A Game-theoretic Formulation of the Homogeneous Self-Reconfiguration Problem

In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.Comment: 8 pages, 5 figures, 2 algorithm

3D reconfiguration using graph grammars for modular robotics

The objective of this thesis is to develop a method for the reconfiguration of three-dimensional modular robots. A modular robot is composed of simple individual building blocks or modules. Each of these modules needs to be controlled and actuated individually in order to make the robot perform useful tasks. The presented method allows us to reconfigure arbitrary initial configurations of modules into any pre-specified target configuration by using graph grammar rules that rely on local information only. Local in a sense that each module needs just information from neighboring modules in order to decide its next reconfiguration step. The advantage of this approach is that the modules do not need global knowledge about the whole configuration. We propose a two stage reconfiguration process composed of a centralized planning stage and a decentralized, rule-based reconfiguration stage. In the first stage, paths are planned for each module and then rewritten into a ruleset, also called a graph grammar. Global knowledge about the configuration is available to the planner. In stage two, these rules are applied in a decentralized fashion by each node individually and with local knowledge only. Each module can check the ruleset for applicable rules in parallel. This approach has been implemented in Matlab and currently, we are able to generate rulesets for arbitrary homogeneous input configurations.MSCommittee Chair: Magnus Egerstedt; Committee Member: Jeff Shamma; Committee Member: Patricio Antonio Vel

Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems

Behavior finding: Morphogenetic Designs Shaped by Function

Evolution has shaped an incredible diversity of multicellular living organisms, whose complex forms are self-made through a robust developmental process. This fundamental combination of biological evolution and development has served as an inspiration for novel engineering design methodologies, with the goal to overcome the scalability problems suffered by classical top-down approaches. Top-down methodologies are based on the manual decomposition of the design into modular, independent subunits. In contrast, recent computational morphogenetic techniques have shown that they were able to automatically generate truly complex innovative designs. Algorithms based on evolutionary computation and artificial development have been proposed to automatically design both the structures, within certain constraints, and the controllers that optimize their function. However, the driving force of biological evolution does not resemble an enumeration of design requirements, but much rather relies on the interaction of organisms within the environment. Similarly, controllers do not evolve nor develop separately, but are woven into the organism’s morphology. In this chapter, we discuss evolutionary morphogenetic algorithms inspired by these important aspects of biological evolution. The proposed methodologies could contribute to the automation of processes that design “organic” structures, whose morphologies and controllers are intended to solve a functional problem. The performance of the algorithms is tested on a class of optimization problems that we call behavior-finding. These challenges are not explicitly based on morphology or controller constraints, but only on the solving abilities and efficacy of the design. Our results show that morphogenetic algorithms are well suited to behavior-finding

Evolutionary development of tensegrity structures

Contributions from the emerging fields of molecular genetics and evo-devo (evolutionary developmental biology) are greatly benefiting the field of evolutionary computation, initiating a promise of renewal in the traditional methodology. While direct encoding has constituted a dominant paradigm, indirect ways to encode the solutions have been reported, yet little attention has been paid to the benefits of the proposed methods to real problems. In this work, we study the biological properties that emerge by means of using indirect encodings in the context of form-finding problems. A novel indirect encoding model for artificial development has been defined and applied to an engineering structural-design problem, specifically to the discovery of tensegrity structures. This model has been compared with a direct encoding scheme. While the direct encoding performs similarly well to the proposed method, indirect-based results typically outperform the direct-based results in aspects not directly linked to the nature of the problem itself, but to the emergence of properties found in biological organisms, like organicity, generalization capacity, or modularity aspects which are highly valuable in engineering

Computing multi-scale organizations built through assembly

The ability to generate and control assembling structures built over many orders of magnitude is an unsolved challenge of engineering and science. Many of the presumed transformational benefits of nanotechnology and robotics are based directly on this capability. There are still significant theoretical difficulties associated with building such systems, though technology is rapidly ensuring that the tools needed are becoming available in chemical, electronic, and robotic domains. In this thesis a simulated, general-purpose computational prototype is developed which is capable of unlimited assembly and controlled by external input, as well as an additional prototype which, in structures, can emulate any other computing device. These devices are entirely finite-state and distributed in operation. Because of these properties and the unique ability to form unlimited size structures of unlimited computational power, the prototypes represent a novel and useful blueprint on which to base scalable assembly in other domains. A new assembling model of Computational Organization and Regulation over Assembly Levels (CORAL) is also introduced, providing the necessary framework for this investigation. The strict constraints of the CORAL model allow only an assembling unit of a single type, distributed control, and ensure that units cannot be reprogrammed - all reprogramming is done via assembly. Multiple units are instead structured into aggregate computational devices using a procedural or developmental approach. Well-defined comparison of computational power between levels of organization is ensured by the structure of the model. By eliminating ambiguity, the CORAL model provides a pragmatic answer to open questions regarding a framework for hierarchical organization. Finally, a comparison between the designed prototypes and units evolved using evolutionary algorithms is presented as a platform for further research into novel scalable assembly. Evolved units are capable of recursive pairing ability under the control of a signal, a primitive form of unlimited assembly, and do so via symmetry-breaking operations at each step. Heuristic evidence for a required minimal threshold of complexity is provided by the results, and challenges and limitations of the approach are identified for future evolutionary studies

A Rule Synthesis Algorithm for Programmable Stochastic Self-Assembly of Robotic Modules

Programmable self-assembly of modular robots offers promising means for structure formation at different scales. Rule-based approaches have been previously employed for distributed control of stochastic self-assembly processes. The assembly rate in the process directly depends on the concurrency level induced by the employed ruleset, i.e. the number of concurrent steps necessary to build one instance of the target structure. Our aim here is to design a formal synthesis algorithm to automatically derive rulesets of high concurrency for a given target structure composed of robotic modules. In the literature, self-assembly of (simulated or real) robotic modules has been realized through manually designed rulesets or manually adjusted rulesets generated by employing graph-grammar formalisms or metaheuristic methods. In this work, we employ an extended graph-grammar formalism, adapted for self-assembly of robotic modules, and propose a novel formal synthesis algorithm capable of generating rulesets for robotic modules by natively considering the morphology of their connectors. The synthesized rulesets induce a high level of concurrency in the self-assembly scheme by exploiting controlled information propagation, using solely local communication. Simulation results of microscopic (non-spatial) and submicroscopic (spatial) models of our robotic platform confirm higher performance of rulesets synthesized by our algorithm compared to related work in the literature