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Simultaneous Computation with Multiple Prioritizations in Multi-Agent Motion Planning

Patrick Scheffe, Julius Kahle, Bassam Alrifaee

TL;DR

The paper tackles MAPF under receding-horizon planning by introducing simultaneous computation with multiple prioritizations. It formalizes time-variant coupling and prioritization, then proposes a decentralized Latin-square–style computation schedule to solve PP problems for several prioritizations in parallel, retaining predictive benefits while improving solution quality. The approach is instantiated for multi-vehicle motion planning with kinodynamic constraints (MAMP) using a motion primitive automaton and Monte-Carlo Tree Search within an MPC framework, and is evaluated on road-network scenarios including a real-time ten-vehicle cpmlab experiment. Results show that parallel exploration of prioritizations yields higher-quality solutions with substantially lower worst-case computation times compared to optimizing a single prioritization, demonstrating real-time viability and general applicability to domain-independent PP problems.

Abstract

Multi-agent path finding (MAPF) in large networks is computationally challenging. An approach for MAPF is prioritized planning (PP), in which agents plan sequentially according to their priority. Albeit a computationally efficient approach for MAPF, the solution quality strongly depends on the prioritization. Most prioritizations rely either on heuristics, which do not generalize well, or iterate to find adequate priorities, which costs computational effort. In this work, we show how agents can compute with multiple prioritizations simultaneously. Our approach is general as it does not rely on domain-specific knowledge. The context of this work is multi-agent motion planning (MAMP) with a receding horizon subject to computation time constraints. MAMP considers the system dynamics in more detail compared to MAPF. In numerical experiments on MAMP, we demonstrate that our approach to prioritization comes close to optimal prioritization and outperforms state-of-the-art methods with only a minor increase in computation time. We show real-time capability in an experiment on a road network with ten vehicles in our Cyber-Physical Mobility Lab.

Simultaneous Computation with Multiple Prioritizations in Multi-Agent Motion Planning

TL;DR

The paper tackles MAPF under receding-horizon planning by introducing simultaneous computation with multiple prioritizations. It formalizes time-variant coupling and prioritization, then proposes a decentralized Latin-square–style computation schedule to solve PP problems for several prioritizations in parallel, retaining predictive benefits while improving solution quality. The approach is instantiated for multi-vehicle motion planning with kinodynamic constraints (MAMP) using a motion primitive automaton and Monte-Carlo Tree Search within an MPC framework, and is evaluated on road-network scenarios including a real-time ten-vehicle cpmlab experiment. Results show that parallel exploration of prioritizations yields higher-quality solutions with substantially lower worst-case computation times compared to optimizing a single prioritization, demonstrating real-time viability and general applicability to domain-independent PP problems.

Abstract

Multi-agent path finding (MAPF) in large networks is computationally challenging. An approach for MAPF is prioritized planning (PP), in which agents plan sequentially according to their priority. Albeit a computationally efficient approach for MAPF, the solution quality strongly depends on the prioritization. Most prioritizations rely either on heuristics, which do not generalize well, or iterate to find adequate priorities, which costs computational effort. In this work, we show how agents can compute with multiple prioritizations simultaneously. Our approach is general as it does not rely on domain-specific knowledge. The context of this work is multi-agent motion planning (MAMP) with a receding horizon subject to computation time constraints. MAMP considers the system dynamics in more detail compared to MAPF. In numerical experiments on MAMP, we demonstrate that our approach to prioritization comes close to optimal prioritization and outperforms state-of-the-art methods with only a minor increase in computation time. We show real-time capability in an experiment on a road network with ten vehicles in our Cyber-Physical Mobility Lab.
Paper Structure (28 sections, 5 theorems, 31 equations, 13 figures, 2 algorithms)

This paper contains 28 sections, 5 theorems, 31 equations, 13 figures, 2 algorithms.

Key Result

Theorem 1

In general, *pp with time-variant prioritization is incomplete.

Figures (13)

  • Figure 1: mapf instance in which pp results in a solution only if agent 2 has lowest priority. Example adjusted from ma2019searching.
  • Figure 2: Exemplary illustration of the computation time in different prioritization approaches in an example with three agents represented in $\glslink{sym:classAgents}{ \IfNoValueTF{1} {_{c}} {_{1}}}$, $\glslink{sym:classAgents}{ \IfNoValueTF{2} {_{c}} {_{2}}}$, and $\glslink{sym:classAgents}{ \IfNoValueTF{3} {_{c}} {_{3}}}$; blocks indicate computation time of agents.
  • Figure 3: mapf instance which is not TP-solvable.
  • Figure 4: mapf instance which is not P-solvable ma2019searching, but is TP-solvable with a priority flip in the third time step. Figure redrawn from ma2019searching.
  • Figure 5: Example coupling graph for \ref{['alg:agent-classes']}, and resulting agent classes in sequence.
  • ...and 8 more figures

Theorems & Definitions (25)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6: Completeness
  • Theorem 1
  • proof
  • Definition 7: P-solvable, according to ma2019searching
  • Definition 8: TP-solvable
  • ...and 15 more