Rigid Geometry Formation Subject to Visibility Constraints using Heading Angle Correlation based on Leader-Follower System

This article proposes a tracking model for nonholonomic constraint robots, enabling the realization of leader-steered rigid geometry formations. By employing cameras and local leader-based approaches, the challenge posed by traditional separation-bearing control methods, which are incapable of establishing rigid formation for both translational and rotational control, is resolved. In addition, to maintain the connectivity of the sensing topology, the field-of-view (FOV) constraints of the on-board cameras are integrated into the controller design. A conversion approach is used to translate the FOV constraints into a rigid geometry formation. Additionally, there is a trade-off between visibility constraints and the leader-steered rigid geometry formation, particularly when the trajectory of the global leader has significant curvature. To address this problem, a continuously smooth transition function is employed. Ultimately, a fixed-time distributed control protocol and distributed observers are developed to realize the formation framework. Experimental results demonstrate that the proposed control protocol effectively achieves rigid geometric formations and satisfies FOV constraints.

Note to Practitioners—Robot formations with nonholonomic constraints are widely used in various applications. However, global communication conditions may not be available due to privacy concerns and network load. Additionally, in practical scenarios, it is preferable for the robot formation geometry to be rigid. Traditional formation error models, especially in scenarios involving local leaders, impede achieving rigid geometric formations. This paper proposes an error tracking model based on visual sensing to achieve rigid geometric formations. A PPC method is introduced to ensure that the FOV remains within specified limits. A switching function is employed to maintain the communication topology’s integrity consistently. Differentiators and fixed-time distributed control protocol are utilized to enhance formation performance. Experimental results validate that this approach facilitates rigid geometric formations while consistently maintaining visual constraints. Engineers can implement rigid geometric formations using this approach without needing to redesign controllers, simply by incorporating the additional angular offset proposed in this paper into the existing error model. With this change, we will further explore rigid formation transformations in the presence of obstacles.