

In order to achieve the desired lattice structures, an alternative equation- Equation 33-was developed that omitted this cell property. Using Equation 8 to solve for desired relationships with neighboring robots, it was discovered that oddly-but interestingly-shaped “armed structures” would emerge this result was intuitive, as a cell’s function-relative position is used in this calculation. Motivated by SSP, the algorithm was generalized such that a formation could be defined by any number of mathematical functions-the goal: to produce grids. Using only local information, these robots are able to establish and maintain a variety of formations.Īs described in 1-Dimensional Robot-Space Cellular Automata, the initial conception of the algorithm considered formations defined by a single mathematical function. Each robot cell state consists of its distance and orientation in 2-dimensional space in relation to neighboring robots. It is emphasized that this cell is not a leader, but rather an initiator of the coordination process-thus, this algorithm distinguishes itself as being leaderless. A human operator sends a formation definition to some cell, designating it as the seed of the automaton.

Connectivity of the automaton is guaranteed as it is expressed as the union of all cell neighborhoods. Robots are represented as cells in a “robot-space cellular automaton”. A general purpose distributed robot formations algorithm has been presented.
