In this study, we focused on robotic swarms, allowing multiple anonymous autonomous robots to gather and move mutually in tasks. We proposed a method to design a parameter of the control barrier function (CBF) in a robotic swarm so that the swarm can achieve collision-free deformation considering the environmental conditions. We analyzed the responses to perturbations of swarming robots, to which we applied the CBF. Although we can guarantee a safe distance between mobile robots, the CBF limits their actions and prevents swarm deformation. Through analysis of the frequency domain, we investigated the effects of a selected parameter in the CBF on the deformability of a swarm. We obtained an appropriate range of parameters that realize both distance maintenance and deformability retention.

We consider an autonomous and decentralized mobile robotic swarm that does not require an advanced communication system; moreover, each robot must pass a narrow space preserving the distance with other robots. The control barrier function (CBF) method is useful for robotic swarms to guarantee collision avoidance. However, introducing CBF inequalities can cancel other objectives and sometimes causes a deadlock problem. Therefore, we introduce a coupled oscillator system to generate asymmetric global order by itself to avoid deadlock. By generating an effective global order in the swarm, each robot adequately moves to a target position without requiring high-cost communication systems.

For a robotic swarm system composed of autonomous mobile robots, controlling and using asymmetric global geometric states promotes the task performance of the swarm. This paper presents a systematic method for estimating asymmetric global geometric states over a swarm system. To overcome the limitations of local observation or communication ability, we propose a wave-type interaction among neighboring robots. We assume that each robot has a scalar state variable called a phase, which is manipulated through interactions. Through the analysis of eigenvalues of a graph Laplacian matrix corresponding to a local communication network of robots, we show that a robot can estimate global states, such as the size of an entire swarm, by frequency analysis of its phase. We also analyzed the stability of the wave-type interaction based on von-Neumann stability. We verified the proposed method by computer simulations, in which robots in a swarm detected the deformation in the shape of the swarm when the swarm was passing through a narrow area. The result will contribute to building a control system for swarms that can manipulate their shape or characteristics to adapt themselves based on tasks or environmental requirements.