3D Cartesian Space Research Articles

Certified polyhedral decompositions of collision-free configuration space

Understanding the geometry of collision-free configuration space (C-free) in the presence of Cartesian-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping Cartesian-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the 3D Cartesian space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm’s ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e, and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

Three-Dimensional Multi-Target Tracking Using Dual-Orthogonal Baseline Interferometric Radar.

Multi-target tracking (MTT) generally needs either a Doppler radar network with spatially separated receivers or a single radar equipped with costly phased array antennas. However, Doppler radar networks have high computational complexity, attributed to the multiple receivers in the network. Moreover, array signal processing techniques for phased array radar also increase the computational burden on the processing unit. To resolve this issue, this paper investigates the problem of the detection and tracking of multiple targets in a three-dimensional (3D) Cartesian space based on range and 3D velocity measurements extracted from dual-orthogonal baseline interferometric radar. The contribution of this paper is twofold. First, a nonlinear 3D velocity measurement function, defining the relationship between the state of the target and 3D velocity measurements, is derived. Based on this measurement function, the design of the proposed algorithm includes the global nearest neighbor (GNN) technique for data association, an interacting multiple model estimator with a square-root cubature Kalman filter (IMM-SCKF) for state estimation, and a rule-based M/N logic for track management. Second, Monte Carlo simulation results for different multi-target scenarios are presented to demonstrate the performance of the algorithm in terms of track accuracy, computational complexity, and IMM mean model probabilities.

Sub-grid modeling of pitch-angle diffusion for ion-scale waves in hybrid-Vlasov simulations with Cartesian velocity space

Numerical simulations have grown to play a central role in modern sciences over the years. The ever-improving technology of supercomputers has made large and precise models available. However, this accuracy is often limited by the cost of computational resources. Lowering the simulation's spatial resolution in order to conserve resources can lead to key processes being unresolved. We have shown in a previous study how insufficient spatial resolution of the proton cyclotron instability leads to a misrepresentation of ion dynamics in hybrid-Vlasov simulations. This leads to larger than expected temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a sub-grid numerical model to introduce pitch-angle diffusion in a 3D Cartesian velocity space, at a spatial resolution where the relevant wave–particle interactions were previously not correctly resolved. We show that the method is successfully able to isotropize loss-cone shaped velocity distribution functions, and that this method could be applied to simulations in order to save computational resources and still correctly model wave–particle interactions.

Surface model of the human red blood cell simulating changes in membrane curvature under strain

We present mathematical simulations of shapes of red blood cells (RBCs) and their cytoskeleton when they are subjected to linear strain. The cell surface is described by a previously reported quartic equation in three dimensional (3D) Cartesian space. Using recently available functions in Mathematica to triangularize the surfaces we computed four types of curvature of the membrane. We also mapped changes in mesh-triangle area and curvatures as the RBCs were distorted. The highly deformable red blood cell (erythrocyte; RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a custom apparatus inside an NMR spectrometer. A key observation is the extent to which the maximum and minimum Principal Curvatures are localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. Changes on the nanometre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions, which persist for many hours. This finding is relevant to a proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. However, if the curvature that gates Piezo1 is at a very fine length scale, then membrane tension will determine local curvature; so, curvatures as computed here (in contrast to much finer surface irregularities) may not influence Piezo1 activity. Nevertheless, our analytical methods can be extended address these new mechanistic proposals. The geometrical reorganization of the simulated cytoskeleton informs ideas about the mechanism of concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.

Three-dimensional ISAR image reconstruction technique based on radar network

ABSTRACT Recently, there are few reports on three-dimensional (3D) imaging method based on radar network. Aiming at the 3D imaging problem in radar network, a reconstruction method for 3D inverse synthetic aperture radar (ISAR) image based on radar network is proposed in this paper. The 2D ISAR image is considered as a geometric projection of a target on an imaging projection plane; thus, aerial points might be scatterers of targets if their geometric projection on an imaging projection plane is similar to the 2D ISAR image of the target. The proposed method makes use of the similarity between the ISAR Range-Doppler (RD) image and the target’s geometric projection on the imaging projection plane to construct the 3D image reconstruction model. The reconstructed target 3D ISAR image is obtained by estimating the scattering centre position in 3D Cartesian space. In this paper, the projection formulas designed to calculate the geometric projection of the aerial points on the imaging projection plane are derived to first form the projection image. Depending on the similarity between the 2D ISAR image and the target’s projection, the 3D ISAR image reconstruction model based on the radar network is constructed. Further, a corresponding algorithm for solving the 3D ISAR image reconstruction model is proposed. Finally, the radar distribution influence on reconstruction precision is analysed, and some experimental results are given to illustrate the effectiveness of the proposed method.

Optimal Feet-Forces’ and Torque Distributions of Six-Legged Robot Maneuvering on Various Terrains

SUMMARYAn analytical model with coupled dynamics for a realistic six-legged robotic system locomoting on various terrains has been developed, and its effectiveness has been proven through computer simulations and validated using virtual prototyping tools and real experiment. The approach is new and has not been attempted before. This study investigated the optimal feet-forces’ distributions under body force and foot–ground interaction considering compliant contact and friction force models for the feet undergoing slip. The kinematic model with 114 implicit constraints in 3D Cartesian space has been transformed in terms of generalized coordinates with a reduced explicit set of 24 constrained equations using kinematic transformations. The nonlinear constrained inverse dynamics model of the system has been formulated as a coupled dynamical problem using Newton–Euler method with realistic environmental conditions (compliant foot–ground contact, impact, and friction) and computed using optimization techniques due to its indeterminate nature. One case study has been carried out to validate the analytical data with the simulated ones executed in MSC.ADAMS® (Automated Dynamic Analysis of Mechanical Systems), while the other case study has been conducted to validate the analytical and simulated data with the experimental ones. In both these cases, results are found to be in close agreement, which proves the efficacy of the model.

A Robotic Platform for 3D Forelimb Rehabilitation with Rats.

In an attempt to promote greater functional recovery after spinal cord injury, researchers have begun exploring combinatorial treatments, such as robotic rehabilitation combined with stem cell transplantation. Since these treatment methods are in their nascent stages, rodent models have been proposed for initial investigations. Robots have been built for locomotion rehabilitation and planar forelimb reach and grasp assessment with rodents; however, a robotic platform suitable for three-dimensional movement rehabilitation of the rodent forelimb has not yet been developed. In this paper, a novel three degree of freedom robotic manipulator for automated forelimb rehabilitation combined with stem cell transplantation after cervical spinal cord injury with rats is proposed. The robot interfaces with a rat in an end-effector manner, measuring and interacting with the forelimb in the 3D Cartesian space. In this work, we trained two rats through behavioral shaping to actively interact with the device during two robot control modes. This work provides preliminary investigations into the feasibility of 3D forelimb rehabilitation with rats, which could be translated as a paradigm for combinatorial treatments after spinal cord injury in a controlled manner.

A 3D image reconstruction technique for spinning targets based on Radar networks

ABSTRACTA three-dimensional (3D) image reconstruction method for the spinning target based on the radar network is proposed in this letter and the design concept is sourced from the similarity of the two-dimensional (2D) imaging result with the target’s mapping on the imaging plane. The proposed method has the capacity to generate 3D image of the spinning target by reconstructing the scattering distribution in 3D Cartesian space. Firstly, the inverse Radon transform is applied to obtain the imaging result of the spinning target and the mapping formulas for mapping the air points onto the 2D image plane are derived. In addition, the radar network 3D image reconstruction model for the spinning target is constructed and the corresponding algorithm for solving the reconstruction model is proposed. Finally, some experiment results are given to verify the effectiveness of the proposed method.

Origin of Helical Screw Sense Selectivity Induced by Chiral Constrained Cα-Tetrasubstituted α-Amino Acids in Aib-based Peptides

The mechanisms behind the propensity of chiral constrained Cα-tetrasubstituted amino acids (cCTAAs) to induce one particular helical screw sense, when included in the Ac-Aib2-cCTAA-Aib2-NHMe peptide model, were studied through replica exchange molecular dynamics, potential of mean force, and quantum theory of atoms in molecules calculations. We observed that cCTAAs exert their effect on helical screw sense selectivity through the positioning of the side chain to generate steric hindrance in either the (-x, +y, +z) or (+x, +y, -z) sectors of a right-handed 3D Cartesian space, where the z axis corresponds to the axis of the helix and the Cα lies on the +y semiaxis (0, +y, 0). The different strengthening of the noncovalent interactions, also comprising C-H···O interactions, exerted by the cCTAA in the right-handed or left-handed helix was also found important to define the preference of a cCTAA for a particular helix screw sense.

Bistatic three-dimensional interferometric ISAR image reconstruction

A three-dimensional (3D) bistatic inverse synthetic aperture radar (ISAR) imaging method is proposed in this paper. The proposed method makes use of interferometry and technically speaking, produces a 3D target reconstruction by estimating a scattering center position in 3D Cartesian space. The proposed method makes use of a combined ISAR/interferometry technique that also allows the ISAR image plane to orientation to be estimated. Cross- or L-shaped antenna configurations are discussed, and the effects of the baseline length along the horizontal and vertical direction on the scatterer’s position estimation are analyzed in detail. Finally, numerical simulations are used to evaluate the proposed method’s performance.

Mechanism of stabilization of helix secondary structure by constrained Cα-tetrasubstituted α-amino acids.

The theoretical basis behind the ability of constrained Cα-tetrasubstituted amino acids (CTAAs) to induce stable helical conformations has been studied through Replica Exchange Molecular Dynamics Potential of Mean Force Quantum Theory of Atoms In Molecules calculations on Ac-l-Ala-CTAA-l-Ala-Aib-l-Ala-NHMe peptide models. We found that the origin of helix stabilization by CTAAs can be ascribed to at least two complementary mechanisms limiting the backbone conformational freedom: steric hindrance predominantly in the (+x,+y,-z) sector of a right-handed 3D Cartesian space, where the z axis coincides with the helical axis and the Cα of the CTAA lies on the +y axis (0,+y,0), and the establishment of additional and relatively strong C-H···O interactions involving the CTAA.

Engine Map and Optimal Operation Path Construction for an Engine-CVT Powertrain System

Rising fuel costs increase the importance of CVT powertrains in the automotive industry. Their benefit is that they allow an engine to operate at any condition which motivates development of fuel economy mode control strategies. In this work, an engine map is multiplied by the efficiency of a hydrostatic continuously variable transmission (HCVT). Therefore, the map is pictured in a 3D Cartesian space which is functioned into 3 parameters of indicated engine torque, engine speed, and transmission ratio. Operation of the engine powertrain system can be set to support any required power and speed of the vehicle at the highest efficiency point. The study examines a 900 cc. gasoline engine connected to the HCVT. To generate the operating range of the engine, the engine speed and hydraulic pressure were controlled by an electronic throttle and pump swash plate variation, respectively. The operating range is 3.353 - 10.442 kW. This power corresponds to a vehicle ground speed of 43.065 61.488 km/hr through a gear ratio of 0.5-1.5. Consequently, the system efficiency map was created and then used to construct the best operating path according to the required driving cycle. The points on the path were selected by the concept of the highest overall efficiency in the 3D map. As a result, the optimal operation path was found by connecting each point which is directed to the best solution for vehicle operation.

