Multi-Robot Connected Fermat Spiral Coverage

TL;DR

MCFS presents a novel fusion of computer graphics and planning to solve multi-robot coverage in environments with irregular obstacles. By lifting Connected Fermat Spiral into a multi-robot setting and reducing MCPP to the Min-Max Rooted Tree Cover problem, the framework delivers smooth, obstacle-contouring coverage paths without workspace decomposition. It adds two optimizations—isograph augmentation and MMRTC solution refinement—that reduce makespan, curvature, and overlap, outperforming grid-based baselines at the expense of longer solve times. The approach advances practical multi-robot coverage by enabling flexible start positions, scalable stitching, and balanced task distribution, with public code for reproduction.

Abstract

We introduce the Multi-Robot Connected Fermat Spiral (MCFS), a novel algorithmic framework for Multi-Robot Coverage Path Planning (MCPP) that adapts Connected Fermat Spiral (CFS) from the computer graphics community to multi-robot coordination for the first time. MCFS uniquely enables the orchestration of multiple robots to generate coverage paths that contour around arbitrarily shaped obstacles, a feature that is notably lacking in traditional methods. Our framework not only enhances area coverage and optimizes task performance, particularly in terms of makespan, for workspaces rich in irregular obstacles but also addresses the challenges of path continuity and curvature critical for non-holonomic robots by generating smooth paths without decomposing the workspace. MCFS solves MCPP by constructing a graph of isolines and transforming MCPP into a combinatorial optimization problem, aiming to minimize the makespan while covering all vertices. Our contributions include developing a unified CFS version for scalable and adaptable MCPP, extending it to MCPP with novel optimization techniques for cost reduction and path continuity and smoothness, and demonstrating through extensive experiments that MCFS outperforms existing MCPP methods in makespan, path curvature, coverage ratio, and overlapping ratio. Our research marks a significant step in MCPP, showcasing the fusion of computer graphics and automated planning principles to advance the capabilities of multi-robot systems in complex environments. Our code is available at https://github.com/reso1/MCFS.

Figures (10)

• Figure 1: The unified version of CFS on a workspace (grey region). Colored squares represent the stitching tuples. From left to right: The input isograph, the path resulting from the CFS selector, and the path resulting from the MCS selector.
• Figure 2: The CFS paths for (a) the original unidirectional $O_{u\rightarrow v}$ in zhao2016connected, with the artifacts outlined in red dashed circles, and (b) our bidirectional $O_{u, v}$.
• Figure 3: Left: The augmented isograph with original edges (solid lines) and an augmented edge (dashed line). Right: Three sequences of stitching tuples (black boxes) for $O_{v_1,v_3}$.
• Figure 4: Pairwise isovertices splitting from $u, v$ into $a, b$ at stitching tuples $o_1, o_2$. (a) Isograph $G$. (b)(c) Two trees of $G$ (in dashed and solid lines, respectively) before and after the splitting. (d) The layered isolines, each corresponding to the isovertex in the same color, and their post-split segments.
• Figure 5: Three MMRTC solutions $\mathcal{T}$$=$$\{T_i\}_{i=1}^4$ on isograph $G$ depicted in three rows. The weight of an isovertex corresponds to its marker size. An isovertex filled with color is covered by multiple trees. In the third row, PIS split the isovertices in the same marker (except circles) in $G$ into new isovertices in the same marker and assigned to trees in $\mathcal{T}$.