A Decoupled Nonuniform Guiding Vector Field for Multirobot Coordinated Path-Following on 2-D Manifolds

This paper proposes a decoupled non-uniform guiding vector field (DNGVF) for coordinated path-following of a robot team on 2D manifolds embedded in 3D space. The DNGVF comprises three components: a propagation term that steers the robots along the desired path, a convergence term that drives path-following errors to zero, and a coordination term, decoupled from the convergence term, that enforces the predefined formation on the surface. Additionally, a speed coordination strategy is developed to construct the non-uniform guiding vector field, which assigns desired velocities to each robot in the vector field, thereby improving coordination accuracy. Finally, a surface generation method based on moving frame is introduced to enhance surface design flexibility. The key contribution of this work is the decoupling of the convergence and coordination terms by formulating the latter within the tangent space of the surface, thereby improving both path-following accuracy and coordination performance. Numerical and software-in-the-loop simulations validate that the proposed DNGVF reduces path-following errors while simultaneously improving coordination accuracy.