Institute of Fundamental Technological Research

This paper introduces MorphoGen — an integrated reliability-based topology optimization and nonlinear finite element analysis system for 2D and 3D domains. The system’s key innovation is its seamless prototyping of scientific formulations for computational problems in topology optimization. Its layered and object-oriented architecture, based on the template method design pattern, facilitates effortless modifications of algorithms and the introduction of new types of finite elements, materials, and analyses. MorphoGen also offers flexible handling of objective functions and constraints during topological optimization, enhancing its adaptability. It empowers researchers and practitioners to explore a wide range of engineering challenges, fostering a deeper understanding of complex structural behaviors and efficient design solutions. There are many topology optimization software and open source codes, especially based on the classical SIMP method. Unlike these codes our package is freely distributed among users and since it is distributed on the MIT licence, which allows for its easy modification depending on the particular needs of the users. For this purpose, we use the topology optimization algorithm proposed for the first time in our previous paper (Blachowski et al., 2020). The algorithm is based on a fully stress design-based optimality criteria and can be applied for topology optimization of either linearly elastic and elastoplastic structures. Additionally, the novelty of the proposed system is related to its ability of solving optimal topology under various constraints such as displacement, stresses and fatigue in both deterministic and probabilistic cases. Another application are modular structures, which reduce design complexity and manufacturing costs as well as rapid reconfiguration. However, in the realm of structural optimization, modular systems are more challenging due to various: modes of operation of the modules and the stresses configurations. Moreover, this area of research is dramatically less explored. Thus the effectiveness of MorphoGen for structural engineering is demonstrated with examples of topological shape optimization of two Extremely Modular Systems: a planar robotic manipulator Arm-Z and spatial free-form ramp Truss-Z.

Stress Constrained Topology Optimizatio,Extremely Modular System,Object-oriented software architecture,MATLAB-based array programming,First Order Reliability Analysis

Arm-Z to koncepcja hiperredundantnego manipulatora robotycznego opartego na sekwencji szeregowo połączonych identycznych modułów. Każdy moduł ma tylko jeden stopień swobody (1-DOF) – skręt względem poprzedniego. Moduły systemu Arm-Z mogą być masowo produkowane i łatwo wymieniane w przypadku awarii. Sterowanie Arm-Z jest stosunkowo trudne, dlatego zwykle wymaga stosowania metod inteligencji obliczeniowej. W artykule przedstawiono kilka koncepcji kinetycznych obiektów małej architektury opartych na Arm-Z: spiralną kolumnę o regulowanej wysokości, system nadążania słonecznego, kinetyczną rzeźbę bioniczną i kinetyczny zraszacz/fontannę. Prezentowane koncepcje są zasadniczo nisko-technologiczne (“low-tech”). W każdym przypadku moduł bazowy jest przymocowany do podstawy (podłoża). Dla prostoty napęd jest przykładany bezpośrednio do pierwszego modułu, a następnie przenoszony za pomocą wewnętrznych przekładni na kolejne moduły. Każdy moduł jest wyposażony w zestaw cylindrycznych i stożkowych kół zębatych z zębami prostymi o profilu spiralnym (do połączeń miedzy modułami).

Arm-Z, hiperredundancja, manipulator, mała architektura, systemy modularne

W artykule przedstawiono program badawczy mający na celu wstępne określenie potencjału technologii iPAD-LiDAR w inwentaryzacji obiektów budowlanych.
Autorzy skupili się na wykorzystaniu komercyjnie dostępnych urządzeń (telefonów komórkowych
i tabletów) wyposażonych w sensor LiDAR. Urządzenia takie można potraktować jako nisko kosztowe aparaty pomiarowe i zastosować do pomiarów inżynierskich. Pierwszym możliwym obszarem wykorzystania omawianych urządzeń są szeroko rozumiane inwentaryzacje budowlane, które przy wykonywaniu ich tradycyjnymi metodami zawsze wiążą się z dużym
nakładem pracy. Automatyzacja tego procesu oraz jakość i ilość danych pozyskanych przy
wykonywaniu inwentaryzacji tworzy zupełnie nową rzeczywistość techniczną i związane z tym
możliwości pomiarowo-diagnostyczne.

iPAD, LiDAR, skaning, tablet, nisko kosztowy

Emergency bridges are used to restore the lifeline of damaged bridges after disasters. However, the design specification of existing emergency bridges do not afford rapid bridging. Therefore, a trial deployable bridge (Scissors Bridge) using a scissors structure that folds compactly has been experimentally produced. But, the assembly process for the bridge has not been considered and there are no practical design examples or design methods for scissors bridges. In this paper, as for existing bridges, we established a design method of scissors bridges when considering the live load. In addition, a general-purpose member cross-sectional dimension optimization method, aimed at minimizing weight, was developed and proposed. Considering the problem of insufficient strength of the scissors bridge, the optimum reinforcing pattern and its cross-sectional dimensions were determined through two methods of reinforcement and optimization of the cross-sectional dimension of the member. Finally, a trial of practical design calculation was performed using the results of the study to determine whether a scissors bridge satisfying the standard of the Specifications for Highway Bridges can be designed.

scissors structure,deployable bridge,stress analysis

Arm-Z is a concept of a hyper-redundant manipulator based on linearly joined sequence of congruent units. Each unit has only one degree of freedom (1-DOF) - the twist relative to the previous unit.
This paper presents the approach to design of modular robotic manipulator based on computer simulations. The approach is rather standard nowadays, however, it is applied to rather unique robotic system. The
CAD model of the module structure for a manipulator with 6 degrees of freedom and respective Denavit-Hartenberg notation are presented. Simulink - a MATLAB-based graphical programming environment was
used to determine the torques of individual modules. The results of three simulations are presented and discussed. Finally, based on critical observations, the drive and gear for the module of Arm-Z system were selected.

