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Asynchronous Spatial-Temporal Allocation for Trajectory Planning of Heterogeneous Multi-Agent Systems

Yuda Chen, Haoze Dong, Zhongkui Li

TL;DR

A novel asynchronous spatial-temporal allocation method is proposed to determine their corresponding derivable time-stamped space and can be updated in an asynchronous way, by inserting a waiting duration between two consecutive replanning steps.

Abstract

To plan the trajectories of a large-scale heterogeneous swarm, sequentially or synchronously distributed methods usually become intractable due to the lack of global clock synchronization. To this end, we provide a novel asynchronous spatial-temporal allocation method. Specifically, between a pair of agents, the allocation is proposed to determine their corresponding derivable time-stamped space and can be updated in an asynchronous way, by inserting a waiting duration between two consecutive replanning steps. Via theoretical analysis, the inter-agent collision is proved to be avoided and the allocation ensures timely updates. Comprehensive simulations and comparisons with five baselines validate the effectiveness of the proposed method and illustrate its improvement in completion time and moving distance. Finally, hardware experiments are carried out, where $8$ heterogeneous unmanned ground vehicles with onboard computation navigate in cluttered scenarios with high agility.

Asynchronous Spatial-Temporal Allocation for Trajectory Planning of Heterogeneous Multi-Agent Systems

TL;DR

A novel asynchronous spatial-temporal allocation method is proposed to determine their corresponding derivable time-stamped space and can be updated in an asynchronous way, by inserting a waiting duration between two consecutive replanning steps.

Abstract

To plan the trajectories of a large-scale heterogeneous swarm, sequentially or synchronously distributed methods usually become intractable due to the lack of global clock synchronization. To this end, we provide a novel asynchronous spatial-temporal allocation method. Specifically, between a pair of agents, the allocation is proposed to determine their corresponding derivable time-stamped space and can be updated in an asynchronous way, by inserting a waiting duration between two consecutive replanning steps. Via theoretical analysis, the inter-agent collision is proved to be avoided and the allocation ensures timely updates. Comprehensive simulations and comparisons with five baselines validate the effectiveness of the proposed method and illustrate its improvement in completion time and moving distance. Finally, hardware experiments are carried out, where heterogeneous unmanned ground vehicles with onboard computation navigate in cluttered scenarios with high agility.
Paper Structure (19 sections, 3 theorems, 16 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 3 theorems, 16 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Dynamic Models
  4. Inter-Agent Collision Avoidance
  5. Problem Statement
  6. Proposed Method
  7. Spatial-Temporal Allocation
  8. Allocation Update
  9. Trajectory Planning Using STA
  10. The Overall Algorithm
  11. Algorithm Analysis
  12. Simulations and Experiments
  13. Algorithm Implementation
  14. Numerical Simulations
  15. Hardware Experiments
  16. ...and 4 more sections

Key Result

Theorem 1

For a pair of agents $i$ and $j$, if i) agents $i$'s and $j$'s trajectories do not collide with each other when they establish their allocation, and ii) in every following replanning step, they obey their corresponding allocations, then $\forall t > t^{R_1}$, they will not collide with each other.

Figures (10)

  • Figure 1: Eight UGVs are crossing a crowded region.
  • Figure 2: The components of the proposed method. A solid line and its normal vector are used to demonstrate a half space, where the solid line represents its boundary and the normal vector points toward its safe region.
  • Figure 3: A demonstration about the STA update for two cars. Both cars stay at waiting time and reach a new renewal, and the TSHS beyond $t_s^{R_m}$ are regenerated to adapt the new situation.
  • Figure 4: Left: The trajectories of the underlying agents. Right: The inter-agent distance.
  • Figure 5: Top: The simulation of $16$ agents exchanging their positions. Bottom: The simulation of $8$ agents changing lanes.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof