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This paper presents design workflows for the representation, analysis and fabrication of braided structures. The workflows employ a braid pattern and simulation method which extends the state-of-the-art in the following ways: by supporting the braid design of both pre-determined target shapes and exploratory, generative, or evolved designs; by incorporating material and fabrication constraints generalised for both hand and machine; by providing a greater degree of design agency and supporting real-time modification of braid topologies. The paper first introduces braid as a technique, stating the objectives and motivation for our exploration of braid within an architectural context and highlighting both the relevance of braid and current lack of suitable design modelling tools to support our approach. We briefly introduce the state-of-the-art in braid representation and present the characteristics and merits of our method, demonstrated though four example design and analysis workflows. The workflows frame specific aspects of enquiry for the ongoing research project flora robotica. These include modelling target geometries, automatically producing instructions for fabrication, conducting structural analysis, and supporting generative design. We then evaluate the performance and generalisability of the modelling against criteria of geometric similarity and simulation performance. To conclude the paper we discuss future developments of the work.
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Design Tools and Workflows for Braided Structures
Petras Vestartas1, Mary Katherine Heinrich1, Mateusz Zwierzycki1, David Andres
Leon1, Ashkan Cheheltan1,2, Riccardo La Magna3, and Phil Ayres1
1 Centre for Information Technology and Architecture, The Royal Danish Academy of Fine
Arts, School of Architecture, 1435 Copenhagen, Denmark
2 Berlin University of the Arts, 10623 Berlin, Germany
3 Konstruktives Entwerfen und Tragwerksplanung, Berlin University of the Arts,
10623 Berlin, Germany
petrasvestartas@gmail.com
Abstract. This paper presents design workflows for the representation, analysis
and fabrication of braided structures. The workflows employ a braid pattern and
simulation method which extends the state-of-the-art in the following ways: by
supporting the braid design of both pre-determined target shapes and exploratory,
generative, or evolved designs; by incorporating material and fabrication con-
straints generalised for both hand and machine; by providing a greater degree of
design agency and supporting real-time modification of braid topologies.
The paper first introduces braid as a technique, stating the objectives and mo-
tivation for our exploration of braid within an architectural context and highlight-
ing both the relevance of braid and current lack of suitable design modelling tools
to support our approach. We briefly introduce the state-of-the-art in braid repre-
sentation and present the characteristics and merits of our method, demonstrated
though four example design and analysis workflows. The workflows frame spe-
cific aspects of enquiry for the ongoing research project flora robotica. These
include modelling target geometries, automatically producing instructions for
fabrication, conducting structural analysis, and supporting generative design. We
then evaluate the performance and generalisability of the modelling against crite-
ria of geometric similarity and simulation performance. To conclude the paper we
discuss future developments of the work.
Keywords: Braided structures, Braid representation, Computational design.
1 Introduction - Context, Motivation and Objectives
Braid technique is based on a principle of oblique interlacing of three or more strands
of yarn, filament or strapping [Rana & Fangueiro, 2015]. The technique is used to pro-
duce artifacts that are larger, stronger, more resilient and, often, more aesthetically
charged than the original material. Braid offers tremendous versatility in terms of ma-
terial, scale of artifact, and method of production (Fig. 1). As such, braid is applied
across a broad range of industries, including medicine (stents), agriculture (industrial
2
hoses) and leisure equipment (ropes). Braid is also used to produce preforms for ad-
vanced composite manufacture [Potluri et al., 2003]. The resulting composites are
amongst the lightest yet strongest components currently produced and are utilised in
high-performance arenas such as cycling, racing and aeronautics [Rana & Fangueiro,
2015]. Despite the versatility, resilience, and scalability demonstrated by braid across
many industries and functional uses, it is not a commonly used or discussed technique
within contemporary architecture. In parallel to the limited use of braid in architecture,
there is also a lack of suitable design modelling tools for freely exploring complex braid
topologies against architectural design, analysis, and fabrication considerations. In the
work presented here, we concentrate on exploring hollow tubular braids (typically re-
ferred to as ‘2D braid’ in industrial contexts [Ayranci & Carey, 2008]). Tubular braids
offer a rich space of topological freedom, as well as structural potential when approach-
ing architectural scale.
