2012 - 2013
Philippe Morel & Thibault Schwartz
Applications of robotics to discrete and continuous spatial lattices
The past ten years of architectural research, more intimately related to algorithmic and other computational methodologies, have highlighted a massive use of discrete mathematical models. Whether through cellular automata and (multi) agent-based modelling, or simply due to the intrinsic discrete nature of modern computational processes, the way in which we deal with mathematics has radically evolved. Nevertheless, this evolution has not been fully addressed within the discipline of architecture which remains largely influenced by continuous models of geometrical thinking. Beyond the fact that architecture is usually highly hybridised and component-based – and therefore discrete – our use of continuous models persists because of the phenomenology of our perception or due to diverse constructive traditions. Thus, many of us have a tendency to perceive a brick construction as continuous and homogeneous while it is discrete and heterogeneous, and to perceive a construction made of steel beams and columns as discrete while, thanks to welding, it can become rather continuous. Even if contemporary approaches inspired by rapid prototyping techniques allow us to envision a more perfect continuous future, it seems that, in architecture, discrete and continuous logics are still highly intricate, due to diverse practical constraints that include transportability or a machine’s maximum fabrication size. Therefore, either because of the embedded complexity of architecture which differs from sculpture, because of idiosyncratic constructive practices, because of the multiple disciplinary uses of mathematical models – e.g. the finite elements method in engineering – or simply because of the diverse intrinsic logics of materials, the discrete vs. continuous problem cannot be escaped. All this is especially true when one tries to associate highly different logics such as the discrete logic of Cellular Automata in computer simulations and the usually continuous logic of concrete in construction.
This confrontation between contradictory logics lies at the heart of the Research Cluster Applications of robotics to discrete and continuous spatial lattices. By following Henri Poincaré’s conventionalist viewpoint in his philosophy of mathematics, asserting that “one geometry cannot be truer than another, it can merely be more convenient”, we will challenge the architectural and constructive relevance of novel branches of geometry including Digital Geometry. First created in order to overcome the limits of “the usual notions of Cartesian geometries and also the notions of approximate mathematical analysis” in the domain of image analysis, this branch is gaining importance, due partly to the rapidly evolving amount of images available through the Internet. Indeed, in more and more fields associated with materiality – e.g. in medical imaging where for instance a body organ has to be precisely modelled – the adequacy between the reality of the geometric object studied and its digital model is a crucial issue. In order to attain such accuracy, as well as geometrical integrity in terms of the model with the application of sophisticated and robust algorithms, every source of error or approximation has to be minimized or removed. This is the case with real numbers that necessitate floating point arithmetic in order to be correctly represented in a computer, and this is one of the reasons why Digital Geometry only deals with integers. According to Jean Françon, in his preface to the book Géométrie discrète et images numériques (Digital Geometry and Digital Images), in Digital Geometry an object “is considered as a geometrical object in a discrete space (a set of points with whole coordinates). “Digital geometry studies geometry in such a space without reference to the usual Cartesian geometry. The continuous is abandoned, a very radical position. The only links between digital geometry and Cartesian geometry are in the analogy of notions and the geometer’s inspiration for these analogies, as we can see (…) with for instance the notions of discrete convexity, straight lines and circles, and discrete distances; more generally, it then appears that a notion of the continuous naturally produces several non-equivalent discrete definitions by analogy”.
Even if we are not entirely convinced that “the discrete theory will reach the point where we jettison the idea that the discrete is an approximation of the continuous” and that “one day we will think and calculate in a single geometry, which will be totally discrete and totally adapted to discrete machines”, we have to admit that the exponentially growing refinement of discretization is producing a new and strong contemporary phenomenology. Beyond the speculative aspect of such a phenomenology, which is “subversive because it contests the absolute reign of the continuous in geometry”, we will in RC5 emphasize its practical consequences. The most interesting one is related to the performances of recent fibre-reinforced materials such as carbon tubes or plates and high-performance concretes (FRHPC). Thanks to their lightness, fluidity or ductility such materials allow us to deal with the fine grain of computer simulations. Contrary to the modernist optimal structures mostly derived from 2-dimensional surfaces – e.g. surfaces of revolution and hyperbolic paraboloids –, quasi-optimal computational architecture structures are based on large data sets that give rise to larger topological and geometrical configurations. While most of these configurations can be represented through analytic representations thanks to the flexibility of contemporary parametric functions – e.g. NURBS functions – it can be highly inefficient to follow such a path; this is particularly true when architectural geometries based on Agent or CA processes is natively expressed by a couple of simple rules.
According to these elements, through the use of Mathematica, Grasshopper and the HAL robot control plugin for Grasshopper, we will investigate in RC5 novel applications of robotics to constructions based on fibre reinforced materials, and challenge our perception of architecture.
In addition to the studio work and to the regular classes on Grasshopper and HAL with Thibault Schwartz, the Research Cluster 5 will organize: 2 open workshops with engineers, computer scientists and mathematicians; 2 computer sciences master classes on robotics and agent-based modeling; 4 Mathematica sessions with Philippe Morel; 5 internal lectures.
P. M. an architect (dipl. Summa cum Laude) and theorist, cofounder of EZCT Architecture & Design Research (2000), is Associate Professor at the Ecole nationale superieure d’architecture Paris-Malaquais where he cofounded the Digital Knowledge program and department. Before teaching at the Bartlett he has taught at the Berlage Institute (seminar and studio) and at the Architectural Association (HTS Seminar and AADRL studio). His published essays include The Integral Capitalism (2001-2002), Research On the Biocapitalist Landscape (2002), Why Research and Contemporary Architecture should be Different (Archilab 2004), Notes on Algorithmic Design (2003), Notes on Computational Architecture (2004), A Few Precisions on Architecture and Mathematics (Mathematica Day, Henri Poincare Institute, Paris, January 2004), Forms of Formal Languages: Introduction to Algorithmics and Bezier Geometry with Mathematica (2005), Embedded Positivism: or Everything is Theoretical (2005), N Extensions to Extension of the Grid (2005), Some Geometries (2005), Computational Intelligence: the Grid as a Posthuman Network (Architectural Design, 2006), Mathematica in Architecture and Architectural Education, an Introduction, (IMS’2006, 8th International Mathematica Symposium) and Sense and Sensibilia (Architectural Design, 2011). Philippe Morel lectured and/or exhibited at Loopholes within Discourse and Practice (Harvard GSD, 2005), Script (Firenze, 2005), The Architecture of Possibility (Mori Art Museum, Tokyo, 2005), GameSetMatchII (TU Delft, 2006), at Columbia GSAPP, MIT Department of Architecture (A Few Remarks on Epistemology and Computational Architecture, Lecture, March 2006), at Architectural Association (Information Takes Command, 2007; The Laws of Thought, 2008; Pangaea Proxima, 2008; or recently What is computationalism?, 2012), at UCL Bartlett (Prolegomena to a Global Theory of Computationalism, 2011), at the Ecole des hautes études en sciences sociales (EHESS, Paris) and at the Ecole normale supérieure in Lyon. In February 2007, he curated the exhibition Architecture beyond Forms: The Computational Turn of Architecture at the Maison de l’architecture et de la ville PACA in Marseille). His work is in the FRAC Centre and Centre Pompidou permanent collections, as well as in private collections. His book Empiricism & Objectivity: Architectural Investigations with Mathematica (2003-2004), subtitled A Coded Theory for Computational Architecture, exhibited at ScriptedByPurpose (Philadelphia, Sept. 2007), is the first architectural theory book entirely written in code.
T. S. is a young architect based in Paris. He explores the evolution of architectural design practices in relation to generative algorithms and automated fabrication processes. Working in close collaboration with EZCT Architecture & Design Research, he is currently developing several hardware and software tools for robot-assisted construction and design. The “HAL” plugin for ABB robots programming via Grasshopper is part of these tools. Paying particular attention to the development of industrial manufacturing strategies applied to architectural projects, he is attached to a systematic prototyping exercise aiming to complete and evaluate digital experiments. As a teacher, he has been sharing the knowledge gained from these experiments in numerous pedagogical events in several European schools of architecture and design such as TU Wien, the Berlage Institute, the Ecole nationale supérieure d’architecture Paris-Malaquais and the ENSCI (Paris).
 H. Poincaré, Science and Hypothesis, Chap. “Non-Euclidean Geometries”, 1905.
 Jean Françon, foreword to Géométrie discrète et images numériques, Editions Lavoisier, Paris, 2007.
 Jean Françon, Ibid. it has to be noticed that the main proponents of American Digital Philosophy, as Stephen Wolfram or Edward Fredkin, are sharing the same view, enriched with specific philosophical hypotheses.
 Jean Françon, Ibid.