Detection and Modelling of Nonlinear Elastic Response in Damaged Composite Structures

In this paper the nonlinear material response of damaged composite structures under periodic excitation is experimentally and numerically investigated. In particular, the nonlinear wave propagation problem was numerically analysed through a finite element model able to predict the nonlinear interaction of acoustic/ultrasonic waves with damage precursors and micro-cracks. Such a constitutive model is based on the Landau’s semi-analytical approach to account for anharmonic effects of the medium, and is able to provide an understanding of nonlinear elastic phenomena such as the second harmonic generation. Moreover, Kelvin tensorial formulation was used to extend the wave propagation problem in orthotropic materials to the 3D Cartesian space. In this manner, the interaction of the stress waves with the 3D crack could be analysed. This numerical model was then experimentally validated on a composite plate undergone to impact loading. Good agreement between the experimental and numerical second harmonic response was found, showing that this material model can be used as a simple and useful tool for future structural diagnostic applications.

Generic fitted shapes (GFS): Volumetric object segmentation in service robotics

In this paper, a simultaneous 3D volumetric segmentation and reconstruction method, based on the so-called Generic Fitted Shapes (GFS) is proposed. The aim of this work is to cope with the lack of volumetric information encountered in visually controlled mobile manipulation systems equipped with stereo or RGB-D cameras. Instead of using primitive volumes, such as cuboids or cylinders, for approximating objects in point clouds, their volumetric structure has been estimated based on fitted generic shapes. The proposed GFSs can capture the shapes of a broad range of object classes without the need of large a-priori shape databases. The fitting algorithm, which aims at determining the particular geometry of each object of interest, is based on a modified version of the active contours approach extended to the 3D Cartesian space. The proposed volumetric segmentation system produces comprehensive closed object surfaces which can be further used in mobile manipulation scenarios. Within the experimental setup, the proposed technique has been evaluated against two state-of-the-art methods, namely superquadrics and 3D Object Retrieval (3DOR) engines.

An Open Loop Walking on Different Slopes for NAO Humanoid Robot

Dynamic gait planning for humanoid robots encounters difficulties such as stability, speed, and smoothness. In most of previous studies, joints’ trajectories are calculated in 3D Cartesian space, then, introducing boundary conditions and using polynomials, the first and second derivatives of the motion are ensured to be continuous. Then, the stability of the motion is guaranteed using Zero Moment Point (ZMP) stability criterion. In this study, a trajectory planner is presented using the semi-ellipse equations of the motion; the continuity of the derivatives is preserved. Stabilization of motion is attained through using ZMP criterion and 3d inverted pendulum equations in three slope conditions. The effectiveness of the proposed approach is investigated using Webots software. Implementing proposed approach, smoothness, stability, and convenient speed (rather than 17cm/s in flat condition) are achieved

Hamiltonians and variational principles for Alfvén simple waves

The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet–Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler–Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole–Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection.

Accelerating the Sweep3D for a Graphic Processor Unit

Abstract —As a powerful and flexible processor, the Graphic Processing Unit (GPU) can offer a great faculty in solving many high-performance computing applications. Sweep3D, which simulates a single group time-independent discrete ordinates (Sn) neutron transport deterministically on 3D Cartesian geometry space, represents the key part of a real ASCI application. The wavefront process for parallel computation in Sweep3D limits the concurrent threads on the GPU. In this paper, we present multi-dimensional optimization methods for Sweep3D, which can be efficiently implemented on the fine-grained parallel architecture of the GPU. Our results show that the overall performance of Sweep3D on the CPU-GPU hybrid platform can be improved up to 4.38 times as compared to the CPU-based implementation. Keywords —Sweep3D, Neutron Transport, GPU, CUDA 1. I NTRODUCTION When the first GPU was introduced in 1999, the GPU mainly had been used to transform, light and to rasterize triangles in three dimension (3D) graphics applications [1]. The perform-ance of GPU doubles about every six to nine months, which means that it outperforms the Cen-tral Processing Unit (CPU) by a lot [2]. The modern GPUs are throughput-oriented parallel processors that can offer peak performance up to 2.72 Tflops single-precision floating-point and 544 Gflops double-precision floating-point [3]. At the same time, the GPU programming models, such as NVIDIA’s Compute Unified Device Architecture (CUDA) [4], AMD/ATI’s Streaming Computing [5] and OpenCL [6], have matures and they simplify the processing of developing non-graphics applications. The enhancement of computing performance, and the development of programming models and software makes GPU more and more suitable for general purpose computing. At present, GPU has been successfully applied to medical imaging, universe explo-ration, physics simulation, linear system solutions, and other computation intensive domains [7]. There is a growing need to accurately simulate physical systems whose evolutions depend on the transport of subatomic particles coupled with other complex physics [8]. In many simula-tions, particle transport calculations consume the majority of the computational resources. For example, the time devoted to particle transport problems in multi-physics simulations takes up