Fig. 1. The versatility of braid technique spans across scales, materials and production processes.
3
Our motivation for exploring braid derives from the on-going flora robotica project
[Hamann et al., 2015], focusing on symbiotic relationships between biological plants
and distributed robotics, for the purpose of constructing architectural artifacts and
spaces. The project pursues braided structures as adaptive mechanical scaffolds, on
which biological (plant) and artificial (robot) materials can grow and act (Fig. 2, left).
Spatial and topological organisation of the bio-hybrid system is steered over time by a
combination of high-level design objectives, distributed robot controllers, and user in-
teraction. Achieving this broader goal requires that the braided scaffolds have the abil-
ity to reorganise continuously in situ, through a distributed construction process. The
scaffolds may be collaboratively fabricated by stationary centrally-controlled braid ma-
chines [Richardson, 1993], swarms of distributed mobile braiding robots [Heinrich et
al., 2016], or manual braiding by users (Fig. 2, right). To achieve these aims, it has been
necessary to develop tools and workflows that can support design speculation and spec-
ification, and provide an adequate representation of braid in the context of diverse and
often independent design and evaluation tasks. Within flora robotica, these include the
modelling of complex braids produced by hand, the generation of fabrication instruc-
tion for both hand and automated methods, the analysis of mechanical performance of
braids, and the adaptive generation of braid morphology.
Fig. 2. (left) Braided scaffolds supporting plants and robotic elements in the flora robotica pro-
ject. (right) Hand braided examples of self-supporting complex braid topologies.
2 Braid Representation Method
This section briefly reviews our developed braid representation method [Heinrich et al,
2017]. In general, the method uses a precomputed set of tiles, which, in their underlying
logic, combine different approaches seen in the literature [e.g., Mercat, 2001; Kaplan
& Cohen, 2003; Akleman et al., 2009]. The method works directly on polygon meshes
that can be modified in real-time.
The first step in the method is tiling. Following the approach defined by Mercat
[2001], a predefined tile dictionary provides a complete description of possible braid
strip organizations (Fig. 3). In the tile dictionary utilised in this paper, there are three
possible relationships between neighboring tiles: no connection (green colour in Fig.
3); connection with two separated strips (yellow); connection with two crossing strips
(blue). To be able to simulate the physical characteristics of the braiding pattern, it is
4
necessary to translate the tile notation into geometry. The method uses a point grid,
with each strip declared as a series of grid-based coordinates on the mesh.
The next step is relaxation. In evaluating the physical properties of the digital model,
the braid cannot be approximated to a grid-shell due to torsion occurring in the flat
strips. The mesh topology is therefore constructed from triangle meshes with varying
density. The constraint-based geometry solver Kangaroo 2 (update to [Piker, 2013]) is
used to perform relaxation, with objectives to equalise mesh edges, detect collisions for
zero length mesh manifolds, and add shell-like behaviour. The problem of ‘overshoot-
ingmay occur when mesh faces are undesirably stretched or compressed by large per-
centages, so a dynamic constraint incrementally increases initial edge lengths to reach
the target. This results in longer calculation time, but achieves tight braids with strips
that, if unrolled, approximate the straightness of physical strips.
Fig. 3. An example of a complete set of tiles for 3 colours and 4-sided polygons. 24 tiles guarantee
all the combinations of colours.
5
Fig. 4. Initial geometry (left) and three example relaxation results when changing target mesh
edge length.
3 Design Workflows
In this section, we describe four examples that integrate the braid representation method
with possible design workflows (Fig. 5). As outlined in the previous section, these
workflows support design efforts of the flora robotica project.
In the first workflow (modelling target geometries), we compare our method to existing
state-of-the-art approaches by tiling the input of a manually modelled mesh. In the sec-
ond (generating fabrication instructions), we interpret a model to provide the output of
textual instructions for hand braiding. Third (analysing mechanical properties), we ad-
dress calibrated simulations for the output of assessing structural performance. Fourth
(generative design), we generate braids from the input of an environmentally respon-
sive robotic controller. In combination, these workflows show that our braid represen-
tation is sufficiently generalised that it is able to both receive multiple inputs (workflow
1 and 4) and be interpreted for multiple outputs (workflow 2 and 3).
Fig. 5. Overview of the workflows supported by the generalised modelling approach for braided
artifacts. The generalised modelling method can receive one of the following inputs: target phys-
ical artifact (Fig. 2), target master surface (workflow 1), or generative input (workflow 4). The
mesh resulting from the generalised modelling approach can be interpreted in multiple comple-
mentary ways, such that it can be analysed (workflow 3), visualized (Fig. 4 and 6), and used to
generate instructions for hand braiding or braiding robots (workflow 2).
6
3.1 Workflow 1: modelling target geometries
In this workflow we demonstrate modelling to pre-defined design targets, such as those
shown in Figure 2. In these cases, material geometry is a hard constraint that must be
considered to ensure an adequate representational approximation. In addition, conform-
ing to local braid conditions such as asymmetric bifurcations (in terms of strip num-
bers), inversion and ‘cornering’ displayed by these physical prototypes present further
modelling challenges. This workflow has five stages. First, a low-poly quad mesh
model is created of the physical prototype. Next, quad mesh edges are equalised by
using a custom Kangaroo 2 solver with spherical collision and equal length line con-
straints in a parallel thread for faster calculation time. Thirdly, all braid conditions are
specified by the application of tile colours to the quad mesh. The braid tiles are then
applied from the existing tile dictionary (Fig. 3). Finally, strip-strip simulation is used
to achieve a tight and realistic braid model. Within flora robotica the making of phys-
ical prototypes is an essential mode of exploration, as is the ability to accurately repre-
sent these complex morphologies once produced.
Fig. 6. 3D modelling braid typology informed by the hand-braided structures. Modelling steps
from left to right are: a) 3D mesh modelling; b) Equalise edge lengths; c) Assign colours to mesh
edges; d) Apply tiling; e) Strip-Strip relaxation.
7
3.2 Workflow 2: generating fabrication instructions
Fig. 7. Example instructions for hand braiding, generated using a low-level graph representation
interpreted through an instruction dictionary.
In this workflow, a braid result from the solver is used to automatically generate fabri-
cation instructions for distributed robots, centralised robots, or hand fabrication. In this
example, we look at hand fabrication of a simple 12-strip bifurcating braid. We devel-
oped a method, firstly, to generate a low-level graph representation of the braid’s or-
ganisation and, secondly, to interpret that graph into instructions using a string replace-
ment dictionary. The low-level graph represents the braid as a series of connections, in
which each intersection of braid strips receives a unique ID, and the under or over con-
dition of a strip is indicated by a sign attached to the intersection ID. In order to generate
this low-level graph, an agent starting at the beginning of each strip walks it until it
finds a new strip intersection point. Once it has found an intersection, it waits there until
it sees that its neighbors have also found intersections. At this time, the agents each log
their newly found connection, and resume walking along their assigned strips. This
process is continued until the agents all find the end of their assigned strip. Conceptu-
ally, this method could be extended to be used in real-time with a continuous fabrication
process. After the low-level graph is produced, their connections are interpreted
through a dictionary into instructions for hand braiding (Fig. 7). These instructions
could potentially be implemented into a user interface and combined with a braid visu-
alisation to interactively show the intended result of each instruction step.
8
3.3 Workflow 3: analysing mechanical properties
Fig. 8. Strip-strip interaction for testing physical properties of braid (tension).
Explicit and dynamic formulations of structural elements are particularly attractive for
the simulation of large deformations and nonlinear phenomena. Especially in the con-
text of form-finding, new and alternative approaches have recently emerged which are
well-suited for these types of problems. The results shown in this paper clearly demon-
strate the capacity and versatility of such formulations. Modern nonlinear Finite Ele-
ment packages, the de facto standard in engineering simulation, are completely
equipped to perform simulations of complex mechanical systems and accurately de-
scribe their behaviour, but it still requires a certain effort to organise entire simulation
routines for large design explorations in Finite Elements environments. For this reason,
analysis and evaluation of mechanical performance of braided systems could be divided
into the following two steps:
1. Strip-strip interaction (form-finding and system generation, as developed so far)
2. Shell-like behavior (subsequent Finite Element Analysis for evaluation of system
stiffness and buckling behavior, through further developments)
As in most cases, pre-stressing effects emerging from the deformation of thin and slen-
der elements can be safely disregarded. The geometry emerging from the form-finding
step of this paper could therefore represent the direct input for FEM analysis. This two-
step workflow aims to explore and analyse the characteristics of mechanical perfor-
mance, focusing in particular on the assessment of axial, bending and torsional stiff-
ness, along with potential buckling behaviour of the braided systems (Fig. 8).
3.4 Workflow 4: generative design
In this workflow, a generative input is given to the braid solver. As an example of such
an input, we use a low-level robotic controller from the literature the Vascular Mor-
phogenesis Controller (VMC) [Zahadat et al., 2017] to supply a macro scale graph
that grows over time based on environmental conditions. In a case where a braided
artifact is manufactured robotically in situ and sensors are embedded in the physical
braid, a controller like the VMC could be used to guide the shape of the braid in a way
that is adaptive to dynamics of the environment (and provides behavior diversity [Za-
hadat and Schmickl, 2014]). Therefore, in this workflow, we use a simulated VMC
graph output to generate a mesh topology for the braid solver (Fig. 9).
9
Fig. 9. Three example time-steps from the simulated growth of a VMC graph, and the braided
artifacts resulting from those graphs.
Unlike the inputs of a physical target or a master surface, which can be manually
defined, a generative input necessitates a solver to automate the integration of fabrica-
tion constraints. To guarantee that a generated braiding pattern can be fabricated by
hand or with a braiding robot, the underlying mesh has to have all the faces marked
with a direction pointing in the fabrication direction. A macro scale directed graph ap-
proach was developed to generate meshes following this constraint (Fig. 10). The graph
serves as a scaffold for the mesh tiling, and has to comply with several constraints to
satisfy the fabrication method and mesh generation routine.
10
Fig. 10. Example mesh solution (center) from a weighted macro scale directed graph topology
(left) and the eventual result from the braid solver (right).
4 Evaluation
We evaluate the performance and generalisability of the method against geometric sim-
ilarity and simulation performance. To assess simulation performance, we compare ap-
proaches to collision detection within the braid relaxation phase of the method to ex-
trapolate the limits on complexity of currently achievable models. To assess geometric
similarity we compare geometries of simulated results against physical examples.
Simulation performance is a limiting factor to the complexity that can be repre-
sented, with the relaxation phase being the most computationally demanding due to
monitoring line-to-line collision detection in the mesh. We tested several methods to
evaluate collision detection performance. Using an input mesh with 11105 edges we
obtained the following results:
using a Spatial-Grid method (Teschner et al. 2003) without multi-threading
results in a running speed of 60 - 100 ms per frame;
using an R-Tree search method results in 80 - 200 ms per frame;
using a conventional line-to-line constraint when calculating collision be-
tween all possible pairs runs at 6.1 - 7.5 sec per frame and runs out of memory
for larger models.
The geometric similarity of relaxed braid meshes is visually assessed. In Fig. 11, two
features are physically prototyped, and then modelled for comparison. In both cases,
the macro geometry of the model conforms closely to the physical prototype, whilst
yarn-to-yarn relations show some geometric deviation. The modelled braid appears
looser around regions of large geometric transition (Fig. 11, right).
11
Fig. 11. Evaluation of the method by visual comparison to physical prototypes.
