
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<p>(<b>a</b>) Real-world VAWT model (with stator); (<b>b</b>) CAD model of the VAWT without stator.</p>
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<p>(<b>a</b>) 2D models of the VAWTs with and without stator; (<b>b</b>) Flow domain of the VAWTs.</p>
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<p>Spatial discretisation of the flow domains.</p>
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<p>Variations of φ in the near-wall regions of the VAWT (<b>a</b>) without stator; (<b>b</b>) with stator.</p>
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<p>Variations of τ in the vicinity of VAWT (<b>a</b>) without stator; (<b>b</b>) with stator.</p>
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<p>Rotational characteristics of the VAWT without stator.</p>
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<p>Rotational characteristics of the VAWT without stator.</p>
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<p>(<b>a</b>) Static gauge pressure and (<b>b</b>) flow velocity magnitude variations in the vicinity of the VAWT without stator.</p>
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<p>(<b>a</b>) Static gauge pressure and (<b>b</b>) flow velocity magnitude variations in the vicinity of the VAWT without stator.</p>
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<p>Rotational characteristics of the VAWT with stator.</p>
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<p>Rotational characteristics of the VAWT with stator.</p>
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<p>(<b>a</b>) Static gauge pressure and (<b>b</b>) flow velocity magnitude variations in the vicinity of the VAWT with stator.</p>
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<p>(<b>a</b>) Static gauge pressure and (<b>b</b>) flow velocity magnitude variations in the vicinity of the VAWT with stator.</p>
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<p>Variations in the Tip Speed Ratio of the VAWTs with and without stator.</p>
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<p>Variations in the torque generated by the VAWTs with and without Stator.</p>
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24 pages, 9064 KiB  
Article
Optimal PID Control of a Brushed DC Motor with an Embedded Low-Cost Magnetic Quadrature Encoder for Improved Step Overshoot and Undershoot Responses in a Mobile Robot Application
by Ricard Bitriá and Jordi Palacín
Sensors 2022, 22(20), 7817; https://doi.org/10.3390/s22207817 - 14 Oct 2022
Cited by 15 | Viewed by 6285
Abstract
The development of a proportional–integral–derivative (PID) control system is a simple, practical, highly effective method used to control the angular rotational velocity of electric motors. This paper describes the optimization of the PID control of a brushed DC motor (BDCM) with an embedded [...] Read more.
The development of a proportional–integral–derivative (PID) control system is a simple, practical, highly effective method used to control the angular rotational velocity of electric motors. This paper describes the optimization of the PID control of a brushed DC motor (BDCM) with an embedded low-cost magnetic quadrature encoder. This paper demonstrates empirically that the feedback provided by low-cost magnetic encoders produces some inaccuracies and control artifacts that are not usually considered in simulations, proposing a practical optimization approach in order to improve the step overshoot and undershoot controller response. This optimization approach is responsible for the motion performances of a human-sized omnidirectional mobile robot using three motorized omnidirectional wheels. Full article
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<p>(<b>a</b>) Image of the APR-02 mobile robot. (<b>b</b>) Details of the internal structure supporting the three BDCMs that drive the three omnidirectional wheels of the mobile robot.</p>
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<p>Image of the BDCM used in the APR-02 mobile robot, which includes a 64:1 planetary gearbox and a low-cost magnetic encoder attached to the motor shaft. The motor is supported by an aluminum support structure that has some (red) support elements made of flexible rubber in order to reduce the transmission of vibrations.</p>
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<p>Electronic control board implementing the PID controller.</p>
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<p>PID block diagram.</p>
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<p>Representation of all steps and modules required to practically implement the PID controller of one motor of the APR-02 mobile robot.</p>
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<p>(<b>a</b>) Representation of the six-pole magnet of the encoder that is attached to the motor shaft and the two fixed hall-effect sensors, HA and HB, placed at a 90° phase offset. (<b>b</b>) Logical quadrature output signals generated by the rotation of the encoder and the edges detected by the microcontroller using the input capture module.</p>
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<p>Open-loop wheel speed measurement deduced from the raw time-elapsed edge measurements gathered from the magnetic encoder of the BDCM for the different PWM duty cycles applied: (<b>a</b>) 20% or low-speed example; (<b>b</b>) 50% or medium-speed example; (<b>c</b>) 100% or full-speed example.</p>
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<p>Corrected open-loop wheel speed measurement deduced from the raw time-elapsed edge measurements gathered from the magnetic encoder of the BDCM for the different PWM duty cycles applied and the correction coefficients displayed in <a href="#sensors-22-07817-t001" class="html-table">Table 1</a>: (<b>a</b>) 20% PWM case; (<b>b</b>) 50% PWM case; (<b>c</b>) 100% PWM case.</p>
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<p>(<b>a</b>) PWM and RPM relationship in different load scenarios. (<b>b</b>) Motor current consumption depending on the applied PWM duty cycle in different load scenarios.</p>
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<p>Motor step response for different PWM cycles.</p>
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<p>Acceleration curve and inverted deceleration curve moved to <span class="html-italic">t</span> = 0.0 s.</p>
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<p>Calibration data required for model calculation: (<b>a</b>) PWM duty cycle sequence applied to the motor; (<b>b</b>) measured angular rotational velocity of the output shaft (gray line) and generated by the continuous-time (blue dotted line) and discrete-time (red dotted) models found by the SIT Toolbox.</p>
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<p>(<b>a</b>) Real motor setup. (<b>b</b>) Simulation of the motor model.</p>
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<p>Open-loop motor step response comparison: real motor speed gathered from the encoder (blue line), continuous-time (red line) model simulation, and discrete-time (brown line) model simulation.</p>
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<p>Histogram of the encoder’s time-elapsed (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> </mrow> </semantics></math>) values obtained with different PWM duty cycles (cases represented in <a href="#sensors-22-07817-f009" class="html-fig">Figure 9</a>a with no load), colored in order to differentiate the cases analyzed.</p>
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<p>Simulink<sup>®</sup> continuous control loop model used by the FRB PID tuner.</p>
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<p>Simulink<sup>®</sup> discrete control loop model used by the FRB PID tuner.</p>
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<p>BDCM output in a closed-loop PID control: real evolution of the angular rotational velocity measured from the information gathered by the magnetic quadrature encoder (blue line) and simulated motor velocity (yellow line). Response to steps with target speeds of 5, 10, 20, 40, and 60 rpm.</p>
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<p>Evaluation of the NIAE values for different sampling periods (<math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> </semantics></math>) and different target speeds: 10 (blue line), 30 (green line), and 60 (yellow line) rpm.</p>
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<p>A 3D representation of the NIAE of the PID controller according the planes defined by the <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>p</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>d</mi> </msub> </mrow> </semantics></math> parameters. The white point depicts the location of the baseline values proposed by the FRB PID Tuner procedure. The leftmost plane is for <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> <mo> </mo> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and the bottom plane is for <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Details of the two horizontal planes defined in <a href="#sensors-22-07817-f020" class="html-fig">Figure 20</a>. The white point depicts the location or projection of the NIAE baseline values obtained with the FRB PID tuner procedure while the red point depicts the location of the minimum NIAE in each plane. The values of the NIAE are also displayed for reference: (<b>a</b>) plane with <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>0.0182</mn> <mrow> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </semantics></math>; (<b>b</b>) plane with <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>d</mi> </msub> <mo>=</mo> <mn>0</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>.</p>
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<p>Step overshoot results measured in the real motor using the reference PID parameters obtained with the FRB PID tuner procedure (yellow line) and the best PID parameters, which minimize the NIAE. The target speed is 30 rpm.</p>
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19 pages, 3212 KiB  
Article
Implementation of Omni-D Tele-Presence Robot Using Kalman Filter and Tricon Ultrasonic Sensors
by Hassan Tariq, Muhammad Rashid, Asfa Javed, Muhammad Aaqib Riaz, Mohammed Sinky and Muhammad Yousuf Irfan Zia
Sensors 2022, 22(10), 3948; https://doi.org/10.3390/s22103948 - 23 May 2022
Cited by 2 | Viewed by 2697
Abstract
The tele-presence robot is designed to set forth an economic solution to facilitate day-to-day normal activities in almost every field. There are several solutions to design tele-presence robots, e.g., Skype and team viewer, but it is pretty inappropriate to use Skype and extra [...] Read more.
The tele-presence robot is designed to set forth an economic solution to facilitate day-to-day normal activities in almost every field. There are several solutions to design tele-presence robots, e.g., Skype and team viewer, but it is pretty inappropriate to use Skype and extra hardware. Therefore, in this article, we have presented a robust implementation of the tele-presence robot. Our proposed omnidirectional tele-presence robot consists of (i) Tricon ultrasonic sensors, (ii) Kalman filter implementation and control, and (iii) integration of our developed WebRTC-based application with the omnidirectional tele-presence robot for video transmission. We present a new algorithm to encounter the sensor noise with the least number of sensors for the estimation of Kalman filter. We have simulated the complete model of robot in Simulink and Matlab for the tough paths and critical hurdles. The robot successfully prevents the collision and reaches the destination. The mean errors for the estimation of position and velocity are 5.77% and 2.04%. To achieve efficient and reliable video transmission, the quality factors such as resolution, encoding, average delay and throughput are resolved using the WebRTC along with the integration of the communication protocols. To protect the data transmission, we have implemented the SSL protocol and installed it on the server. We tested three different cases of video resolutions (i.e., 320×280, 820×460 and 900×590) for the performance evaluation of the video transmission. For the highest resolution, our TPR takes 3.5 ms for the encoding, and the average delay is 2.70 ms with 900 × 590 pixels. Full article
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Figure 1
<p>Difference between the motion of the Holonomic and Non-Holonomic robots.</p>
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<p>Kinematic model of the omnidirectional Holonomic robot.</p>
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<p>The schematic diagram of the DC motor.</p>
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<p>Ten ultrasonic sensors mounted in a circular order.</p>
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<p>Tricon (three) ultrasonic sensors mounted in circular order.</p>
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<p>Architecture of robot kinematics and integration of Kalman filter in TPR.</p>
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<p>A generic overview for the integration of WebRTC in TPR.</p>
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<p>Complete sequence of WebRTC, Javascript signalizing API implementation.</p>
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<p>(<b>a</b>) Case 1: square, L and I shape hurdles; (<b>b</b>) Case 2: polygon, I and triangular hurdles; (<b>c</b>) Case 3: square, L and I shape hurdles; (<b>d</b>) Case 1: Histogram of tricon sensors; (<b>e</b>) Case 2: Histogram of tricon sensors; (<b>f</b>) Case 3: Histogram of tricon sensors.</p>
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<p>Simulation of Kalman filter for autonomous drive.</p>
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<p>Simulation of the Kalman filter for velocity and position estimation.</p>
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<p>Final hardware demonstration of tele-presence robot (TPR).</p>
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<p>Working of robot during the testing from a remote location.</p>
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<p>Final testing of tele-presence robot (TPR).</p>
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<p>(<b>a</b>) Round transmission time (ms) for multiple locations; (<b>b</b>) throughput (kbps) with respect to multiple locations.</p>
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18 pages, 5936 KiB  
Article
Omnidirectional Manipulation of Microparticles on a Platform Subjected to Circular Motion Applying Dynamic Dry Friction Control
by Sigitas Kilikevičius, Kristina Liutkauskienė, Ernestas Uldinskas, Ribal El Banna and Algimantas Fedaravičius
Micromachines 2022, 13(5), 711; https://doi.org/10.3390/mi13050711 - 30 Apr 2022
Cited by 6 | Viewed by 1984
Abstract
Currently used planar manipulation methods that utilize oscillating surfaces are usually based on asymmetries of time, kinematic, wave, or power types. This paper proposes a method for omnidirectional manipulation of microparticles on a platform subjected to circular motion, where the motion of the [...] Read more.
Currently used planar manipulation methods that utilize oscillating surfaces are usually based on asymmetries of time, kinematic, wave, or power types. This paper proposes a method for omnidirectional manipulation of microparticles on a platform subjected to circular motion, where the motion of the particle is achieved and controlled through the asymmetry created by dynamic friction control. The range of angles at which microparticles can be directed, and the average velocity were considered figures of merit. To determine the intrinsic parameters of the system that define the direction and velocity of the particles, a nondimensional mathematical model of the proposed method was developed, and modeling of the manipulation process was carried out. The modeling has shown that it is possible to direct the particle omnidirectionally at any angle over the full 2π range by changing the phase shift between the function governing the circular motion and the dry friction control function. The shape of the trajectory and the average velocity of the particle depend mainly on the width of the dry friction control function. An experimental investigation of omnidirectional manipulation was carried out by implementing the method of dynamic dry friction control. The experiments verified that the asymmetry created by dynamic dry friction control is technically feasible and can be applied for the omnidirectional manipulation of microparticles. The experimental results were consistent with the modeling results and qualitatively confirmed the influence of the control parameters on the motion characteristics predicted by the modeling. The study enriches the classical theories of particle motion on oscillating rigid plates, and it is relevant for the industries that implement various tasks related to assembling, handling, feeding, transporting, or manipulating microparticles. Full article
(This article belongs to the Special Issue Flexible Micromanipulators and Micromanipulation)
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Figure 1
<p>Scheme of the dynamic model of omnidirectional manipulation of particles on a platform subjected to circular motion: (1) platform; (2) particle.</p>
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<p>Principle of dynamic dry friction control.</p>
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<p>Experimental setup for omnidirectional manipulation applying dynamic dry friction control: (<b>a</b>) General view; (<b>b</b>) Scheme where the following components are shown: (1) platform; (2) elastic rods; (3) piezoelectric actuator; (4) eccentric mechanism; (5) direct current power supply; (6) piezoelectric actuators; (7) manipulation plate; (8) microparticles; (9) optical reference sensor; (10) vibration analyzer; (11) arbitrary waveform generator; (12) piezo linear amplifier; (13) digital oscilloscope; (14) high-speed camera.</p>
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<p>Nondimensional displacement of the particle when <span class="html-italic">γ</span> = 4.9, <span class="html-italic">µ</span><sub>0</sub> = 0.2, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">λ</span> = <span class="html-italic">π</span>, <span class="html-italic">ϕ</span> = 0: (<b>a</b>) motion trajectories of the particle and the angle of displacement <span class="html-italic">α</span>. (<b>b</b>) horizontal <span class="html-italic">ξ</span> and vertical <span class="html-italic">ψ</span> components of the nondimensional displacement vs. the nondimensional time and the variation of the effective dry friction coefficient.</p>
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<p>Trajectories of the particle: (<b>a</b>) under different values of <span class="html-italic">λ</span> after 8 cycles of the circular motion of the platform when <span class="html-italic">ϕ =</span> 0, <span class="html-italic">µ</span><sub>0</sub> = 0.2, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">γ</span> = 4; (<b>b</b>) under different values of the phase shift <span class="html-italic">ϕ</span> after two cycles when <span class="html-italic">µ</span><sub>0</sub> = 0.2, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">γ</span> = 4.9, <span class="html-italic">λ = π</span> (solid line), <span class="html-italic">λ =</span> 13<span class="html-italic">π</span>/9 (dashed line).</p>
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<p>Variation of the angular velocity vector during the period of the eighth cycle of circular motion in polar coordinates when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">γ</span> = 4.9: (<b>a</b>) <span class="html-italic">µ</span><sub>0</sub> = 0.1; (<b>b</b>) <span class="html-italic">µ</span><sub>0</sub> = 0.2.</p>
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<p>Angular velocity vector vs. the nondimensional time when <span class="html-italic">µ</span><sub>0</sub> = 0.2, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">γ</span> = 4.9: (<b>a</b>) magnitude <span class="html-italic">ρ</span> during the period of the 8th cycle; (<b>b</b>) phase <span class="html-italic">θ</span> during the first four cycles.</p>
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<p>Average nondimensional velocity depending on the following: (<b>a</b>) <span class="html-italic">λ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 5, <span class="html-italic">ϕ</span> = 0; (<b>b</b>) <span class="html-italic">γ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">ϕ</span> = 0, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25; (<b>c</b>) ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> when <span class="html-italic">γ</span> = 9, <span class="html-italic">ϕ</span> = <span class="html-italic">π</span>/2; (<b>d</b>) <span class="html-italic">µ</span><sub>0</sub> when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>/2.</p>
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<p>Average nondimensional velocity depending on the following: (<b>a</b>) <span class="html-italic">λ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 5, <span class="html-italic">ϕ</span> = 0; (<b>b</b>) <span class="html-italic">γ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">ϕ</span> = 0, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25; (<b>c</b>) ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> when <span class="html-italic">γ</span> = 9, <span class="html-italic">ϕ</span> = <span class="html-italic">π</span>/2; (<b>d</b>) <span class="html-italic">µ</span><sub>0</sub> when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>/2.</p>
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<p>Average nondimensional velocity depending on the following: (<b>a</b>) <span class="html-italic">λ</span> and <span class="html-italic">γ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">ϕ</span> = 0; (<b>b</b>) ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> and <span class="html-italic">µ</span><sub>0</sub> when <span class="html-italic">γ</span> = 5, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>; (<b>c</b>) ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> and <span class="html-italic">λ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 5, <span class="html-italic">ϕ</span> = 0; (<b>d</b>) <span class="html-italic">γ</span> and <span class="html-italic">µ</span><sub>0</sub> when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 4, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>.</p>
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<p>Displacement angle α depending on: (<b>a</b>) <span class="html-italic">ϕ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 8.8, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25; (<b>b</b>) <span class="html-italic">λ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">ϕ</span> = 0, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25; (<b>c</b>) <span class="html-italic">µ</span><sub>0</sub> when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>/2; (<b>d</b>) <span class="html-italic">γ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">ϕ</span> = 0, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25.</p>
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<p>Displacement angle α depending on: (<b>a</b>) <span class="html-italic">λ</span> and <span class="html-italic">ϕ</span> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 8, ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25; (<b>b</b>) ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> and <span class="html-italic">µ</span><sub>0</sub> when <span class="html-italic">γ</span> = 5, <span class="html-italic">λ = π</span>, <span class="html-italic">ϕ</span> = 0; (<b>c</b>) <span class="html-italic">λ</span> and ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> when <span class="html-italic">µ</span><sub>0</sub> = 0.1, <span class="html-italic">γ</span> = 5, <span class="html-italic">ϕ</span> = 0; (<b>d</b>) <span class="html-italic">µ</span><sub>0</sub> and <span class="html-italic">γ</span> when ⟨<span class="html-italic">µ<sub>m</sub></span>⟩/<span class="html-italic">µ</span><sub>0</sub> = 0.25, <span class="html-italic">ϕ</span> = 0, <span class="html-italic">λ = π</span>.</p>
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<p>Experimental results of the average velocity depending on the following: (<b>a</b>) <span class="html-italic">λ</span> when <span class="html-italic">ω</span> = 62.83 rad/s, <span class="html-italic">ϕ</span> = 0; (<b>b</b>) the radius of the circular motion of the platform <span class="html-italic">R</span> when <span class="html-italic">ω</span> = 62.83 rad/s, <span class="html-italic">ϕ</span> = 0.</p>
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<p>Experimental results of α depending on the following: (<b>a</b>) <span class="html-italic">ϕ</span> when <span class="html-italic">R</span> = 0.49 mm, <span class="html-italic">ω</span> = 62.83 rad/s; (<b>b</b>) <span class="html-italic">λ</span> when <span class="html-italic">R</span> = 0.49 mm, <span class="html-italic">ω</span> = 62.83 rad/s.</p>
