Versatile Distributed Maneuvering with Generalized Formations using Guiding Vector Fields

TL;DR

This work addresses versatile distributed maneuvering for multi-robot systems by decomposing maneuvers into interception and enclosing, each parameterized by independent virtual coordinates and combined into a composite 2D manifold. It develops a singularity-free guiding vector field (GVF) plus a consensus-based coordination mechanism to drive formation tracking, target enclosing, and circumnavigation, mapping the GVF to a unicycle controller for real robots. The framework is validated through extensive simulations in 2D and 3D settings and real-world experiments on small robotic teams, demonstrating scalable coordination with minimal communication and robustness to dynamic targets. The approach offers a unified, robust, and scalable pathway to complex cooperative maneuvers in heterogeneous and dynamic environments, with future work on state estimation and collision avoidance formalization.

Abstract

This paper presents a unified approach to realize versatile distributed maneuvering with generalized formations. Specifically, we decompose the robots' maneuvers into two independent components, i.e., interception and enclosing, which are parameterized by two independent virtual coordinates. Treating these two virtual coordinates as dimensions of an abstract manifold, we derive the corresponding singularity-free guiding vector field (GVF), which, along with a distributed coordination mechanism based on the consensus theory, guides robots to achieve various motions (i.e., versatile maneuvering), including (a) formation tracking, (b) target enclosing, and (c) circumnavigation. Additional motion parameters can generate more complex cooperative robot motions. Based on GVFs, we design a controller for a nonholonomic robot model. Besides the theoretical results, extensive simulations and experiments are performed to validate the effectiveness of the approach.

Figures (5)

• Figure 1: An illustration of versatile maneuvering: taking the $i$-th robot's at $t=7\mathrm{s}$ as an example. The red and green arrows depict the interception and enclosing behaviors, respectively, and the yellow arrow denotes the combined result for realizing versatile maneuvering.
• Figure 2: The first simulation results. The squares represent the initial positions of the robots, whereas the solid circles denote their final positions. The red dashed line is the target's path, and the thin lines are trajectories of $82$ robots. a) formation tracking. b) Coordination errors $w_1^{[i]}-w_1^{[j]}-\Delta_1^{[i,j]}$ and $w_2^{[i]}-w_2^{[j]}-\Delta_2^{[i,j]}$ converge to zero eventually, for $i,j\in\mathbb{Z}_1^{82}$, $i<j$. c) Formation errors $\phi_j^{[i]}$ for $i\in\mathbb{Z}_1^{82}$, $j\in\mathbb{Z}_1^3$.
• Figure 3: The second simulation results. The squares and circles represent the initial and final positions of the robots, respectively. The red dashed line is the target's path, and the thin lines are trajectories of $10$ robots.
• Figure 4: The third simulation results. The squares represent the initial positions of $27$ unicycle robots, whereas the blue rectangles are the robots at the final instant. The thin lines are the robots' trajectories. Solid lines with different colors denote the formed orbits at the final instant.
• Figure 5: Five robots circumnavigate on the a) circular and b) star-shaped orbits. We label the positions of robots and the target at two instants.

Theorems & Definitions (4)

• Definition 1
• Theorem 1
• proof
• Remark 1