5 Conclusion & Further Work
This paper has reported on a method and its integration within design workflows that
address a gap in suitable tools for braid pattern generation and physics-based simula-
tion. We have described and demonstrated workflows that target the exploration of gen-
erative or target based geometry, the production of fabrication instructions, and the
conducting of structural analysis. These workflows support current research efforts in
the flora robotica project, but are sufficiently generalised for the exploration of braid
patterns beyond this project.
Further work aims to develop calibrated modelling of mechanical performance of mod-
elled braids, and to fully test fabrication workflows using braiding machines and dis-
tributed robotic methods currently under development within the flora robotica project.
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Acknowledgements
We would like to thank Payam Zahadat for feedback on the generative section and for
providing us with example VMC graphs, from simulations tailored to braided structures.
Project flora robotica has received funding from the European Union’s Horizon 2020 re-
search and innovation program under the FET grant agreement, no. 640959.
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Besides the life-as-it-could-be driver of artificial life research there is also the concept of extending natural life by creating hybrids or mixed societies that are built from natural and artificial components. In this paper we motivate and present the research program of the project flora robotica. Our objective is to develop and to investigate closely linked symbiotic relationships between robots and natural plants and to explore the potentials of a plant-robot society able to produce architectural artifacts and living spaces. These robot-plant bio-hybrids create synergies that allow for new functions of plants and robots. They also create novel design opportunities for an architecture that fuses the design and construction phase. The bio-hybrid is an example of mixed societies between ‘hard artificial and ‘wet natural life, which enables an interaction between natural and artificial ecologies. They form an embodied, self-organizing, and distributed cognitive system which is supposed to grow and develop over long periods of time resulting in the creation of meaningful architectural structures. A key idea is to assign equal roles to robots and plants in order to create a highly integrated, symbiotic system. Besides the gain of knowledge, this project has the objective to create a bio-hybrid system with a defined function and application – growing architectural artifacts.
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Numéro spécial "La Science des Nœuds" http://entrelacs.net/ N° SAP : 077615
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Braiding is a very old textile manufacturing technique and is being traditionally used for many years to produce ropes, shoe laces, cables, and so on. Recently, this technology is getting special attention in various technical fields, such as medical, aerospace industries, civil engineering, transportation, and others, due to its ability to produce structures that can fulfill the demands imposed by these technical sectors. Each of these applications needs special structures with special functionalities. Therefore, designing of these technical products needs proper understanding of the process, mechanics, materials, structures, and various parameters. Some of these important aspects of braiding technology have been discussed separately in books and mainly in research articles. However, the main aim of writing this book is to discuss all these important information together, focusing on the practical applications of braiding technology. This effort will be very fruitful for the engineers and scientists working in various industries to design their products or for the students and researchers to know this technology starting from the concept up to the product designing and applications. This book presents various applications of braiding technology, which are already commercialized or in research stage and the recent advancements in terms of materials, processes, and structures to achieve the required functionalities. Each application sector has been dealt in detail in separate chapters and written by the leading experts from each field, identifying the requirements and discussing the type of material, process, structure, and design strategy to fulfill these requirements. One import issue dealt in this book is the mechanics of the braiding process. It is extremely necessary to understand the mechanics to identify the main parameters influencing the braiding process and produced structures, and to control these parameters to achieve the desired material characteristics. This book also discusses the modeling of structure and various properties of braided structures and available techniques and software tools used for that purpose. This discussion will be highly helpful for designing various types of braided products with required properties. One complete chapter of the book has been written on braided composites. This new type of composite materials is becoming very attractive due to their benefits over conventional materials and composites. This chapter discusses the types of braided composites, their production process and new developments, properties, and applications. Detailed analysis of structure and braided composites is also presented in a separate chapter of the book. In the last chapter of the book, the importance of recently developed multiscale braided structures and composites is highlighted. The understanding of these new materials can help to develop multifunctional products with various interesting features using braiding technology. The specialty of this book is that it discusses the basic principles, processes, mechanics, analysis, product designing, and applications, as well as recent developments in braiding technology in terms of materials, processes, structures and, product designing. Therefore, this book has been written targeting students, teachers, researchers, engineers, and scientists working in various industries. We express our sincere thanks and gratitude to all authors, who participated in the various chapters of this book, for the efforts and valuable contributions. Sincere thanks are also due to our colleagues from Fibrous Materials Research Group, University of Minho, for their kind help and support. We believe that this book will be an important reference to learn about the basic concepts related to braiding process and structures, to know the various applications of these materials and also to get knowledge about the advanced analytical techniques required for product designing purposes. We have no doubt that a wide range of readers including students, teachers, engineers, researchers, and scientists will benefit from the discussions about braiding process, materials, products, applications, and modeling, presented in various chapters of this book.
