Coordinated Guiding Vector Field Design for Ordering-Flexible Multi-Robot Surface Navigation

TL;DR

This work addresses multi-robot surface navigation with arbitrary ordering by introducing a distributed coordinated guiding vector field (CGVF) that combines surface convergence, surface traversal, and coordination. The authors elevate the problem to a higher-dimensional setting by treating surface parameters as two virtual coordinates, yielding a singularity-free GVF $\chi^{hgh}$ that globally guides robots to the desired surface and along it. Coordination relies on local interactions of two virtual coordinates per robot, plus a moving virtual target, enabling ordering-flexible behavior with reduced communication and computation compared to geodesic-distance-based schemes. Theoretical results establish uniqueness of the closed-loop dynamics, convergence to the surface, consistent surface maneuvering, and ordering-flexible coordination, all validated by large-scale numerical simulations on a torus showing robust, flexible formation without fixed agent orderings.

Abstract

We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a traversing direction for maneuvering on the desired surface, and a coordinated term to achieve the surface motion coordination with an arbitrary ordering of the robotic group. By setting the surface parameters as additional virtual coordinates, the proposed approach eliminates the potential singularity of the CGVF and enables both the global convergence to the desired surface and the maneuvering on the surface from all possible initial conditions. The ordering-flexible surface motion coordination is realized by each robot to share with its neighbors only two virtual coordinates, i.e. that of a given target and that of its own, which reduces the communication and computation cost in multi-robot surface navigation. Finally, the effectiveness of the CGVF is substantiated by extensive numerical simulations.

Figures (4)

• Figure 1: Illustration of the ordering-flexible motion coordination.
• Figure 2: (a)-(d) Two complex cases of 22-robot surface navigation tasks on a desired torus surface with different initial states. Subfigures (a), (c): Moving trajectories of the 22 robots with the CGVF \ref{['desired_law']}. Subfigures (b), (d): Top view of the initial and final positions of the robots to show the ordering-flexible coordination. (Here, the black and red arrows denote the initial and final positions of the robots, respectively. The dashed lines represent the trajectories of the robots. The green surface is the desired torus surface).
• Figure 3: Temporal evolution of the position errors $\phi_{i,1}, \phi_{i,2}, \phi_{i,3}, i\in\mathbb{Z}_1^{22}$ in Fig. \ref{['20_torus_trajectories']} (Case 1).
• Figure 4: Temporal evolution of the ordering-flexible motion coordination terms $c_i\omega_{i,j}-\eta_{i,j}, i\in\mathbb{Z}_1^{22}, j=1, 2$ in Fig. \ref{['20_torus_trajectories']} (Case 1).

Theorems & Definitions (12)

• Definition 1
• Remark 1
• Definition 2
• Remark 2
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof