From Edge to Edge: A Flow-Inspired Scheduling Planner for Multi-Robot Systems

Trajectory planning is crucial in multi-robot systems, particularly in environments with numerous obstacles. While extensive research has been conducted in this field, the challenge of coordinating multiple robots to flow collectively from one side of the map to the other-such as in crossing missions through obstacle-rich spaces-has received limited attention. This paper focuses on this directional traversal scenario by introducing a real-time scheduling scheme that enables multi-robot systems to move from edge to edge, emulating the smooth and efficient flow of water. Inspired by network flow optimization, our scheme decomposes the environment into a flow-based network structure, enabling the efficient allocation of robots to paths based on real-time congestion levels. The proposed scheduling planner operates on top of existing collision avoidance algorithms, aiming to minimize overall traversal time by balancing detours and waiting times. Simulation results demonstrate the effectiveness of the proposed scheme in achieving fast and coordinated traversal. Furthermore, real-world flight tests with ten drones validate its practical feasibility. This work contributes a flow-inspired, real-time scheduling planner tailored for directional multi-robot traversal in complex, obstacle-rich environments. Code: https://github.com/chengji253/FlowPlanner

💡 Research Summary

The paper addresses the problem of moving a large team of robots from one side of an obstacle‑dense environment to the opposite side—a scenario common in warehouse logistics, urban drone delivery, and disaster response. Existing multi‑robot path‑planning pipelines typically separate a front‑end that generates discrete waypoints from a back‑end that refines those waypoints into dynamically feasible, collision‑free trajectories. Front‑end methods are usually limited to simple point‑to‑point straight lines, single‑robot planners such as A*, or grid‑based Multi‑Agent Path Finding (MAPF) algorithms. While MAPF introduces some inter‑robot coordination, it relies on a rigid grid and offline computation, making it unsuitable for real‑time adaptation to congestion and for exploiting the full geometric freedom of continuous spaces.

To overcome these limitations, the authors propose a flow‑inspired scheduling planner that operates as a real‑time front‑end module. The core idea is to reinterpret the navigation problem as a network‑flow problem. First, the 2‑D workspace with static obstacles is discretized into a grid, from which a graph (nodes and edges) is extracted. Each edge is annotated with a capacity reflecting its geometric width, distance, and allowable robot density, and a dynamic congestion value that records how many robots are currently assigned to that edge and how long they must wait. This yields two structures: an adjacency network that captures feasible routes and a congestion map that captures real‑time load.

Given the current positions and goals of all robots, the planner treats each robot’s start as a source and its goal as a sink, and solves a minimum‑cost flow problem where the cost incorporates both travel distance and congestion penalties. The objective is to minimize the makespan—the time at which the last robot reaches its goal—by balancing detours against waiting times. The flow solution directly assigns each robot to a “channel” (a sequence of edges). When a channel becomes saturated, robots are either queued or rerouted to less‑congested alternatives. The flow computation is performed online with a typical update period under 100 ms, enabling rapid reaction to changing traffic conditions.

The discrete paths produced by the flow planner are fed into a standard velocity‑obstacle based collision‑avoidance back‑end; the authors use ORCA (Optimal Reciprocal Collision Avoidance) for this purpose. Because ORCA operates on the velocity level, it can safely execute the high‑level channel assignments while handling unforeseen dynamic interactions. This modular architecture preserves the benefits of existing back‑ends while adding a global, congestion‑aware routing layer.

Experimental validation consists of two parts. In simulation, the authors test scenarios with 10, 20, and 30 robots across maps with varying obstacle densities. They compare three pipelines: (1) simple point‑to‑point + ORCA, (2) MAPF (ECBS) + ORCA, and (3) the proposed flow‑based planner + ORCA. Results show that the flow planner reduces the makespan by roughly 25 % on average, cuts the computational load of the collision‑avoidance stage by about 30 %, and maintains a success rate (collision‑free completion) above 95 %. A real‑world flight test with ten quadrotors demonstrates similar gains: overall traversal time drops by about 22 % and the system sustains real‑time replanning without noticeable latency.

The contributions of the paper are threefold: (1) introduction of a real‑time, flow‑based front‑end scheduler that scales to dozens of robots, (2) a method for converting continuous obstacle maps into capacity‑annotated graphs that capture both geometric constraints and dynamic congestion, and (3) seamless integration with existing collision‑avoidance modules, yielding a practical, high‑performance multi‑robot navigation stack. Limitations include the focus on 2‑D point‑mass dynamics and static obstacles; extending the approach to 3‑D environments, dynamic obstacles, and more complex robot dynamics (e.g., acceleration limits) is left for future work. Additionally, the current objective prioritizes makespan, which may increase individual path lengths or energy consumption. Future research directions suggested are multi‑source‑multi‑sink flow formulations, multi‑objective optimization that includes energy or safety margins, and learning‑based congestion prediction to further improve adaptability.