Parallel-distributed model in three-dimensional soft-fingered grasping and manipulation

This paper presents a general dynamic model that describes the two-dimensional grasp by two robotic fingers with soft fingertips. We derive the system's kinematics and dynamics by incorporating rolling constraints that depend on the deformation and on the rolling distance characteristics of the fingertips' material. We analyze the grasp stability at equilibrium, and conclude that the rolling properties of the fingertips can play an important role in grasp stability, especially when the width of the grasped object is small compared to the radius of the tips. Subsequently, a controller, which is based on the fingertips' rolling properties, is proposed for stable grasping concurrent with object orientation control. We evaluate the dynamic model under the proposed control law by simulations and experiments that make use of two different types of soft fingertip materials, through which it is confirmed that the dynamic model can successfully capture the effect of the fingertips' deformation and their rolling distance characteristics. Finally, we use the dynamic model to demonstrate by simulations the significance of the fingertips' rolling properties in grasping thin objects.

This paper analyzes the dynamics and control of pinch motions generated by a pair of two multi-degrees-of-freedom robot fingers with soft and deformable tips pinching a rigid object. It is shown firstly that passivity analysis leads to an effective design of a feedback control signal that realizes dynamic stable pinching (grasping), even if extra terms of Lagrange's multipliers arise from holonomic constraints of tight area-contacts between soft finger-tips and surfaces of the rigid object and exert torques and forces on the dynamics. It is shown secondly that a principle of superposition is applicable to the design of additional feedback signals for controlling both the posture (rotational angle) and position (some of task coordinates of the mass center) of the object provided that the number of degrees of freedom of each finger is specified for satisfying a condition of stationary resolution of controlled position state variables. The details of feedback signals are presented in the case of a special setup consisting of two robot fingers with two degrees of freedom.

This study focuses on the derivation of elastic force models of a hemispherical soft fingertip and reveals the existence of a local minimum of elastic potential energy (LMEE) induced by the deformation of the fingertip. The proposed model can be written in a straightforward equation when the geometric nonlinearity of the fingertip is applied in the derivation process, which is suitable for analyzing the stability of robotic handling system with soft fingertips. We also show complete elastic force and potential energy equations by incorporating the material nonlinearity into the derived model. Furthermore, we compare our models with the Hertzian contact theory that is applicable to the practical usage for the strength design of a lot of machines. Finally, we demonstrate the validity of our models by comparing simulation results and experimental results.

The development of dexterous and robust anthropomorphic hands with rich sensor feedback remains a challenging task for both humanoid robotics as well as prosthetics as of today. The design of hands that are scalable in size and equipped with integrated multimodal sensor systems is a key requirement for advanced control schemes and reactive behaviour. In this paper, we present the design of a scalable and low cost robotic finger with a soft fingertip and position, temperature as well as normal and shear force sensors. All cables and sensors are completely enclosed inside the finger to ensure an anthropometric appearance. The finger is modelled based on a 50th percentile male little finger and can be easily adapted to other dimensions in terms of size and sensor system configuration. We describe the design of the sensor system, provide an experimental analysis for the characterization of the different sensor types in terms of sensor range, resolution, creep, spatial response as well as temperature flux.

This paper is an exploration of the numeric and visual properties of a square numerical grid containing 81 elements (“J9 Space”). J9 Space has been derived from the standard multiplication grid through the calculation of digital roots. Nested within J9 Space are eight smaller square grids. A three-dimensional representation of J9 Space has been created from the two-dimensional numerical grid, displaying the highly symmetrical properties contained within it. The three-dimensional representation is fundamentally a collection of two-dimensional triangular polygons that create a surface in three-dimensional space. J9 Space appears to be a fundamental part of the framework of the number system and has some interesting mathematical features. This paper also summarises the recording of a three-dimensional printed model of J9 Space as a denisyuk reflection hologram. This is an artistic impression of the model using a volume holographic technique. The author who has contributed the mathematical concept (Prashant Jadav) suggests that the use of digital roots to develop three-dimensional models from well-known mathematical tools is a new method by which to create and visualise structures within the number system.

Lower envelopes are fundamental structures in computational geometry, which have many applications, such as computing general Voronoi diagrams and performing hidden surface removal in computer graphics. We present a generic, robust and efficient implementation of the divide-and-conquer algorithm for computing the envelopes of surfaces in IR3. To the best of our knowledge, this is the first exact implementation that computes envelopes in three-dimensional space. Our implementation is based on CGAL (the Computational Geometry Algorithms Library) and is designated as a CGAL package. The separation of topology and geometry in our solution allows for the reuse of the algorithm with different families of surfaces, provided that a small set of geometric objects and operations on them is supplied. We used our algorithm to compute the lower and upper envelope for several types of surfaces. Exact arithmetic is typically slower than floating-point arithmetic, especially when higher order surfaces are involved. Since our implementation follows the exact geometric computation paradigm, we minimize the number of geometric operations, and by that significantly improve the performance of the algorithm in practice. Our experiments show interesting phenomena in the behavior of the divide-and-conquer algorithm and the combinatorics of lower envelopes of random surfaces.

In this paper we are concerned with the problem of fine positioning of a soft robotic fingertip on a flat rigid surface by evoking a rolling motion while regulating force. A simple control law is proposed that uses a reference rolling trajectory that is state dependent. The non-linear asymptotic stability of the system equilibrium is proved. Computer simulation for a planar revolute robotic finger with 3 d.o.f has been performed in order to verify the effectiveness of the control law.

In this paper a detailed derivation is made of the kinematics and dynamics of a pair of robotic fingers manipulating a rectangular object with soft fingertips that are allowed to roll along the object surface. The whole system is confined to the horizontal plane. Two contact motion models for the soft area contact are considered and it is shown that they significantly affect contact mode and type of finger rolling constraints. A discussion on contact forces and a grasp analysis at object’s equilibrium is made. Last, simple feedback control solutions that have been proposed for stabilizing the grasping and regulating the object’s posture are presented.

Particle modeling of liquid drop formation on a solid surface in 3-D

Bathymetric mapping is an important tool for reservoir management, typically completed before reservoir construction. Historically, bathymetric maps were produced by interpolating between points measured at a relatively large spacing throughout a reservoir, typically on the order of a few, up to 10, meters or more depending on the size of the reservoir. These measurements were made using traditional survey methods before the reservoir was filled, or using sonar surveys after filling. Post-construction issues such as sedimentation and erosion can change a reservoir, but generating updated bathymetric maps is difficult as the areas of interest are typically in the sediment deltas and other difficult-to-access areas that are often above water or exposed for part of the year. We present a method to create complete reservoir bathymetric maps, including areas above the water line, using small unmanned aerial vehicle (sUAV) photogrammetry combined with multi-beam sonar data—both established methods for producing topographic models. This is a unique problem because the shoreline topographic models generated by the photogrammetry are long and thin, not an optimal geometry for model creation, and most images contain water, which causes issues with image-matching algorithms. This paper presents methods to create accurate above-water shoreline models using images from sUAVs, processed using a commercial software package and a method to accurately knit sonar and Structure from Motion (SfM) data sets by matching slopes. The models generated by both approaches are point clouds, which consist of points representing the ground surface in three-dimensional space. Generating models from sUAV-captured images requires ground control points (GCPs), i.e., points with a known location, to anchor model creation. For this study, we explored issues with ground control spacing, masking water regions (or omitting water regions) in the images, using no GCPs, and incorrectly tagging a GCP. To quantify the effect these issues had on model accuracy, we computed the difference between generated clouds and a reference point cloud to determine the point cloud error. We found that the time required to place GCPs was significantly more than the time required to capture images, so optimizing GCP density is important. To generate long, thin shoreline models, we found that GCPs with a ~1.5-km (~1-mile) spacing along a shoreline are sufficient to generate useful data. This spacing resulted in an average error of 5.5 cm compared to a reference cloud that was generated using ~0.5-km (~1/4-mile) GCP spacing. We found that we needed to mask water and areas related to distant regions and sky in images used for model creation. This is because water, objects in the far oblique distance, and sky confuse the algorithms that match points among images. If we did not mask the images, the resulting models had errors of more than 20 m. Our sonar point clouds, while self-consistent, were not accurately georeferenced, which is typical for most reservoir surveys. We demonstrate a method using cross-sections of the transition between the above-water clouds and sonar clouds to geo-locate the sonar data and accurately knit the two data sets. Shore line topography models (long and thin) and integration of sonar and drone data is a niche area that leverages current advances in data collection and processing. Our work will help researchers and practitioners use these advances to generate accurate post-construction reservoir bathometry maps to assist with reservoir management.

