Conflict-Based Search for Multi Agent Path Finding with Asynchronous Actions

Abstract

Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective start locations to their respective goal locations while minimizing path costs. Most existing MAPF algorithms rely on a common assumption of synchronized actions, where the actions of all agents start at the same time and always take a time unit, which may limit the use of MAPF planners in practice. To get rid of this assumption, Continuous-time Conflict-Based Search (CCBS) is a popular approach that can find optimal solutions for MAPF with asynchronous actions (MAPF-AA). However, CCBS has recently been identified to be incomplete due to an uncountably infinite state space created by continuous wait durations. This paper proposes a new method, Conflict-Based Search with Asynchronous Actions (CBS-AA), which bypasses this theoretical issue and can solve MAPF-AA with completeness and solution optimality guarantees. Based on CBS-AA, we also develop conflict resolution techniques to improve the scalability of CBS-AA further. Our test results show that our method can reduce the number of branches by up to 90%.

Figures (10)

• Figure 1: A motivating example of MAPF-AA where the yellow car moves fast and the green truck moves slowly in continuous time. The circled numbers show the time points: e.g., in (a), the truck moves from B1 to B2 during the time range $[0.0,2.3]$. This work considers the agent to occupy both ends of an edge when the agent goes through it. As a result, a constraint (as shown in (d)) at B2 with time range $[0.0,4.6]$ is imposed on the yellow car to avoid collision as shown in (c).
• Figure 2: Toy example for the issues of CCBS.
• Figure 3: Three Conflict Types. (a): IN-IN; (b): OUT-IN; (c): WAIT-IN
• Figure 4: Changes in the search space of low-level after adding constraints. Duration time from $A$ to $B$ and from $B$ to $C$ are abbreviated as $\tau_{AB}$ and $\tau_{BC}$. (a) MC $\langle{i},A\rightarrow B,[l, r)\rangle_{m}\xspace$: before time $l$, the interval at which moving from $A$ to $B$ can be started is $[0,l)$; after time $r$, the interval is $[r,\infty)$. (b) WC $\langle{i},B, [l, r) \rangle_{w}\xspace$: before time $l$, the interval at which an IN in $B$ can be started is $[0,l-\tau_{AB})$ and the interval at which an OUT in $B$ can be started is $[\tau_{AB},l)$; after time $r$, the interval about IN in $B$ is $[r-\tau_{AB},\infty)$ and the interval about OUT in $B$ is $[r,\infty)$; the safe interval of $B$ is $[0,l)$ and $[r,\infty)$. (c) OC $\langle{i},B, t \rangle_{o}\xspace$: before time $t$, the interval at which an IN in $B$ can be started is $[0,t-\tau_{AB}-\tau_{BC}]$ (by Def. \ref{['def:DO']}, $t-\tau_{AB}-\tau_{BC}$ is included) and the interval at which an OUT in $B$ can be started is $[\tau_{AB},t-\tau_{BC}]$; after time $t$, the interval about IN in $B$ is $[t,\infty)$ and the interval about OUT in $B$ is $[t+\tau_{AB},\infty)$; the safe interval of $B$ is $[0,t-\tau_{BC})$ and $[t+\tau_{AB},\infty)$.
• Figure 5: Expanding states in SIPPS-WC. The parent state $s_p$ at vertex $v$ with safe interval $[0,8.29)$ can get two child states $s_{c1}$ and $s_{c2}$ at vertex $v'$. State $s_{c1}$ has safe interval $[1,\infty)$ (starts moving at $t=0$, arrives at $v'$ at $t=1$) and $s_{c1}.c^w_v = 2$. State $s_{c2}$ has safe interval $[6.37,\infty)$ (waits at $v$, starts moving at $t=5.37$, arrives at $v'$ at $t=6.37$) and $s_{c2}.c^w_v$ = 1

Theorems & Definitions (10)

• Definition 1: Duration Occupancy
• Example 1
• Remark 1
• Example 2
• Example 3
• Definition 2
• Lemma 1
• Lemma 2
• Lemma 3
• Theorem 1