Simulation,Robotic arm,Manipulator,Arm-Z,MATLAB Simulink

This paper presents the design and construction process of the Arm-Z manipulator, which represents the concept of a hyper-redundant manipulator based on a connected sequence of identical modules. Each
module provides a single degree of freedom (1-DOF), specifically a twist relative to the previous module. The uniformity of the modules gives Arm-Z the potential to be cost-effective and robust. Standardized modules allow for mass production and can be easily replaced in case of failure. This paper discusses each stage of the design process from mechanical perspective, including: module’s geometry, simulation based on Denavit-Hartenberg parameters, and manufacturing process. The section covering work on the electrical system discusses issues such as selection of: motors, power supply, protections, and the network’s topology connecting EPOS controllers.

Robotic arm, Manipulator, Hyperredundant, Arm-Z, Extremely Modular System

Arm-Z is a concept of a hyper-redundant manipulator based on linearly joined sequence of congruent modules by oblique swivel joint mechanism. Each module has one degree of freedom only, namely a twist relative to the previous module in the sequence. Although the concept of this type of manipulator is relatively old and simple, its control is very difficult an nonintuitive, which results in a limited use in industrial practice. This paper presents a simple simulation of Arm-Z in Mathematica programming environment which demonstrates a few simple but potentially useful movements.

Arm-Z, Extremely Modular System, hyper-redundant manipulator, Mathematica, oblique swivel joint

Arm-Z to koncepcja hiperredundantnego manipulatora robotycznego składającego się z przystających modułów o jednym stopniu swobody (1-DOF) i realizującego (prawie) dowolne ruchy w przestrzeni. Zasadnicze zalety Arm-Z to: ekonomizacja (dzięki masowej produkcji identycznych elementów) oraz odporność na awarie (po pierwsze – zepsute moduły mogą być łatwo zastąpione, po drugie – nawet gdy jeden lub więcej modułów ulegnie awarii – manipulator taki może ciągle wykonywać, prawdopodobnie w stopniu ograniczonym, zakładane zadania). Podstawową wadą systemu Arm-Z jest jego nieintuicyjne, bardzo trudne sterowanie. Innymi słowy, połączenie koncepcji nietrywialnego modułu z formowaniem praktycznych konstrukcji oraz sterowanie ich rekonfiguracją (transformacją ze stanu A do B) są bardzo złożone obliczeniowo. Mimo to prezentowane podejście jest racjonalne, zważywszy powszechną dostępność wielkich mocy obliczeniowych w kontraście z wysokimi kosztami i „delikatnością” niestandardowych rozwiązań i urządzeń. W artykule nakreślono ogólną koncepcję manipulatora Arm-Z i zaprezentowano wstępne prace zmierzające do wykonania prototypu.

Arm-Z, odporność na awarie, sterowanie kształtem ogólnym, systemy modularne

This paper presents a concept of an extremely simple planar manipulator composed of 24 congruent modules. Each module has only two possible discrete positions in relation to the previous module: left (− π 6 ) or right ( π 6 ). However, despite its conceptual simplicity, this manipulator can perform relatively demanding tasks, for example as an inspection device. The manipulator is placed in an experimental environment, and the goal is to place its tip in close proximity to five given points without collisions. Despite the constraints of its motion, the manipulator effectively “crawls” inside the working space and visits assigned points. The control of the manipulator is executed by manual placing to desired configurations and interpolating the intermediate transitions. The preliminary results are promising and show that for certain practical types of tasks, the functionality and precision of this extremely simple manipulator could be sufficient, e.g., visual inspection, provision of survival supplies, placing of explosives, etc.

discrete manipulator,hyper-redundant,snake robot,modular

Arm-Z - a hyper-redundant manipulator based on linearly joined sequence of congruent units is presented. Each unit has 1-DOF (one degree of freedom) only, namely a twist relative to the previous unit in the sequence. Arm-Z has a potential of being economical and robust. The control of Arm-Z, however, is not intuitive and difficult. This paper presents the preliminary results of designing a prototype of a modular Sun-tracking device comprised of four congruent units with possible application as a solar energy harvester or a Sun-shade.

Extremely modular system, Arm-Z, Hyper-redundant manipulator, Rapid prototyping, Low-tech

Arm-Z is a concept of a hyper-redundant manipulator based on linearly joined sequence of congruent units. Each unit has only one degree of freedom (1-DOF), namely a twist relative to the previous unit in the sequence. Since each module is identical, Arm-Z has a potential of being economical and robust: the modules can be mass-produced and, in case of failure, easily replaced. However, the control of Arm-Z is nonintuitive and difficult, thus it usually requires application of computational intelligence methods. This paper presents a number of concepts for kinetic street furniture based on Arm-Z: a spiral column of adjustable height, a sun-tracking shade/solar energy harvester, bio-mimicry sculpture, kinetic sprinkler/fountain. The proposed concepts are low-tech in principle. Therefore in each case, the first module in the sequence is fastened to a solid base (ground). For simplicity, the drive is applied directly to the first module and transferred to subsequent units by internal gears. Each module is equipped with a set of cylindrical and bevel gears with straight teeth with involute profile (for connecting the modules).

Arm-Z, extremely modular system, low-tech, street furniture

Arm-Z is a hyper-redundant manipulator based on a sequence of linearly joined identical modules. Each module has only one degree of freedom—a twist relative to the previous module. Arm-Z can be potentially economical, as the modules can be mass-produced. Arm-Z is also robust, as the malfunctioning module can be replaced. Moreover, if some modules malfunction, the device can still execute tasks with certain accuracy. However, the disadvantage of Arm-Z is a non-intuitive and difficult control. This paper presents a concept of a modular tracking device comprised of four identical modules. As an example, the Sun-tracking setup is used with possible application for solar energy harvesting.

Extremely modular system, Arm-Z, Hyper-redundant manipulator, Sun-tracking

Arm-Z is a concept of a robotic manipulator comprised of linearly joined congruent modules with possibility of relative twist. The advantages of Arm-Z are: economization (mass-production) and robustness (modules which failed can be replaced, also if some fail the system can perform certain tasks). Non-intuitive and difficult control are the disadvantages of Arm-Z. It has been introduced over six years ago. The theretofore research focused on the control of the virtual Arm-Z manipulator through the relative twists of its constituent units. This paper documents the fabrication and testing of the preliminary physical prototype of a simple Arm-Z, which has been built using relatively low-tech approach. The modules have been assembled from 3D-printed elements using PET-G filament. Each module is equipped with a transmission mechanism allowing to pre-set the spin of its twist (either positive/right or negative/left). Although the presented system is very simple it demonstrates certain meaningful kinematic actions and sets clear paths for the future research in the area of Extremely Modular Systems.

extremely modular system, arm-Z, hyper-redundant manipulator, rapid prototyping, low-tech

Improving the architectural layout for diverse objectives using rigorous mathematical optimization methods gradually receives more attention by the researchers. Such optimization however, is usually reduced to a much simpler and relatively well-defined problem such as: facility layout optimization, quadratic assignment problem, rectangle partitioning. Nonetheless, architects are usually skeptical about such approaches since they produce solutions which lack certain architectural qualities. This paper proposes a framework where architectural functional layout (FL) is optimized for the following objectives: functionality (defined by users), insolation (calculated according to geographical conditions), outside view attractiveness (assessed on-site) and external noise (measured on-site). Incorporating the latter two and simultaneous optimization of FLs for objectives related specifically to the site: position and orientation are the novel contributions of this paper. Firstly, a set of candidate FLs is generated, next they are evaluated for optimal location and orientation on a given site. Optimality is conceived here as maximization of real-valued objective function combining: user's satisfaction level of the outside views, shielding from external noise, and insolation
preference. The importance of these factors for each type of room is assessed by the user (as weights). A case study on an existing site is presented. The view quality was arbitrarily assessed and the noise map was assessed by A-weighted equivalent sound level measurements. A general gradient-based method for finding optimal and near-optimal solutions was applied. The output of this optimization is a set of room configurations with their locations and orientations on the site returned to the user for final selection.

architectural optimization, subjective evaluation, functional layout, acoustic comfort, coarse grid

Extremely Modular Systems (EMSs) are comprised of as few types of modules as possible and allow creating structurally sound free-form structures that are not constrained by a regular tessellation of space. Truss-Z is the first EMS introduced, and its purpose is to create free-form pedestrian ramps and ramp networks in any given environment. This paper presents an overview of various multi-objective optimization methods applied to Truss-Z structures.

Truss-Z, extremely modular system, discrete optimization, multi-objective

This paper proposes an approach for multicriterial optimization of modular structures with respect to their structural and geometrical properties. The approach is tested using the quickly deployable and reconfigurable modular ramp system Truss-Z intended for pedestrian traffic. The focus is on modular structures composed of a moderate number of relatively complex modules, which feature an irregular, noncuboidal geometry. Such modules can be assembled into a variety of geometrically different configurations which do not adhere to any predefined spatial grid; their global geometry can be treated as free-form and determined in situ during construction. The optimization variables represent local-level geometrical and structural properties of a single module. The Pareto front is used to balance between two kinds of objectives. The geometrical objective quantifies the ability of the modules to generate geometrically versatile global structures that are well-suited to comply with spatial constraints of real construction sites. The structural objective is formalized in analogy to the minimum weight problem with upper bound constraints imposed on the von Mises stress and the Euler buckling load ratio. A two-level optimization scheme is employed with NSGA-II at the top level and a simulated annealing with adaptive neighborhood at the lower level.

modular structures, multicriterial optimization, shape optimization, sizing optimization, NSGA-II, simulated annealing with adaptive neighborhood

Truss-Z (TZ) is an Extremely Modular System for creating skeletal free-form ramps and ramp networks. The TZ structures are comprised of four variations of two types of basic unit subjected to rotation. The two types of units are: R and L being a mirror reflection of each other. This paper presents a novel method based on image processing, evolutionary algorithm and intensive parallelization of multi-objective optimization of TZ layouts.
The algorithm returns a sequence of modules. The result guarantees a TZ connection between two given points (regions) and minimizes the fitness function representing certain costs associated with setting up the TZ structure.
The fitness function depends on the cost of TZ structure as well as the variety of costs related to the environment where the it is to be placed. E.g.: the earthworks, vegetation removal, obstacles avoidance, etc. There are no restrictions on the fitness function definition. It can depend on any variable which can be represented by a two-dimensional map of any property of the environment.
The formulation of the presented method is suited for application of well-established image processing methods which efficiently evaluate candidate solutions on a GPU. As a result, the employed genetic algorithm efficiently probes the search space. The practical applicability of this approach is demonstrated with three case-studies:
1) simultaneous paving of a path with congruent units in a hilly environment with trees & bushes and finding the best location for a pier over an existing river;
2) constructing of a TZ connector spanning over a mountain valley with lakes (where supports can not be placed);
3) retrofitting of an existing railway station with a large wheelchair TZ ramp of over 10 m elevation while preserving trees and minimizing the earthworks.

Truss-Z, Extremely Modular System, Retrofitting, accessibility, multi-objective, discrete, combinatorial, optimization, genetic algorithm, parallel computing, GPU, GPGPU

A novel concept of hyper-redundant, snake-like manipulator is presented. It is based on the reconfigurable modular construction system–Arm-Z (AZ). AZ is comprised of linearly joined congruent modules with possibility of relative twist. AZ is an Extremely Modular System, i.e. it is composed of a single basic unit and allows for creating free-form shapes. Required level of usefulness and efficiency are among the most challenging design aspects of such reconfigurable systems. Here AZ is considered in the context of kinematics of robotic arms. In general, due to its highly non-linear nature, it is very difficult to find transitions between given states (configurations), especially under realistic environmental and structural constraints. As a way to control the manipulator, an implementation of Particle Swarm Optimization (PSO) for finding transitions between AZ states in realistic scenarios is proposed. Four practical examples are presented which are variations of two distinct problems: bending of a hexagonal AZ in a narrow slot (strong environmental constraints), and reaching a given point in 3D space by the tip of dodecagonal AZ (acting as a robotic arm). The problem of AZ transformation has been defined as a multi-objective optimization. The methodology is general with no restrictions to the objective function. Since the problem is strongly non-linear, in order to cover large space of potential solutions, the algorithm runs for a relatively large number of random initial swarms. This task was distributed on a computer cluster. Although the nature of AZ reconfiguration is discrete, the optimization algorithm is continuous.

Extremely modular system, Arm-Z, Pipe-Z, Discrete optimization, Dihedral rotation, Reconfiguration, Particle Swarm Optimization, Redundant robot, Hyper-redundant manipulator

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks. The previous research on TZ focused on global discrete geometric optimization of the spatial configuration of modules. This paper reports on the first attempts at structural optimization of the module for a single-branch TZ. The internal topology and the sizing of module beams are subject to optimization. An important challenge is that the module is to be universal: it must be designed for the worst case scenario, as defined by the module position within a TZ branch and the geometric configuration of the branch itself. There are four variations of each module, and the number of unique TZ configurations grows exponentially with the branch length. The aim is to obtain minimum-mass modules with the von Mises equivalent stress constrained under certain design load. The resulting modules are further evaluated also in terms of the typical structural criterion of compliance.

Extremely Modular System, Truss-Z, structural optimization, modular structures, minimum mass design, frame structures

This paper presents a concept of deployable Pipe-Z (dPZ): a modular structural system which takes advantage of the robustness of rigid-panel mechanism and allows to create free-form links which are also reconfigurable and deployable. The concept presented can be applied for building habitats and infrastructures for human exploration of oceans and outer space. dPZ structures can adapt to changing requirements e.g. mission objectives, crew condition and technological developments. Furthermore, such lightweight and adaptable structural concept can assist in sustainable exploration development. After brief introduction, the concept of Pipe-Z (PZ) is presented. Next, the reconfigurability of PZ is explained and illustrated with continuous and collision-free transition from a PZ forming a Trefoil knot to a Figure-eight knot. The following sections introduce, explain and illustrate the folding mechanism of a single foldable Pipe-Z module (fPZM) and entire dPZ structure. The latter is illustrated with asynchronous (delayed) unfolding of a relatively complex Unknot. Several applications of PZ are suggested, namely for underwater and deep-space and surface habitats, for permanent, but in particular, temporary or emergency passages. As an example, a scenario of a failure of one of the modules of the International Space Station is presented where a rigid structure of 40 fPZMs bypasses the “dead link”. A low-fidelity prototype of a 6-module octagonal dPZ is presented; several folding schemes including concentric toric rings are demonstrated. Practical issues of pressurization and packing are briefly discussed.

Ocean and space outpost, Banana-split, Deployable structure, Rigid-panel folding, Free-form

This paper concerns multi-branch Truss-Z networks (MTZ). A possible scenario for creating a “multi-branch bridge” linking 6 terminals of pedestrian and cycling communication is presented. This process is formulated as a constrained minimization problem. New, biology-inspired nomenclature for MTZ and encoding for MTZ are introduced. Several operations for MTZs are introduced and illustrated. The functionality of these operations is illustrated with transformation from a random MTZ to a “proper” 6-branch MTZ network. A population-based heuristic experiment is presented to demonstrate that the introduced operators allow us to create any desirable MTZ. A cost function for the considered scenario is introduced. The genetic operations are interpreted and visualized. A number of feasible MTZ layouts produced by an evolution strategy-based algorithm are presented. One of these layouts is used for creation of the spatial 6-terminal MTZ, which is also visualized.

Extremely modular system, Modular ramp system, Multi-branch network, Modular structure encoding, Evolution strategy, Discrete layout optimization

This paper presents a method for an automated geometrical evaluation (AGE) intended as a design support tool for urban design of a plaza (P). AGE is based on three normalized properties derived from a plan of P, namely: smallness, enclosure, and regularity. 19 worldwide plazas have been evaluated by 20 respondents in, what is called here, human subjective evaluation (HSE). A brief analysis of HSE including the identification of redundant categories is presented. Two P evaluation methods based on all four (S,C,E,R) and selected three (S,E,R) properties are discussed. Good agreement of AGE based on S,E, and R (NPSER) with HSE is shown. P quality rating (excellent, good, fair) based on NPSER is introduced. Exceptional cases are briefly discussed

Urban composition, Public square, Plaza, Layout evaluation, Design support tool, Normalized accumulated quality

The original prototype of the cellular automaton (CA) shading system (CASS) for building facades was based on rectangular array of cells and used liquid crystal technology. This paper introduces polarized film shading system (PFSS) – an alternative approach based on opto-mechanical modules whose opacity is a function of the rotation of polarized film elements. PFSS in regular tessellations: triangular, square and hexagonal are discussed. Simulations for each type of tessellation are presented and visualized. Visual attractiveness of emergent CA patterns manifested by ‘‘particles’’ and ‘‘solitons’’ is discussed.

Adaptive architecture, Organic architecture, Building envelope, CA shading

Installing pedestrian ramps is a common improvement towards a barrier-free environment. This paper introduces a graph-theoretical method of retrofitting of a single-branch Truss-Z (TZ) ramp in a constrained environment. The results produced by this exhaustive search method are usually ideal and better than those produced previously with meta-heuristic methods. A large case study of linking two sections of the Hongo Campus of Tokyo University using an overpass in an extremely constrained environment is presented. TZ modules with 1:12 (8.3%) slope are used, which is allowable in most countries for ramps for self-powered wheelchairs. The results presented here are highly satisfactory both in terms of structural optimization and aesthetics. Visualizations of the TZ ramp system, composed of 124 units, are presented.

Truss-Z, Modular lightweight system, Organic design, Discrete structural optimization, Retrofitting, Pedestrian ramp, Breadth-first search, Wavefront algorithm, Unknown graph exploration

This paper introduces Crowd-Z (CZ): a framework that provides a user-friendly platform where architects can perform simple crowd simulations on floor plans. A simple but robust and flexible agent-based system is used for modeling of the crowd dynamics. Such simulations can be performed at any stage of design – from rough sketches to the final blueprints. CZ allows acquiring the layouts for the simulations in a number of ways: freehand sketches, importing already prepared images and appropriating preprocessed images from commercially available Computer Aided Design programs. These three methods are illustrated with practical examples, followed by a number of simulations compared with the literature or other commercially available programs.

Pedestrian dynamics, Agent based modeling, Design support, Digitized floor plan

Truss-Z (TZ) is a concept of a modular system for creating free-form links and ramp networks. It is intended as a universal transportation system for cyclists and pedestrians, especially ones with strollers or carts, and in particular – by persons on wheelchairs, the elders, etc. In other words, TZ is for people who have difficulties using regular stairs or escalators. With only two types of modules, TZ can be designed for nearly any situation and therefore is particularity suited for retrofitting to improve the mobility, comfort and safety of the users. This paper presents an application of evolution strategy (ES) and genetic algorithm (GA) for optimization of the planar layout of a TZ linkage connecting two terminals in a given environment. The elements of the environment, called obstacles, constrain the possible locations of the TZ modules. Criteria of this multi-objective optimization are: the number of modules to be the smallest, which can be regarded as quantitative economical optimization, and the condition that none of the modules collides with any other objects, which can be regarded as qualitative satisfaction of the geometrical constraints. Since TZ is modular, the optimization of its layout is discrete and therefore has combinatorial characteristic. Encoding of a planar TZ path, selection method, objective (cost) function and genetic operations are introduced. A number of trials have been performed; the results generated by ES and GA are compared and evaluated against backtracking-based algorithm and random search. The convergence of solutions is discussed and interpreted. A visualization of a realistic implementation of the best solution is presented. Further evaluation of the method on three other representative layouts is presented and the results are briefly discussed.

Truss-Z, Modular skeletal system, Organic design, Meta-heuristic discrete optimization, Retrofitting, Pedestrian ramp

This paper presents an application of evolutionary algorithm (EA) for multi-objective optimization of the sequence of initial conditions (SIC) for a cellular automaton (CA) used for a potential implementation in the field of architecture. In the proposed application, a modular shading system for building facade is driven by a two color, one dimensional, range 2 CA rule {3818817080,2,2}. The SIC optimization criteria are: visual attractiveness, gradual and intuitive transition from one density level to another and even distribution of the pattern over the entire array. The ideal solutions for 10 square arrays of 7×7, 8×8,..., 16×16 cells are found by an exhaustive search method – the backtracking. The encoding of SICs using the order-based representation is introduced. A cost function evaluating both monotonicity of the average density transition, and the distribution of shading pattern is introduced. For a 100×100 cell array EA is implemented with three setups: without crossover but with intensive mutation, with crossover and without mutation, and with both crossover and mutation. Two types of crossover operations are used: uniform (UX) and one-point (OPX). A number of experiments with various combinations of parameters were performed. The results are compared and the recommended strategy is briefly discussed. The best result was produced by EA with OPX and mutation rate 0.4.