In this paper we describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently. Unlike prior approaches, which act on springs or individual strain components, this method acts on the strain tensors in a coordinate-invariant fashion allowing isotropic behavior. Our method applies to both two-and three-dimensional strains, and only requires computing the singular value decomposition of the deformation gradient, either a small 2x2 or 3x3 matrix, for each element. We demonstrate its use with triangular and tetrahedral linear-basis elements. For triangulated surfaces in three-dimensional space, we also describe a complementary edge-angle-limiting method to limit out-of-plane bending. All of the limits are enforced through an iterative, non-linear, Gauss-Seidel-like constraint procedure. To accelerate convergence, we propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy. Compared with other constraint-based techniques, our isotropic multi-resolution strain-limiting method is straightforward to implement, efficient to use, and applicable to a wide range of shell and solid materials.

Architectural fabrics are an integral part of fabric architecture, a term used to describe tensile fabric membranes – also known as fabric structures or textile buildings. This chapter discusses architectural fabrics in the context of their physical properties, durability, aesthetics and suitability for a given application. The account is preceded by a brief background to fabric structures and related design issues. Images of samples of different types of architectural fabrics, their descriptions and examples of application in real projects are used to clarify the subject. There are numerous factors affecting the choice of architectural fabric and these include a manufacturing design stage, known as patterning – the creation of a tensile surface in three-dimensional space out of a series of two-dimensional, unstrained pieces of fabric. Patterning is presented in a concise manner, sufficient to highlight design issues, together with problems of choice of fabric and behaviour in a full-scale tension structure. The chapter ends with a brief discussion of factors influencing the choice of architectural fabric, future research trends and development of new materials.

The main subject of this chapter is surfaces in three-dimensional space. In preparation for this, we begin with a study of some special curves in the plane —the conic sections. In the last two sections, we will do some calculus with curves in space. Applications of calculus to surfaces are given in Chapters 15 and 16.

Разработана методика расчета и анализа статистических характеристик боковых пиков двумерных, авто- и взаимных корреляционных функций шумоподобных сложных сигналов, определенных как поверхности в трехмерном пространстве с координатами, соответствующими частоте и времени. Суть и новизна методики состоит в установлении для любой двумерной корреляционной функции сигнала взаимосвязи значений ее боковых пиков, а также параметров их функции распределения со спектральной плотностью мощности исходного сигнала, рассчитанной по его реализации конечной длительности, и, в конечном итоге, с характеристиками боковых пиков различных одномерных автокорреляционных функций псевдослучайной последовательности, на основе которой он сформирован. Результатом данного подхода являются установленные количественные взаимосвязи статистических характеристик боковых пиков двумерной корреляционной функции сложного сигнала с длиной псевдослучайной последовательности, соответствующей ему в зависимости от ее типа. A technique has been developed for calculating and analyzing the statistical characteristics of the side peaks of two-dimensional and auto- and cross-correlation functions of spread spectrum signals, defined as surfaces in threedimensional space with coordinates corresponding to frequency and time. The essence and novelty of the technique is to establish for any two-dimensional correlation function of a signal the relationship between the values of its side peaks, as well as the parameters of their distribution function, with the power spectral density of the original signal, calculated from its implementation of finite duration, and, ultimately, with the characteristics of the side peaks of various one-dimensional autocorrelation functions of the pseudo-random sequence on the basis of which it is formed. The result of this approach is the established quantitative relationships between the statistical characteristics of the side peaks of the two-dimensional correlation function of a complex signal with the length of the pseudo-random sequence corresponding to it, depending on its type.

The study of geometric flows for smoothing, multiscale representation, and analysis of two- and three-dimensional objects has received much attention in the past few years. In this paper, we first survey the geometric smoothing of curves and surfaces via geometric heat-type flows, which are invariant under the groups of Euclidean and affine motions. Second, using the general theory of differential invariants, we determine the general formula for a geometric hypersurface evolution which is invariant under a prescribed symmetry group. As an application, we present the simplest affine invariant flow for (convex) surfaces in three-dimensional space, which, like the affine-invariant curve shortening flow, will be of fundamental importance in the processing of three-dimensional images.