[Paper Review] Time-Independent Planning for Multiple Moving Agents

Keisuke Okumura, Yasumasa Tamura+1 more|arXiv (Cornell University)|May 27, 2020

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes time-independent planning for multi-agent path finding (MAPF), a distributed and online approach that ensures agents reach their destinations despite stochastic delays. By modeling agent behavior as a transition system with atomic actions—requesting, moving, and contracting—and using Causal-PIBT for deadlock recovery, the method achieves guaranteed reachability and robust performance under timing uncertainty, outperforming synchronized and dependency-preserving policies in simulations with stochastic delays.

ABSTRACT

Typical Multi-agent Path Finding (MAPF) solvers assume that agents move synchronously, thus neglecting the reality gap in timing assumptions, e.g., delays caused by an imperfect execution of asynchronous moves. So far, two policies enforce a robust execution of MAPF plans taken as input: either by forcing agents to synchronize or by executing plans while preserving temporal dependencies. This paper proposes an alternative approach, called time-independent planning, which is both online and distributed. We represent reality as a transition system that changes configurations according to atomic actions of agents, and use it to generate a time-independent schedule. Empirical results in a simulated environment with stochastic delays of agents' moves support the validity of our proposal.

Motivation & Objective

• To address the reality gap in MAPF planning caused by imperfect, asynchronous execution of moves.
• To develop a distributed, online planning method that does not rely on fixed timing assumptions.
• To ensure all agents reach their destinations within finite time despite stochastic delays.
• To improve robustness over existing policies like fully synchronized (FSP) and minimum communication (MCP) policies.
• To evaluate the effectiveness of using offline MAPF plans as hints in enhancing time-independent planning.

Proposed method

• Model the system as a transition system with three atomic actions: requesting next location, moving (extended), and releasing past locations or staying (contracted).
• Define a time-independent model where no a priori timing knowledge is assumed, representing non-deterministic environmental behavior.
• Implement Causal-PIBT, a decentralized algorithm based on priority inheritance and backtracking, to resolve conflicts and ensure reachability.
• Use a virtual depth-first search tree to guide priority inheritance and backtracking propagation in case of blocked agents.
• Integrate offline MAPF plans as hints in Causal-PIBT+ to improve convergence and reduce cost.
• Use a two-phase timestep model: one phase for state transitions (requesting/contracting), and one for actual moves, treating move time as dominant.

Experimental results

Research questions

• RQ1 Can a time-independent planning approach ensure reachability for all agents under arbitrary timing delays?
• RQ2 How does time-independent planning compare to FSP and MCP policies in terms of solution cost and robustness under stochastic delays?
• RQ3 To what extent do offline MAPF plans improve the performance of time-independent planning?
• RQ4 Does the proposed method maintain efficiency and scalability in large, complex environments with bottlenecks?
• RQ5 Can Causal-PIBT handle dynamic failures and delays without global coordination or fixed timing assumptions?

Key findings

• Causal-PIBT+ succeeded in all 100 simulation runs across all benchmarks, demonstrating guaranteed reachability and robustness under stochastic delays.
• In small benchmarks, Causal-PIBT+ achieved solution costs competitive with MCPs, the best-performing baseline, especially under high delay probabilities.
• When delay probability or agent count increased, time-independent planning outperformed MCPs in terms of solution cost and success rate.
• On large, biconnected fields like den312d, the method succeeded despite bottlenecks, though solution cost increased significantly due to structural constraints.
• The use of offline MAPF plans as hints in Causal-PIBT+ led to a notable reduction in solution cost and faster convergence, particularly in dense environments.
• GREEDY failed in most trials due to deadlocks, while FSPs showed higher solution costs than MCPs, confirming the advantage of time-independent planning.