Modular shading system, initial conditions, multi-objective optimization, discrete optimization, backtracking, order-based representation, evolutionary algorithm

A practical application of cellular automata (CA) in the field of Architecture is presented, where one-dimensional CA on a square grid drives a modular shading system of a building facade. Examples of three classes: general, semi-totalistic and totalistic of two-color one-dimension range-two automata are analyzed for potential practical use. The problem of desired change in the opacity of the shading array as a function of the sequence of initial conditions (SIC) is discussed. The ideal SlCs for selected CAs on 12 x 12 cell arrays found by backtracking algorithm are presented. The influenee of the type of boundary conditions (BC) is discussed and a special type of a fixed BC is introduced. The robustness of the system under two types of permanent failure is analyzed - the single cell failure, and deactivation of a single column of cells.

Adaptive architecture, modular shading system, fixed boundary conditions, Robustness, failure

This paper presents the concept of Truss-Z (TZ) – a skeletal system for pedestrian traffic which is composed of only two modules and allows the creation of complex three-dimensional self-supporting networks connecting any number of terminals in a given environment. TZ is intended as a universal, feasible and practical system for newly designed situations and most importantly, for retrofitting, especially where the use of heavy equipment is impossible or uneconomic.
TZ allows automated creation of optimal spatial links where the only required inputs are the coordinates of the terminals and the geometry of the obstacles. As an example a six-terminal network created with a backtracking based algorithm is shown. An alternative method of aligning consecutive modules to a given 3D path is also presented.
A preliminary static analysis of the TZ module is carried out – the topological qualities of rigidity and independence are demonstrated.

Truss-Z, Modular skeletal system, Self-supporting structure, Organic design, Discrete structural optimization, Retrofit pedestrian link, Pathfinding with backtracking

A design support system with a new strategy for finding the optimal functional configurations of rooms for architectural layouts is presented. A set of configurations satisfying given constraints is generated and ranked according to multiple objectives. The method can be applied to problems in architectural practice, urban or graphic design—wherever allocation of related geometrical elements of known shape is optimized. Although the methodology is shown using simplified examples—a single story residential building with two apartments each having two rooms—the results resemble realistic functional layouts. One example of a practical size problem of a layout of three apartments with a total of 20 rooms is demonstrated, where the generated solution can be used as a base for a realistic architectural blueprint. The discretization of design space is discussed, followed by application of a backtrack search algorithm used for generating a set of potentially ‘good’ room configurations. Next the solutions are classified by a machine learning method (FFN) as ‘proper’ or ‘improper’ according to the internal communication criteria. Examples of interactive ranking of the ‘proper’ configurations according to multiple criteria and choosing ‘the best’ ones are presented. The proposed framework is general and universal—the criteria, parameters and weights can be individually defined by a user and the search algorithm can be adjusted to a specific problem.

Architecture, design support, architectural layout optimization, multi-objective, discrete Optimization, CSP

Extremely Modular System (EMS) is a relatively new concept introduced a few years ago. It represents a new approach to the design of engineering structures and architectural objects where assembly of congruent units allows for the creation of free-form shapes. The main difference from the traditional modular systems used in engineering, is the emphasis of the minimal diversity of types of modules, ideally - just one. This is why these system are called "extremely" modular. One of the most natural areas for use of EMSs are deployable structures. This paper presents rigid body folding mechanisms for two selected EMSs: Pipe-Z - a parametric system comprised of one type of module allowing for creation of three-dimensional knots, and Truss-Z - a modular system for creating free-form ramps and ramp networks among any number of terminals.

Extremely Modular System, Deployable Structure, Free-form. Pipe-Z, Truss-Z

This contribution considers the problem of topology optimization of modular structures. A bionic trunk-like robotic “Arm-Z” manipulator is considered. The manipulator is modular, that is, it is composed of a sequence of identical modules. In geometric terms, each module is essentially an obliquely cut section of an elliptical pipe, so in the cutting plane it forms a circle. With respect to the previous module, it has a single degree of freedom: the relative twist. Therefore, the total number of the degrees of freedom of the entire manipulator equals the number of its modules. Such a manipulator belongs to the family of Extremely Modular Systems. The advantages of such systems are the economization (due to the possible mass production of modules) and robustness (replacement of a failed module instead of a complex repair).

Topology optimization, Modular manipulator, Multiple loadings, Geometric transformations, Kinematics, Stress constraints.

We show that the Soft Actor-Critic Reinforced Learning algorithm is able to find efficient motion patterns for a hyper-redundant robot consisting of 6 identical modules connected in a chain like fashion. The control is done by applying relative angular velocities between the modules. Analogous system has been studied before in the context of a robotic trunk-like manipulator.

Reinforced Learning, Robotic Locomotion, Hyperreduntant Modular Manipulator, Arm-Z, Extremely Modular System

Emergency bridges are used to restore the lifeline of damaged bridges after
disasters. However, the design specification of existing emergency bridges do not afford rapid
bridging. Therefore, a trial deployable bridge (Scissors Bridge) using a scissors structure that
folds compactly has been experimentally produced. But, the assembly process for the bridge has
not been considered and there are no practical design examples or design methods for scissors
bridges. In this paper, as for existing bridges, we established a design method of scissors bridges
when considering the live load. In addition, a general-purpose member cross-sectional dimension
optimization method, aimed at minimizing weight, was developed and proposed. Considering
the problem of insufficient strength of the scissors bridge, the optimum reinforcing pattern
and its cross-sectional dimensions were determined through two methods of reinforcement and
optimization of the cross-sectional dimension of the member. Finally, a trial of practical design
calculation was performed using the results of the study to determine whether a scissors bridge
satisfying the standard of the Specifications for Highway Bridges can be designed.