SU‐FF‐J‐27: Calibration of the Dual‐Transducer Focused Acoustic Radiation Field for a Multimodal Sono‐Contrast NIR Spectroscopy System

Purpose: To calibrate the dual‐transducer focused acoustic radiation field, register the focus center in the imaging ultrasound system, and establish a monthly calibration protocol for a noninvasive multi‐modal breast cancer scanning system. Method and Materials: The scanhead incorporated two 1MHz focused transducers aligned orthogonally to deliver acoustic radiation force (ARF) in a 2.4cm region. A commercial ultrasound probe, located in the same vertical plane as the focused transducers, was used in the system for image co‐registration. Dielectric fluid was filled into the scanhead as the ultrasound transmission media. The scanhead was merged into a water tank filled with degassed distilled water. A function generator connected with an amplifier was used to drive the focused transducers. The imaging ultrasound probe was connected to a commercial ultrasound system. The focused transducers were excited by 1MHz continuous sine wave with amplitude of 200mv from a function generator, amplified by the amplifier. A hydrophone was aligned vertically below the bottom plate and moved by a 3D motion platform (resolution 0.05mm) in the 3D Cartesian space at a step of 0.1mm. An oscilloscope was connected with the hydrophone for data display and acquisition of the voltage signals for calculating the acoustic intensity. Results: The focal spot that has the maximum peak‐positive voltage signal on the oscilloscope was found at 2.34 cm below the bottom plate, which is the designed intersection of the axes of the two focused transducers. The Spatial Peak Temporal Average Intensity was determined to be 0.4 W⋅cm−2, below the FDA therapeutic ultrasound limits (0.72 W⋅cm−2). The focal spot was then registered in the imaging ultrasound images. Conclusions: This study established the baseline of the dual‐transducer focus acoustic radiation field. A monthly calibration protocol has been developed following the same procedure for the focused acoustic radiation field.Acknowledgement: supported by NCI Grant CA107860.

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

Simulation and experiments for a vision-based control of a 6R robot

In this paper, we present both the simulation and experimental results for position-based visual servoing control of a 6R robot using two stationary cameras . This method can deal with real-time changes in the relative position of the target with respect to the robot, while providing greater accuracy. In addition, the servo control structure is independent of the target pose coordinates. Direct and inverse kinematics equations, in addition to dynamic equations of the 6R robot, have been derived and simulated. Then we prescribe simulation of image processing, object recognition and pose estimation for the end effector and target-object in 3D Cartesian space and visual control of the robot. Afterwards, performance tests of 6R robot using two cameras have been implemented. Finally, experimental results obtained from actual implementation of visual control and tests of 6R robot in lab are presented. Analysis of error and test data has been carried out according to ISO9283, ANSI-RIA R15.05–2 standards and the MATLAB statistical toolbox. An efficient algorithm is designed for collision detection and contact determination between the 6R robot links and its environment during their rotation in controlling and performance tests. In this technique, bounding spheres on different parts of 6R robot are used to detect collisions among them.