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This paper presents a stability analysis of swarm robots, a group of multiple robots. In particular, we focus on robot swarms with heterogeneous abilities, in which each robot has a different sensing range and physical limitations, including maximum velocity and acceleration. In addition, each robot has a unique sensing region with a limited angle field of view. We previously proposed a decentralized navigation method for such heterogeneous swarm robots consisting of one leader and multiple followers. With the decentralized navigation method, a single leader can navigate for followers while maintaining connectivity and satisfying the physical limitations unique to each robot; i.e., each follower has a target robot and follows it without violating its physical limitations. In this paper, we focus on a stability analysis of such swarm robots. When the leader moves at a constant velocity, we mathematically prove that the shape and orientations of all robots eventually converge to the equilibrium state. For this, we must first prove that the equilibrium state exists. Then, we show the convergence of the state to its equilibrium. Finally, we carry out experiments and numerical simulations to confirm the stability analysis, i.e., the convergence of the swarm robots to the equilibrium states.

This paper addresses the navigation of a robotic swarm with nonhomogeneous abilities, including sensing range, maximum velocity, and acceleration. With this method, the robotic swarm moves in a two-dimensional plane, and each follower distributedly constructs and maintains local directed connection using only local information to achieve maintenance of global connectivity. We also ensure the swarm is stable when the leader moves at a constant velocity. Validity and effectiveness of the proposed control strategy are shown by theoretical analysis, experiments with real robots, and numerical simulations.