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Abstract A controller of biological or artificial organism (e.g., in bio-inspired cellular robots) consists of a number of processes that drive its dynamics. For a system of processes to perform as a successful controller, different properties can be mentioned. One of the desirable properties of such a system is the capability of generating sufficiently diverse patterns of outputs and behaviors. A system with such a capability is potentially adaptable to perform complicated tasks with proper parameterizations and may successfully reach the solution space of behaviors from the point of view of search and evolutionary algorithms. This article aims to take an early step towards exploring this capability at the levels of individuals and populations by introducing measures of diversity generation and by evaluating the influence of different types of processes on diversity generation. A reaction-diffusion-based controller called the artificial homeostatic hormone system (AHHS) is studied as a system consisting of different processes with various domains of functioning (e.g., internal or external to the control unit). Various combinations of these processes are investigated in terms of diversity generation at levels of both individuals and populations, and the effects of the processes are discussed representing different influences for the processes. A case study of evolving a multimodular AHHS controller with all the various process combinations is also investigated, representing the relevance of the diversity generation measures and practical scenarios.
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Morphology of an artificial structure can be designed beforehand or it can be developed over time via interactions between different parts of the structure. Since structures are supposed to sustain and act in their surrounding environments, a successful generative process needs to consider both the global and local effects of environment during morphogenesis. As in their biological counterparts, many morphogenesis models are distributed over the growing structure. In this paper, a novel distributed model, called Vascular Morphogenesis Controller (VMC), is introduced by being inspired from branching mechanisms in plants where every branch of a plant acts as an autonomous agent competing with the other agents for a larger share of the resources for growth. To the best of our knowledge, this is the first explicit use of distribution of limited resources in morphogenesis process of artificial structures. The model is implemented for growing a simulated modular robot that is designed based on a physical robot. The parameters of model are successfully evolved to direct the growth of robots in different environmental condition, i.e., in harsh and calm environments, in various light conditions, and in a layered environment. The results demonstrate usability of the model despite simplicity of its logic.
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A trained architect, who works with the Specialist Modelling Group (SMG) at Foster + Partners, Daniel Piker is also the developer of the Kangaroo plug-in for Rhinoceros® and Grasshopper®. He explains how Kangaroo has been devised to simulate aspects of the behaviour of real-world materials and objects in order to modify designs in response to engineering analyses, engendering an intuitive sense of the material world.
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Recent yarn-based simulation techniques permit realistic and efficient dynamic simulation of knitted clothing, but producing the required yarn-level models remains a challenge. The lack of practical modeling techniques significantly limits the diversity and complexity of knitted garments that can be simulated. We propose a new modeling technique that builds yarn-level models of complex knitted garments for virtual characters. We start with a polygonal model that represents the large-scale surface of the knitted cloth. Using this mesh as an input, our interactive modeling tool produces a finer mesh representing the layout of stitches in the garment, which we call the stitch mesh. By manipulating this mesh and assigning stitch types to its faces, the user can replicate a variety of complicated knitting patterns. The curve model representing the yarn is generated from the stitch mesh, then the final shape is computed by a yarn-level physical simulation that locally relaxes the yarn into realistic shape while preserving global shape of the garment and avoiding "yarn pull-through," thereby producing valid yarn geometry suitable for dynamic simulation. Using our system, we can efficiently create yarn-level models of knitted clothing with a rich variety of patterns that would be completely impractical to model using traditional techniques. We show a variety of example knitting patterns and full-scale garments produced using our system.