Self-reconfiguration planning of adaptive modular robots with triangular structure based on extended binary trees

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.