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Scalable Long-Horizon Planning with Staggered Updates for Lifelong MAPF

The paper introduces PUSH, a scalable lifelong Multi-Agent Path Finding planner that achieves high-throughput, long-horizon coordination for thousands of agents on general maps by combining staggered subset planning with windowed path updates and EPIBT-inspired conflict resolution.

Original authors: Vaibhav Sanjay, Jiaoyang Li

Published 2026-08-10

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Vaibhav Sanjay, Jiaoyang Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a bustling city where millions of tiny, invisible cars are zooming around, trying to get from point A to point B without ever crashing into each other. This isn't just a traffic jam; it's a high-stakes dance called Multi-Agent Path Finding (MAPF). In the real world, this is the invisible brain behind warehouses full of robots, sorting centers, and delivery fleets. But here's the tricky part: in these places, robots don't just drive to a spot and leave. They often have to stop, load a package, or wait for a human to do something. This creates a "lifelong" problem where the robots are constantly getting new jobs the moment they finish the old ones.

The big challenge for scientists is figuring out how to coordinate thousands of these robots at once. If you try to plan every single robot's entire journey from start to finish, the computer gets overwhelmed and crashes. If you just tell them to "go forward" without looking ahead, they get stuck in traffic jams or dead ends because they can't see the problem coming. It's a balancing act between looking far into the future to avoid trouble and reacting quickly enough to keep moving.

Enter a new hero in this story: an algorithm called PUSH. Think of it as a super-smart traffic controller that finally figured out how to manage a crowd of 10,000 robots without losing its mind.

The Problem with the Old Ways

To understand why PUSH is special, let's look at the two main ways robots used to be managed, and why they both had flaws.

The "Look-Everything" Approach (RHCR):
Imagine a traffic cop who tries to plan the route for every single car in the city for the next hour, all at once. This is called "Rolling Horizon Collision Resolution" (RHCR). It's great at seeing the big picture and avoiding long-term traffic jams. But it's incredibly slow. If you have 10,000 robots, the computer spends so much time calculating routes that it can't even tell the robots when to move. It's like trying to solve a puzzle with a million pieces while the clock is ticking; you run out of time before you finish.

The "Look-Just-One-Step" Approach (PIBT/EPIBT):
Now, imagine a different traffic cop who only looks one step ahead. "Okay, move forward. If you hit a wall, stop." This is the "Reactive" approach (like PIBT and EPIBT). It's lightning fast and can handle thousands of robots easily. But it suffers from "temporal myopia"—a fancy way of saying it's very short-sighted. If a robot knows it has to wait 20 seconds to load a package, this short-sighted planner doesn't realize that waiting will block the whole hallway behind it. It just sees "move" and "stop," leading to massive, unnecessary traffic jams.

The New Solution: PUSH

The authors of this paper, Vaibhav Sanjay and Jiaoyang Li, created PUSH (Path Updates over Staggered Horizons) to get the best of both worlds. They wanted a system that could see far ahead like the slow planners but move as fast as the reactive ones.

Here is how PUSH works, using a simple analogy:

1. The Staggered Shift (Subset Planning)
Imagine a massive stadium where 10,000 people need to leave. Instead of trying to tell everyone where to go at the exact same second (which causes chaos), PUSH tells a small group of people to move first. Then, a few seconds later, it tells the next group. It "staggered" the updates.
In the paper, this means the computer only plans a small subset of robots at any given moment. This keeps the math easy and fast, just like the reactive planners.

2. The Long View (Windowed Planning)
But here's the twist: even though it only plans for a few robots at a time, it plans far into the future for them. Instead of just saying "move one step," it says, "Here is your path for the next 10 steps." This is the "windowed" part. It lets the robots see around corners and know that a robot ahead is going to be stuck loading a package, so they can slow down before they get there.

3. The Recursive Push (Priority Inheritance)
What happens if two robots still want to go to the same spot? In the old reactive systems, they might just bump into each other or wait awkwardly. PUSH uses a clever trick called "recursive priority inheritance."
Imagine a line of people trying to squeeze through a door. If a high-priority person (someone who has been waiting a long time) needs to move, they can "push" a lower-priority person out of the way. But here's the magic: that lower-priority person doesn't just stop; they immediately look for a new spot and might push another person out of the way. It's a chain reaction of polite shoving that ripples through the crowd until everyone finds a spot. This allows the system to resolve complex traffic jams instantly without getting stuck.

What They Found

The researchers tested PUSH in two very different worlds:

The "Loading Dock" World: Maps where robots have to stop and wait for 20 seconds to do a task. This is where short-sighted planners usually fail because they don't anticipate the blockage.
The "Narrow Hallway" World: Maps with long, skinny corridors and dead ends, where robots have to be very careful not to trap themselves.

The Results:

Speed: PUSH handled up to 10,000 agents (robots) in under a second. That is the same scale as the fastest reactive planners.
Throughput: In the "Loading Dock" tests, PUSH moved significantly more robots to their goals than any other method. In one test (the "random-32-32-20" map), it improved throughput by 300% compared to the previous best method (EPIBT-LNS). In another (warehouse-large), it improved by 25%.
Robustness: When the researchers made the robots wait longer (increasing the task time), the old short-sighted planners crashed and burned, while PUSH kept humming along.
The "Lite" Version: The authors also tested a version called "PUSH-lite" that didn't use the "recursive pushing" trick. It worked fine for small groups but collapsed when the number of robots got too high. This proved that the "pushing" mechanism is essential for handling crowds.

Why It Matters

The paper shows that you don't have to choose between being fast and being smart. By combining the idea of planning for only a few robots at a time (subset planning) with the ability to look far ahead (windowed planning) and a smart way to resolve conflicts (recursive pushing), PUSH solves a problem that has been a bottleneck for years.

It's not just a theoretical win, either. The authors ran these simulations on real-world map layouts used in competitions and industry. They found that while other methods might work for a few hundred robots, they fail miserably when you scale up to the thousands needed for a real, busy warehouse. PUSH is the first method to successfully coordinate that many robots while still looking far enough ahead to avoid the traffic jams that happen when robots have to stop and work.

In short, PUSH is like giving a traffic controller a crystal ball and a megaphone, allowing them to direct a city of 10,000 robots smoothly, even when the roads are narrow and the drivers have to stop for coffee.

Technical Summary: Scalable Long-Horizon Planning with Staggered Updates for Lifelong MAPF

Problem Definition

The paper addresses Lifelong Multi-Agent Path Finding (LMAPF), a variant of the standard MAPF problem where agents continuously receive new goals upon reaching their current ones. The core challenge is to generate collision-free paths for large fleets (thousands of agents) under strict real-time constraints while avoiding temporal myopia (short-sightedness).

Existing approaches face a trade-off between scalability and long-horizon reasoning:

Reactive Planners (e.g., PIBT, EPIBT): Scale effortlessly to thousands of agents using rule-based, step-by-step coordination but suffer from severe temporal myopia, failing in scenarios requiring anticipation of future congestion (e.g., narrow corridors or task execution delays).
Windowed Planners (e.g., RHCR): Plan over multi-step horizons to improve foresight but incur substantial computational overhead when replanning the entire fleet simultaneously, hindering scalability.
Subset Planners (e.g., Token Passing - TP): Scale by replanning only a subset of agents but are restricted to highly structured, "well-formed" maps and cannot handle general topologies.

The paper identifies a gap: there is no existing algorithm that achieves long-horizon planning at scale across general maps while handling congested environments and task execution delays (Task Completion Time, TCT).

Methodology: Path Updates over Staggered Horizons (PUSH)

The authors propose PUSH, a planner that synthesizes the strengths of TP, RHCR, and EPIBT. It achieves scalability by planning only a subset of agents at each timestep while maintaining long-horizon reasoning through staggered windows.

