Modular self-reconfigurable robots hold the promise of being capable of performing a wide variety of tasks. However, many systems fall short of either delivering this promised functionality due to constraints in system architecture or validating it on functional hardware prototypes. This paper demonstrates the functional capabilities of the Planar Adaptive Robot with Triangular Structure (PARTS) and documents the versatility of this robot system using a holistic approach that combines simulations and hardware demonstrations on a prototype with nine fabricated modules. PARTS is a two-dimensional modular robot consisting of modules with a shape-shifting triangular geometry capable of forming adaptable space-covering structures. Meta-modules and mesh restructuring techniques are presented as methods for achieving topological self-reconfiguration. The feasibility of these methods is demonstrated by applying them on a simulated reconfiguration example of 62 modules. The paper showcases the versatility of PARTS on the hardware prototype using task-specific configurations, including locomotion using a meta-module and a walker configuration, module-module interaction by establishing a bridge between two separated module clusters, and interaction with the environment using a gripper and supporting structure configuration. The results validate the versatility and emphasize the potential of the system’s design concept, motivating the transfer of the hardware architecture to the third dimension.

In this paper, we present a parallel reconfiguration algorithm for shape-shifting modular robots with a triangular structure. The reconfiguration planning is based on partitioning the robot’s surface into source and sink sections for modules, using the largest common topology as a reference. Reconfiguration is realized by a synchronous surface flow of modules guided by the prior determination of module sources and sinks. Individual reconfiguration steps are carried out by a multi-step optimization framework, ensuring that intermediate configurations required for topology changes are valid and collision-free. With a configuration containing n modules, the algorithm completes the reconfiguration in O(n) reconfiguration steps and allows for a distributed and asynchronous hardware implementation. We demonstrate the performance of the proposed algorithm on multiple example configurations and compare the results to other reconfiguration approaches.

In this paper, we present a reconfiguration algorithm for shape-shifting modular robots with a triangular structure. The algorithm is derived from a novel description of the configuration space based on extended binary trees. Extended binary trees representing the same configuration are grouped into equivalence classes, which allows for a one-to-one correspondence between a configuration and its mathematical representation. Reconfiguration is then accomplished by a successive construction of the goal configuration, realized by moving individual modules along the surface of the robot and building up the binary tree of the goal configuration by populating unoccupied binary tree indices in ascending order with new modules. The algorithm is capable of solving the self-reconfiguration problem for modular robots with a triangular structure in O(n2) reconfiguration steps and is demonstrated on two reconfiguration examples. We then discuss the limits of the proposed methods, regarding constraints on the implementation and the lack of efficient collision avoidance, and outline possible resolutions.

In this paper, we present a novel description for the configuration space of adaptive modular robots with a triangular structure based on extended binary trees. In general, binary trees can serve as a representation of kinematic trees with a maximum of two immediate descendants per element. Kinematic loops are incorporated in the tree structure by an ingenious extension of the binary tree indices. The introduction of equivalence classes then allows a unique mathematical description of specific configurations of the robot system. Subsequently, we show how the extended binary tree can serve as a systematic tool for reconfiguration planning, allowing to solve the self-reconfiguration problem for modular robots with a triangular structure, which has as yet no general solution. Reconfiguration is performed by populating the binary tree indices of a desired target configuration in an ascending manner, moving modules along the surface of the robot. We demonstrate the planning algorithm on a simple example and conclude by outlining a way to translate the individual reconfiguration steps to specific module movement commands.

In dieser Arbeit stellen wir eine neue Beschreibung des Konfigurationsraumes des modularen Robotersystems PARTS auf der Basis von erweiterten Binarbaumen vor. Binarbaume konnen generell zur Darstellung kinematischer Baume mit maximal zwei Nachkommen pro Element verwendet werden. Durch eine funktionale Erganzung der Indizes konnen kinematische Schleifen in der Baumstruktur berucksichtigt werden. Die Einfuhrung von Aquivalenzklassen ermoglicht daraufhin eine eindeutige mathematische Beschreibung spezifischer Konfigurationen des Robotersystems. Im Anschluss wird aufgezeigt, wie der erweiterte Binarbaum als systematisches Werkzeug zur Planung der Rekonfiguration verwendet werden kann. Durch Besetzen der Binarbaumindizes der Zielkonfiguration in aufsteigender Weise mittels Bewegung von Modulen entlang der Oberflache kann eine Rekonfiguration durchgefuhrt werden. Abschliesend demonstrieren wird den vorgestellten Planungsalgorithmus an einem einfachen Beispiel.