Balanced Collaborative Exploration via Distributed Topological Graph Voronoi Partition

TL;DR

The paper tackles balanced collaborative exploration for multi-robot teams in obstacle-dense environments by formulating Problem 1 to minimize total travel distance while keeping workload balanced within a threshold $\hat{B}$. It introduces an incremental hybrid topological map that encodes both environmental connectivity and global coverage, and couples it with a distributed weighted graph Voronoi partition that guarantees bounded, equitable graph-space partitions. A hierarchical online planner integrates global coverage guidance with local target visitation via a receding-horizon ATSP framework, using dual-layer A* for fast path planning and B-spline trajectories for safe execution, with workload feedback guiding partition updates. Through extensive simulations and real-world experiments, the method demonstrates superior exploration efficiency, complete environment coverage, and improved workload balance over state-of-the-art baselines.

Abstract

This work addresses the collaborative multi-robot autonomous online exploration problem, particularly focusing on distributed exploration planning for dynamically balanced exploration area partition and task allocation among a team of mobile robots operating in obstacle-dense non-convex environments. We present a novel topological map structure that simultaneously characterizes both spatial connectivity and global exploration completeness of the environment. The topological map is updated incrementally to utilize known spatial information for updating reachable spaces, while exploration targets are planned in a receding horizon fashion under global coverage guidance. A distributed weighted topological graph Voronoi algorithm is introduced implementing balanced graph space partitions of the fused topological maps. Theoretical guarantees are provided for distributed consensus convergence and equitable graph space partitions with constant bounds. A local planner optimizes the visitation sequence of exploration targets within the balanced partitioned graph space to minimize travel distance, while generating safe, smooth, and dynamically feasible motion trajectories. Comprehensive benchmarking against state-of-the-art methods demonstrates significant improvements in exploration efficiency, completeness, and workload balance across the robot team.

Figures (12)

• Figure 1: Overview of the proposed balanced online collaborative exploration planner. The framework comprises two main components: constructing an efficient topological map that captures environmental connectivity and exploration completeness in obstacle-dense, non-convex environments; and implementing balanced dynamic exploration task planning with the distributed graph Voronoi guidance.
• Figure 2: Different Voronoi partitions in the non-convex environments.
• Figure 3: An example of graph-based exploration load metric and its decrease property. The metric formulation guarantees an upper bound on feasible exploration paths, $\mathcal{D}^E(\mathcal{P}_i) \leq 2 \cdot \lambda(\boldsymbol{g}_i, N_i)$.
• Figure 4: (a) A small spatial primitive, where a single robot suffices for complete exploration, is unnecessarily partitioned. (b)-(c) When certain nodes connect disproportionately large spatial regions, this induces undesirable load oscillations. (d) Virtual graph Voronoi centers instead of actual robot positions and dual nodes of overloaded nodes are employed to mitigate the excessive oscillations.
• Figure 5: Structure of the hybrid topological map.

Theorems & Definitions (6)

• Remark 1
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