Standardization and modularization are common means of simplification and economization of engineering structures. Extremely modular systems (EMS) are comprised of very few (ideally just one) types of modules and allow for creation of structurally sound free-form constructions. Truss-Z (TZ) is the EMS considered in this paper. It is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and their combination). A family of shapes including: isosceles quadrilaterals (concave and convex), regular and irregular kites and darts, isosceles triangles and trapezoids has been considered for the planar projection of Truss-Z modules (TZMs). It has been shown that isosceles triangles and trapezoids suit best TZ. The universality of TZM has been assessed by measurement of the egularity of distribution reachable points by given TZ built with several such TZMs. It has been shown that the vertex angle (h) of 32.5° gives the most regularly distributed, thus universal TZ.

Truss-Z, Extremely modular system, Isosceles quadrilateral Regularity

Truss-Z (TZ) is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and combination of both). This paper presents a new approach to the optimization of the layout of a singlebranch Truss-Z (STZ) in constrained environment (E). The problem is formulated as follows: create an STZ from a start (sP) to end point (eP) without self-intersections and collisions with two obstacles. This is a multi-criterial optimization problem where three independent objectives are subjected to minimization: the total number of modules (n), the “reaching error” to eP and the “overlapping error”. All three criteria are weighted and aggregated to a single cost function (CF). The calculation of CF is based on image processing of rendered geometry of individual STZs in E. The optimization is performed by population-based classic heuristic method - Evolution Strategy (ES). The computation of CF is the most time consuming, however, its parallelization is rather straightforward. Two parallelization methods are presented: distribution over Wolfram Lightweight Grid and application of general purpose graphical processing units (GPGPUs) with the use of CUDA platform.

Extremely Modular System, Truss-Z, discrete optimization, image processing, rasterization, GPU, CUDA, Mathematica, Wolfram Lightweight Grid.

Pipe-Z (PZ) is a parametric design system which comprised of a congruent modules (PZM) allows the creation of complex three-dimensional, single-branch structures which can be represented by mathematical knots. Once the geometrical parameters are set for the PZM, the shape of PZ is controlled solely by relative twists of the PZMs in a sequence. Therefore each PZM has one degree of freedom (1DOF). This paper presents the preliminary optimization of PZ reconfiguration from a “straight tube” to a half-torus. Here the displacement of PZMs transverse to the “bending direction” is to be minimized. In other words, it resembles “truing” of a wheel. In the considered case, the PZ is comprised of eight hexagonal PZMs. Thus every PZM can have six possible positions relative to the previous module. The initial (PZI) and target (PZT) configurations are given. Since the time-steps and relative twists are discrete, it is a discrete optimization and has combinatorial nature. The number of possible configurations grows astronomically with the assumed number of time-steps from one position to another and the number of PZMs. However, the optimization algorithm can be naturally parallelized. At first the concept of PZ is outlined, followed by the experiment. The results are illustrated and discussed.

Extremely Modular System, Pipe-Z, Arm-Z, discrete optimization, dihedral rotation, “snakebot”, reconfiguration.

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. In an EMS, the assembly, reconfiguration and deployment difficulty is moved towards the module, which is relatively complex and whose assembly is not intuitive. As a result, an EMS requires intensive computation for assembling its desired free-form geometrical configuration, while its advantage is the economization of construction and reconfiguration by extreme modularization and mass prefabrication. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic module (Truss-Z module, TZM) subjected to affine transformations (mirror reflection and rotation). The previous research on TZ focused on global discrete optimization of the spatial configuration of modules. This contribution reports on the first attempts at structural optimization of the TZM for a single-branch TZ. Namely, the internal topology of a TZM and sizing of its elements are subject to optimization. An important challenge is due the fact that TZM is to be universal, i.e., it must be designed for the worst case scenario. There are four variations of each module, and due to symmetries there are thus 4^4 = 256 unique 5-unit configurations. The structural performance of all of them needs to be evaluated in terms of a typical structural criterion (the maximum von Mises effective stress), and used for structural optimization at the level of a single TZM.

Extremely Modular System, Truss-Z, Structural optimization, Effective stress

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. In an EMS, the assembly, reconfiguration and deployment difficulty is moved towards the module, which is relatively complex and whose assembly is not intuitive. As a result, an EMS requires intensive computation for assembling its desired free-form geometrical configuration, while its advantage is the economization of construction and reconfiguration by extreme modularization and mass prefabrication. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic module (Truss-Z module, TZM) subjected to affine transformations (mirror reflection and rotation). The previous research on TZ focused on global discrete optimization of the spatial configuration of modules. This contribution is the first attempt at structural optimization of the TZM for a single-branch TZ. The result is a multicriterial optimization, where the Pareto front provides the means to strike the optimal balance between geometric and structural assessment criteria.

multicriterial optimization, Truss-Z, effective stress, modular systems

Extremely Modular System (EMS for short) is a relatively new concept introduced by the
author a few years ago. It represents a new approach to the design of engineering
structures and architectural objects where assembly of congruent units allows for the
creation of free-form shapes.
The main difference from the traditional modular systems used in engineering, is the
emphasis of the minimal diversity of types of modules, ideally - just one. This is why these
system are extremely modular.

These are six basic advantages of EMSs:
1. Economical - as they are suitable for mass fabrication, thus lowering the cost so they
can be broadly applied;
2. Functional - as they allow for reconfiguration, expansion, reduction;
3. Robust - since every module which failed can be easily replaced with an identical but functional one;
4. Discrete - as they are suitable for intelligent mathematical modeling, and their configurations can be subjected to discrete (multi-objective) optimization using efficient search algorithms;
5. Uniform - this feature is advantageous for rapid deployment and automated assembly.
6. Sustainable - as the entire modules can be reused.

One of the most advantageous areas for implementation of EMSs are deployable structures.
Moreover, it is crucial that the individual modules and entire structure are rigid.
This paper presents folding mechanisms for two selected EMSs: Pipe-Z - a parametric system
comprised of one type of module allowing for creation of three-dimensional knots, and Truss-Z -
a modular system for creating free-form ramps and ramp networks among any number of
terminals.

Extremely Modular System, Deployable Structure, Free-form, Pipe-Z, Truss-Z

Multiple bifurcations due to symmetry are often encountered when analyzing nonlinear motifs of nano-mechanics or structures with axial multiple symmetry. The location of multiple bifurcation points and bifurcation path tracing become problems in numerical analysis. In this paper, as a solution to this problem, the a priori information of group-theoretic bifurcation theory is applied. By utilizing the irreducible representation of the dihedral group, we propose to represent the initial imperfection vectors according to the difference in symmetry of the structural system. A part of the tangent stiffness matrix is corrected by coordinate transformations, and
the modified stiffness method is proposed to separate the multiple bifurcation points to a single point in the direction of the bifurcation path. As a numerical analysis example, a bifurcation analysis of a fullerene structure is performed to demonstrate the feasibility of the presented method.

Graph-theory, Bifurcation, Imperfection, Fulerene, Dihedral group

This study deals with topology optimization of spatial robotic manipulator, the geometry of which was
proposed initially in [1]. The manipulator consists of serially connected modules in a form of a
cylinder cut at a certain angle at its ends. The manipulator constructed in this way allows for relative
rotation of adjacent modules, which gives one degree of freedom per module. The operation of overall
robotic system resembles the elephant trunk manipulator. Previous research involved the possible
kinematic transformations of the manipulator [2], but not its structural optimization [3]. However,
structural design of the involved modules is a challenging task, as the process has to take into account
the current configuration of the module along the manipulator, which results in variable internal force.
It leads to optimization problem under multiple loading conditions with a significantly large number of
loads. This study considers optimal topology of such a modular manipulator structure. Due to the large
variety of possible load conditions, the initial analysis involves a 3D model of the structure with a
continuous set of possible arrangements of individual modules. An additional constraint imposed on
the solution will take into account the symmetry of the optimal topology of a single module, which is
dictated by manufacturing considerations.

optimal topology, modular systems, engineering software

Automation in Construction is currently one of the main new directions in Ł-PIAP. Our department is equipped with state-of-the-art devices, such as: an industrial 3D printer with a workspace of 15/5/5 m, capable of printing with concrete or extruded polystyrene and milling; a mobile 3D printer with a workspace of 5/3/3 m with the same capabilities; an industrial KUKA 500 robot with various designated end-effectors; a Wire Arc Additive Manufacturing (WAAM) multi-dimensional device using alloy and steel, etc. Here we present our ongoing projects and prospects that have the potential to revolutionize the construction industry by setting new standards for efficiency, precision and safety.

This contribution concerns a snake-like robotic manipulator arm proposed first in [1]. The manipulator is composed of linearly but nonaxially joined identical modules with a possibility of relative twist, which amounts to one degree of freedom per module. It is an example of an extremely modular system [2], and its advantages are: economization (due to modularity and possible mass production) and robustness (easy repair by replacement of a failed module). The hitherto research involved the possible geometric transformations of the manipulator arm [3], but not its structural optimization. However, structural design of the involved modules is a challenging task, as the process has to take into account the relative position of the module along the arm, as well as the variety of global configurations of the deployed manipulator. It leads to a multi-load structural optimization problem with a significantly large number of loads. This contribution considers topology optimization of such a modular manipulator structure. Due to the large variety of possible load conditions, the initial analysis involves a 2D model of the structure with a discrete set of two possible relative arrangements of adjacent modules. Such a formulation allows the proposed approach to be preliminarily explored, tested and optimized in a numerically manageable simplified environment. The support of the National Science Centre, Poland, granted under the grant agreement 2019/33/B/ST8/02791 is gratefully acknowledged.

Architectural design is particularly difficult, because it must combine multicriterial engineering optimization with other types of challenges, such as aesthetic and psychological which are usually ill-defined and arbitrary. Single-family house (SFH) is an archetypal architectural problem. Not only because it deals with creating of a habitat for the basic social cell, but also in a nutshell represents the entire spectrum of issues prevailing to architecture. That is environmental, both natural and artificial conditions. Since the scale of this classic problem is relatively small, it is usually manageable by a single architect. Nevertheless, the design conditions (natural and symbolical) are relatively diverse which inspire architects' imagination. This makes SFH probably the most favorable and pleasurable type of architectural design among the architects. In this multicriterial optimization certain aspects are to be minimized (e.g. noise exposition, glare, overheating, etc.) and others to be maximized (e.g. functionality, privacy, etc.). Moreover, some aspects of design have discrete nature (e.g. the functional relationships among rooms), while other are continuous (insolation, etc.). This paper presents preliminary results of the multicriterial architectural optimization of a SFH. A two-step algorithm has been applied: at first, a graph-theoretical combinatorial search produces a set of “good” architectural layouts, which are next evaluated against environmental conditions (noise, insolation and view exposition).

architectural optimization, brute-force, GPU, multicriterial