Core Mechanisms

Staggered Subset Planning:
- Unlike RHCR, which replans the entire fleet simultaneously, PUSH replans only a subset of agents ( $Q$ ) at each timestep.
- Agents are assigned a time2Replan counter. When an agent's counter reaches zero or its current path forces a wait, it enters the replanning queue.
- This staggered approach prevents the computational explosion associated with simultaneous fleet-wide replanning.
Windowed Path Planning with Fallbacks:
- PUSH maintains a global set of safe, collision-free fallback paths ( $\Pi$ ) for all agents.
- Instead of planning full paths to goals (as in TP), agents plan $W$ -step windowed paths.
- If a new plan cannot be found, an agent defaults to its existing fallback path, guaranteeing collision-free execution at all times.
Recursive Priority Inheritance and Pushing:
- To handle congestion and improve path quality, PUSH integrates EPIBT-inspired priority inheritance.
- Agents are assigned global priorities. When a higher-priority agent plans a path that conflicts with a lower-priority agent, the lower-priority agent is "pushed."
- The displaced agent recursively replans its path, temporarily inheriting the higher priority. This continues until a collision-free solution is found or a recursion limit ( $M$ ) is reached.
- Unlike EPIBT, which is limited to 1-step or short-horizon pushes, PUSH uses a modified windowed space-time A* to find optimal $W$ -step paths that collide with at most one lower-priority agent.
Anytime Optimization (LNS):
- After the primary planning cycle, PUSH utilizes remaining time to run a Large Neighborhood Search (LNS).
- It randomly selects agents, removes their paths, and attempts to replan them with higher priority to improve the global objective (minimizing distance to goals).
- The solution is accepted only if it improves the aggregate distance to goals.

Theoretical Guarantees

Completeness: PUSH guarantees returning collision-free paths for all agents in finite time.
Deadlock-Freedom: Under specific conditions (biconnected graphs, zero TCT, and "longer elapsed time" priority ordering), PUSH guarantees that every agent reaches its goal within a finite number of timesteps, matching the guarantees of EPIBT.

Key Contributions

First General-Map Subset Planner: PUSH is the first algorithm to combine subset planning (for scalability) with long-horizon windowed planning, applicable to general map structures without the topological restrictions of Token Passing.
Scalable Long-Horizon Reasoning: It successfully coordinates fleets of up to 10,000 agents with multi-step planning horizons ( $W=10$ ), a capability previously unattainable for general maps.
Robustness to Congestion and Delays: By integrating recursive priority pushing and staggered updates, PUSH effectively handles narrow corridors, deep dead-ends, and stochastic Task Completion Times (TCT) where reactive planners fail.

Experimental Results

The authors evaluated PUSH against baselines (RHCR-PBS, EPIBT-LNS, PIBT, and an ablation PUSH-lite) on two types of scenarios:

TCT Maps (Task Delays):
- Setup: Agents wait at goals for $T=20$ timesteps.
- Results: PUSH and PUSH-LNS achieved the highest throughput across all map sizes (up to 10,000 agents).
- Comparison: While EPIBT-LNS maintained smooth scaling in open maps, it degraded significantly in narrow corridors and dense obstacles. RHCR exhausted its planning budget as congestion increased. PUSH-LNS showed a 25% throughput improvement over EPIBT-LNS in warehouse-large and 300% in random-32-32-20.
Complex Maps (Structural Constraints):
- Setup: Long corridors and dead-ends (Symbotic, Delivery maps) with $T=0$ .
- Results: PUSH-LNS achieved the highest throughput (e.g., 3.8 in Symbotic).
- Failure Modes: EPIBT-LNS struggled with high densities in deep corridors; RHCR frequently timed out. The PUSH-lite ablation (without recursive pushing) suffered catastrophic performance collapse in large fleets, highlighting the necessity of recursive priority displacement.
Ablation Studies:
- TCT Sensitivity: PUSH-LNS retained high throughput even with non-zero TCTs, whereas myopic planners (EPIBT-LNS) degraded significantly.
- Window Size ( $W$ ): Increasing $W$ improved PUSH-LNS performance, allowing it to leverage long-horizon planning without computational collapse. In contrast, EPIBT-LNS performance collapsed at $W=7$ due to the exponential explosion of possible operations, while RHCR defaulted to myopic planning at larger windows.

Significance and Claims

The paper claims that PUSH bridges the critical gap between the extreme scalability of reactive planners and the foresight of long-horizon planners. It is presented as the first LMAPF algorithm capable of:

Coordinating 10,000 agents with long-horizon planning.
Operating on general map structures without restrictive topological assumptions.
Effectively managing congested scenarios and task execution delays that cause reactive planners to fail.

The authors position PUSH as a foundational step toward solving real-world industrial challenges (e.g., robotic sortation centers) that require simultaneous large-fleet coordination and long-term anticipation, a combination previously considered intractable for general maps. Future directions suggested include extending the framework to kinodynamic constraints and dynamic window sizing.