Concurrent-Learning Based Relative Localization in Shape Formation of Robot Swarms

In this article, we address the shape formation problem for massive robot swarms in environments where external localization systems are unavailable. Achieving this task effectively with solely onboard measurements is still scarcely explored and faces some practical challenges. To solve this challenging problem, we propose the following novel results. Firstly, to estimate the relative positions among neighboring robots, a concurrent-learning based estimator is proposed. It relaxes the persistent excitation condition required in the classical ones such as the least-square estimator. Secondly, we introduce a finite-time agreement protocol to determine the shape location. This is achieved by estimating the relative position between each robot and a randomly assigned seed robot. The initial position of the seed one marks the shape location. Thirdly, based on the theoretical results of the relative localization, a novel behavior-based control strategy is devised. This strategy not only enables the adaptive shape formation of large groups of robots but also enhances the observability of inter-robot relative localization. Numerical simulation results are provided to verify the performance of our proposed strategy compared to the state-of-the-art ones. Additionally, outdoor experiments on real robots further demonstrate the practical effectiveness and robustness of our methods. Note to Practitioners—Shape formation has a broad potential for large groups of robots to execute certain tasks, such as object transport, forest firefighting, and entertainment shows. However, most of the existing approaches rely on external localization infrastructures, rendering them impractical in environments where such systems are not available. To address this issue, this article proposes an integrated strategy that can achieve shape formation for large groups of robots by using local distance and displacement measurements. This strategy consists of three main components. Firstly, a relative localization estimator is introduced to estimate the relative positions among neighboring robots. Secondly, a protocol for reaching a consensus on the desired shape’s position is proposed. Thirdly, a behavior-based controller is developed to achieve massive shape formation and enhance the observability of relative localization. More details of the proposed algorithms and swarm robotic systems are provided in this article.