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In complex swarm robotic applications that perform different tasks such as transportation and observation, robot swarms should construct and maintain a formation to adapt and move as a single large-scale robot. For example, transportation and observation tasks require unique robot swarms with either high densities to support the weight of the transported objects or low densities to avoid overlapping field of views and avoid obstructions. Previous literature has not focused on structure optimization because swarming provides a largecollective capability. This paper proposes a leader-follower-controlled collective movement method by calculating direction and distance potentials between robots based on geometric constraints, constricting robot positioning along radial gradients around the leader robot according to these potentials. This paper demonstrates a robot swarm applying the proposed method while maintaining formations with different densities while moving and evaluates the robot swarm structure-maintaining performance.

Swarm robotic systems control multiple robots in a coordinated manner for using this flexible coordination to solve complex tasks in various environments. Such systems can utilize the individual capabilities of robots scattered within the swarm as well as the collective capabilities of the assembled robots. By coordinating these capabilities, swarms can solve tasks with a range of purposes, including carrying out rough sweeps of the overall environment using scattered robots or detailed observation of a part of the environment using assembled robots. This study developed a self-organization method for constructing regular groups of robots from scattered robots to achieve coordination between individual and collective states. An approach that integrates elements of self-organization with different input information requires centralized control to manage them. To provide this self-organization without centralized control, we focus on using the phase-field method and cellular automata to facilitate crystal growth that produces ordered structures from scattered particles. We formulate a method for arranging robots in a self-organizing manner based on the geometrical regularities of tile-able lattices (honeycomb, square, and hexagonal lattices) on a two-dimensional plane, demonstrate the process undertaken in carrying out the proposed method, and quantitatively evaluate the effectiveness of the lattice-based geometrical regularity approach. The proposed method contributes to carrying out tasks with a range of purposes by organizing states with either individual or collective capabilities of robot groups.

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