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<p>Images captured during the experiments: (<b>a</b>) captured trajectory of a single 0603-type MLCC when <span class="html-italic">R</span> = 0.49 mm, <span class="html-italic">ω</span> = 62.83 rad/s, <span class="html-italic">ϕ</span> = 9<span class="html-italic">π</span>/5, <span class="html-italic">λ =</span> 43<span class="html-italic">π</span>/90; (<b>b</b>) two frames separated by a time interval of 0.792 s that were captured during the manipulation of multiple 0603-type MLCC when <span class="html-italic">R</span> = 0.49 mm, <span class="html-italic">ω</span> = 62.83 rad/s, <span class="html-italic">ϕ</span> = 9<span class="html-italic">π</span>/10, <span class="html-italic">λ =</span> 43<span class="html-italic">π</span>/45.</p>
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11 pages, 1386 KiB  
Article
Overcoming Kinematic Singularities for Motion Control in a Caster Wheeled Omnidirectional Robot
by Oded Medina and Shlomi Hacohen
Robotics 2021, 10(4), 133; https://doi.org/10.3390/robotics10040133 - 13 Dec 2021
Cited by 4 | Viewed by 3581
Abstract
Omnidirectional planar robots are common these days due to their high mobility, for example in human–robot interactions. The motion of such mechanisms is based on specially designed wheels, which may vary when different terrains are considered. The usage of actuated caster wheels (ACW) [...] Read more.
Omnidirectional planar robots are common these days due to their high mobility, for example in human–robot interactions. The motion of such mechanisms is based on specially designed wheels, which may vary when different terrains are considered. The usage of actuated caster wheels (ACW) may enable the usage of regular wheels. Yet, it is known that an ACW robot with three actuated wheels needs to overcome kinematic singularities. This paper introduces the kinematic model for an ACW omni robot. We present a novel method to overcome the kinematic singularities of the mechanism’s Jacobian matrix by performing the time propagation in the mechanism’s configuration space. We show how the implementation of this method enables the estimation of caster wheels’ swivel angles by tracking the plate’s velocity. We present the mechanism’s kinematics and trajectory tracking in real-world experimentation using a novel robot design. Full article
(This article belongs to the Topic Motion Planning and Control for Robotics)
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Figure 1
<p>A three wheeled COR. The vectors presented are used to generate the robot’s kinematics.</p>
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<p>A COR robot. Two of the wheel-ground connection points and the COR’s plate may be thought of as a four-bar-mechanism where the third wheel may result in its motion.</p>
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<p>The constraint crawling concept: <span class="html-italic">y</span> is the constraint function we like to maintain.</p>
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<p>On the (<b>left</b>): The COR that was fabricated in the robotic research laboratory. The plaform radius (<math display="inline"><semantics> <msub> <mi>r</mi> <mi>i</mi> </msub> </semantics></math>) is 0.31 m and the caster wheel arm (<math display="inline"><semantics> <msub> <mi>d</mi> <mi>i</mi> </msub> </semantics></math>) is 112.5 m. (<b>right</b>): A camera top view of the experiment arena. A set of 18 Optitrack Flex-13 cameras for detecting the COR position and orientation were used in order to evaluate the mechanism’s performance. The available accuracy is less than one mm in the position and rotational error less than 0.05<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math> of a rigid body.</p>
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<p>A typical result of the COR’s path tracking in a square trajectory (<b>left</b>) and a circle trajectory (<b>right</b>). The blue line indicates the desired path while the red line shows the actual COR’s position as recorded by the Optitrack localization system. Axis units are in cm.</p>
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<p>An illustration of the pure-pursuit path tracking scheme. The planed motion direction (<math display="inline"><semantics> <mover accent="true"> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>) was marked by a brown arrow. High tracking error has caused to <math display="inline"><semantics> <mover accent="true"> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </semantics></math> to be perpendicular to the path as in the (<b>left</b>) case, and vice versa in the (<b>right</b>) one.</p>
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<p>The performances of three swivel angle PF estimator. The graph presents the statistics of over 100 runs.</p>
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